Theoretical Developments

Space-time symmetries and the Yang-Mills gradient flow
Agostino Patella, Luigi Del Debbio, Antonio Rago
Mon, 14:00, Seminar Room B -- Parallels 1B (Slides)

The latest developments have shown how to use the gradient flow (or Wilson flow, on the lattice) for the exploration of symmetries, and the definition of the corresponding renormalized Noether currents. In particular infinitesimal translations can be introduced along the gradient flow for gauge theories, and the corresponding Ward identities can be derived. When applied to lattice gauge theories, this approach leads to a set of possible strategies to renormalize the energy-momentum tensor nonperturbatively, and to study dilatations and scale invariance.

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The Schrödinger Functional in Numerical Stochastic Perturbation Theory
Dirk Hesse, Mattia Dalla Brida, Stefan Sint, Francesco Di Renzo, Michele Brambilla
Mon, 14:20, Seminar Room B -- Parallels 1B (Slides)

The Schrodinger functional (SF) is a widely used tool, playing a key role in many lattice studies. While the SF is non-perturbatively defined, perturbation theory plays an important role and analytic calculations have even been pushed to two-loop order. Here we explore the prospect of applying numerical stochastic perturbation theory in this framework. In the pure SU(3) gauge theory we demonstrate the correctness of our implementation by comparing results for the SF coupling up to two-loop order with known results from the literature (for an application to the gradient flow cf. M. Dalla Brida's talk and for more details on the code in use c.f. the talk by M. Brambilla).

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Numerical Stochastic Perturbation Theory and the Gradient Flow
Mattia Dalla Brida, Dirk Hesse
Mon, 14:40, Seminar Room B -- Parallels 1B (Slides)

The gradient flow in lattice gauge theories allows for finite volume definitions of running couplings which combine a number of advantages. Here, we use numerical stochastic perturbation theory to study the recently proposed gradient flow coupling in a finite volume with Schroedinger functional boundary conditions (see Dirk Hesse's talk for other applications of numerical stochastic perturbation theory to the Schroedinger functional). We present results for pure SU(3) gauge theory up to two-loops in perturbation theory and for various lattice sizes. The results are compared with known analytic results and Monte Carlo simulations at high values of beta.

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On a development of the phenomenological renormalization group
Oleg Borisenko, Vladimir Kushnir, Volodymyr Chelnokov
Mon, 15:00, Seminar Room B -- Parallels 1B (Slides)

We propose a modification of the Nightingale renormalization group for lattice spin and gauge models by combining it with the cluster decimation approximation. Essential ingredients of our approach are: 1) exact calculation of the partition and correlation function on a finite lattice strip; 2) preservation of the mass gap or the second moment correlation length, computed in the infinite strip length limit, on each decimation step. The method is applied for studying general two and three dimensional Z(N) models. A perfect agreement with exact results (whenever available) is found. An extension of the method to models with a continuous symmetry is briefly discussed.

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Schrödinger functional boundary conditions and improvement of the SU(N) pure gauge action for \(N>3\)
Tuomas Karavirta, Ari Hietanen, Pol Vilaseca
Mon, 15:20, Seminar Room B -- Parallels 1B (Slides)

The leading method to study the running of the coupling of gauge theories is based on Schrödinger Functional scheme. However, the boundary conditions and order a improvement have not been systematically generalized for theories with more than three colors. These theories have applications in BSM model building as well as in large N limit. We have studied the boundary conditions and improvement of the gauge fields within SF scheme. We have determined for all values of N the SF boundary fields which provide high signal/noise ratio. Additionally, we have calculated the improvement coefficient \(c_t\) for the pure gauge to one loop order for SU(N) gauge theories with \(N=2,\ldots,8\).

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Comparing Tensor Renormalization Group and Monte Carlo calculations for spin and gauge models
Yannick Meurice, Alan Denbleyker, Zechariah Gelzer, Yuzhi Liu, Judah Unmuth-Yockey, Tao Xiang, Zhiyuan Xie, Ji-Feng Yu, Haiyuan Zou
Mon, 15:40, Seminar Room B -- Parallels 1B (Slides)

We show that the Tensor Renormalization Group method can be applied to O(N) spin models and abelian gauge models on (hyper) cubic lattices. This method allows to blockspin with a better control than the Migdal-Kadanoff approximation and is suitable to study conformality. It also allows to overcome the sign problem, for instance to do calculations at complex values of beta or with a chemical potential. We discuss recent numerical and analytical results regarding the critical properties of the 2D O(2) nonlinear sigma model and 3D Z2 and U(1) gauge models.

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Subtleties of simulating gauge theories with atomic lattices
Peter Orland
Tue, 16:20, Seminar Room E -- Parallels 4E (Slides)

Recently, many physicists have become interested in the possibility of building non-Abelian gauge magnets/quantum-link models in cold atomic lattices. The simplest models of this kind appear to have non-relativistic gluons (in the spin-wave approximation), as was first noted by D. Rohrlich and me. Nonetheless, such systems should display confinement of color. Related models have relativistic gluons, but the nature of the continuum field theory at a nearby fixed point is subtle.

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Quantum Simulation of Non Abelian Lattice Gauge Theories
Michael Bögli, Debasish Banerjee, Marcello Dalmonte, Enrique Rico, Pascal Stebler, Uwe-Jens Wiese, Peter Zoller
Tue, 16:40, Seminar Room E -- Parallels 4E (Slides)

To construct a quantum simulator for \(U(N)\) and \(SU(N)\) lattice gauge theories, we use quantum link models (QLMs). These models replace Wilson's classical link variables by quantum link operators, reducing the Hilbert space to finite dimensions. We show how to embody QLMs with fermionic matter in ultracold alkaline-earth atoms in optical lattices. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at non-zero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time.

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Matrix Product States for Lattice Field Theories
Mari Carmen Banuls, Krzysztof Cichy, Karl Jansen, Ignacio Cirac
Tue, 17:00, Seminar Room E -- Parallels 4E (Slides)

The term Tensor Network States (TNS) refers to a number of families that represent different ansaetze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case, and has become the most precise tool for the numerical study of one dimensional quantum many-body systems, as the basis of Density Matrix Renormalization Group methods. Lattice Gauge Theories, in their Hamiltonian version, offer a challenging scenario for these techniques. While the dimensions and sizes of the systems amenable to TNS studies are still far from those achievable by 4-dimensional systems, Tensor Networks can be readily used for problems which more standard techniques cannot easily tackle, such as the presence of a chemical potential, or out-of-equilibrium dynamics. We have explored the performance of Matrix Product States (MPS) in the case of the Schwinger model, as a widely used testbench for lattice techniques. Using finite-size, open boundary MPS, we are able to determine the low energy states of the model away from any perturbative regime. The precision achieved by the method allows for accurate finite size and continuum limit extrapolations of the ground state energy, but also of the mass gaps, thus showing the feasibility of these techniques for gauge theory problems.

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Crystalline confinement
Debasish Banerjee, Uwe-Jens Wiese, Philippe Widmer, Fu-Jiun Jiang
Tue, 17:20, Seminar Room E -- Parallels 4E (Slides)

Quantum Link models are generalizations of the Wilson formulation of lattice gauge theories, but have finite dimensional Hilbert spaces for gauge fields on the links. The U(1) quantum link model, with quantum spins \(S=1/2\), for example, has a 2d Hilbert space on each link, yet retains an exact \(U(1)\) gauge symmetry. A recently constructed efficient cluster algorithm has been used to study the phase diagram of the model in (2+1)-dimensions, complementing the results already obtained from exact diagonalization and effective theory analysis (see talk by Philippe Widmer). The algorithm is the first efficient cluster algorithm for a U(1) quantum link model and relies on an exact dualization of the model to a height model. There are two different confining phases, both of which have linearly rising potential, but have different bulk structure due to breaking of different symmetries. Confinement occurs via multi-stranded strings in these phases. At high temperatures, there is a Coulomb phase characterized by a logarithmic potential. These features should be visible in a quantum simulator with ultra-cold atoms in optical lattices.

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Emergence of a pseudo-Goldstone Boson in a (2+1)-d U(1) pure gauge theory
Philippe Widmer, Uwe-Jens Wiese, Debasish Banerjee, Fu-Jiun Jiang
Tue, 17:40, Seminar Room E -- Parallels 4E (Slides)

We use a generalization of Wilson's formulation of lattice gauge theories known as quantum link models (QLM) in which the classical gauge fields are replaced by quantum operators, in the U(1) case e.g. by quantum spins \(S=1/2\). This leads to a finite-dimensional (in this case 2-d) Hilbert space per link. The gauge symmetry itself however remains exact. This allows the use of quantum simulators to extract results of interest in particle physics that are not accessible using Monte Carlo simulations, like e.g. real-time evolution of correlation functions for physical operators. We investigated this model using a newly developed, efficient cluster algorithm (see the talk by Debasish Banerjee) and exact diagonalization methods. We find a spontaneously broken approximate SO(2) symmetry emerging at a quantum phase transition separating two different confining phases distinguished by different symmetry breaking patterns. The emergent symmetry can be described by an effective theory that will be derived in the talk and whose low energy parameters are calculated using the exact diagonalization results. The quantum phase transition masquerades as a so-called deconfined quantum critical point. However, since the emergent symmetry is only approximate, the emergent pseudo-Goldstone boson does not qualify as a dual photon.

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Large N Volume Independence vs. Hagedorn (in)stability
Mithat Unsal
Thu, 14:00, Seminar Room E -- Parallels 7E (Slides)

Large-N volume independence in circle-compactified QCD with \(N_f \geq 1\) adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories are believed to possess a Hagedorn density of hadronic states. These properties are in apparent tension with each other, because a Hagedorn density of states typically implies a phase transition at some finite radius. This tension is resolved if there are degeneracies between the spectra of bosonic and fermionic states, as happens in the \(N_f=1\) supersymmetric case. Resolution of the tension for \(N_f>1\) then suggests the emergence of a fermionic symmetry at large N, where there is no supersymmetry. We can escape the Coleman-Mandula theorem since the \(N=\infty\) theory is free, with a trivial S-matrix. We show an example of such a spectral degeneracy in a non-supersymmetric toy example which has a Hagedorn spectrum.

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Monte Carlo studies on the expanding behavior of the early universe in the Lorentzian type IIB matrix model
Yuta Ito, Sang-Woo Kim, Jun Nishimura, Asato Tsuchiya
Thu, 14:20, Seminar Room E -- Parallels 7E (Slides)

Superstring theory is known as the most promising candidate for a unified theory including quantum gravity. The theory requires 10d spacetime, and by compactifying the extra six dimensions, one can obtain various quantum field theories with various gauge groups and matter contents. The problem is that there are too many ways to do that leading to too many different physics at low energy as far as one takes perturbative approaches. On the other hand, if we can construct superstring theory nonperturbatively, we may obtain uniquely our 4d spacetime with the Standard Model particles propagating on it. The type IIB matrix model was proposed as such a nonperturbative formulation of superstring theory. In particular, the model describes 10d spacetime as the eigenvalue distribution of matrices. Recent Monte Carlo studies of the Lorentzian version of the model showed that only three out of nine spatial directions start to expand after a critical time. We extend this work by studying the expanding behavior for much longer time to see whether inflation and the Big Bang occur. We find that the 3d space indeed expand exponentially for some time, which is reminiscent of the inflation. Moreover, by simulating simplified models, which captures important properties of the original model, we observe that the expansion later changes into a power-law behavior \(R(t) = c t^{1/2}\), which is consistent with that of the FRW universe in the radiation dominated era.

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Perturbative analysis of twisted volume reduced theories
Margarita Garcia-Perez, Antonio Gonzalez-Arroyo, Masanori Okawa
Thu, 14:40, Seminar Room E -- Parallels 7E (Slides)

We present the results of a perturbative analysis of pure Yang-Mills theories on a torus with twisted boundary conditions, for generic group SU(N) and non-trivial magnetic flux, generalizing previous results in the literature. The case of large N twisted reduced models will also be considered. In particular, we derive a compact formula for the gluon-self-energy correction at one-loop and discuss the perturbative expansion of Wilson loop expectation values. In this context, the appearance of tachyonic instabilities in the gluon dispersion relation and its consequences for volume reduction are analyzed. In 2+1 dimensions our predictions are compared with the results of a lattice determination of the electric-flux spectrum.

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Lattice simulation of lower dimensional SYM with sixteen supercharges
Daisuke Kadoh, Syo Kamata
Thu, 15:00, Seminar Room E -- Parallels 7E (Slides)

We report on simulations of d=1+0 supersymmetric Yang-Mills theory with sixteen supercharges. We employ the lattice action with two exact supercharges, constructed by F.Sugino. The temperature is introduced through the compactification of the time direction. In the context of gauge/gravity duality, the gauge theory corresponds to N D0-branes in type IIA superstring/supergravity. At large N and low temperature, it is expected that the gauge theory describes physics of black hole. We examine the validity of gauge/gravity duality from comparison between our numerical results of gauge side and analytic solutions of gravity side. In particular, we determine temperature dependence of black hole internal energy and Schwarzschild radius, etc beyond the leading order.

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Chiral Symmetry Breaking from Center Vortices
Roman Höllwieser, Manfried Faber, Urs M. Heller, Thomas Schweigler
Thu, 15:40, Seminar Room E -- Parallels 7E (Slides)

We investigate the chiral properties of near-zero modes for thick classical center vortices in \(SU(2)\) lattice gauge theory. In particular we analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from center vortices. We show that colorful spherical vortex and instanton ensembles have very similar Dirac eigenmodes and also vortex intersections are able to give rise to a finite density of near-zero modes, leading to chiral symmetry breaking via the Banks-Casher formula. We discuss the influence of the magnetic vortex fluxes on quarks and how center vortices may break chiral symmetry.

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The Integrable Bootstrap Program at Large N and its Applications in Gauge Theory
Axel Cortes Cubero
Thu, 16:30, Seminar Room E -- Parallels 8E (Slides)

We study the large N limit of the (1+1)-dimensional principal chiral sigma model. This Model has an \(N\times N\) matrix-valued field, whose excitations are massive and asymptotically free. All the form factors and the exact correlation functions of the Noether-current operator and the energy-momentum tensor are found using the integrable bootstrap program. We study (2+1)-dimensional Yang-Mills theory as an array of principal chiral models with a current-current interaction. We discuss how to use our new form factors to calculate physical quantities in the gauge theory.

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Radial Quantization for Conformal Field Theories on the Lattice
Richard Brower
Thu, 16:50, Seminar Room E -- Parallels 8E (Slides)

Lattice radial quantization is introduced as a nonperturbative method intended to numerically solve Euclidean conformal field theories that can be realized as fixed points of known Lagrangians. As an first example , we employ a lattice shaped as a cylinder with a 2D Icosahedral cross-section to discretize dilatations in the 3D Ising model. Base on this study and analytical methods for the 2D O(N) model at large N, we consider improvements using Finite Element Methods (FEM) to approach the Wilson Fisher fixed point. Possible extensions to infrared conformal fixed points and near conformal theories of interest to Beyond the Standard Model strong gauge dynamics are discussed.

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A possible new phase in non-perturbatively gauge-fixed Yang-Mills theory
Maarten Golterman, Yigal Shamir
Thu, 17:10, Seminar Room E -- Parallels 8E (Slides)

The standard expectation is that gauge fixing cannot alter the physics in the physical sector of a Yang-Mills theory. In this talk, I argue that this may not always be true: in an SU(2) Yang-Mills theory in which the SU(2)/U(1) coset is non-perturbatively gauge fixed, we find that a new phase, with spontaneous symmetry breaking, appears to be a possibility.

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A classification of 2-dim Lattice Theory
Mario Kieburg, Jacobus Verbaarschot, Savvas Zafeiropoulos
Thu, 17:30, Seminar Room E -- Parallels 8E (Slides)

The random matrix approach in the low energy regime of QCD has led to deep insights of non-perturbative effects and has yielded analytical relations between observables and the low energy constants. Recently Random Matrix Theory was extended to lattice QCD as well. In this talk a classification of the naive and, thus also, of the staggered fermions for 2-dim QCD-like theories will be presented. This classification is based on the global symmetries of the lattice models and is shared by Random Matrix Theory. We have compared the random matrix predictions for the spectral statistics with lattice simulations of the quenched theory and found astoundingly good agreement for the lowest eigenvalues in almost all universality classes.

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A new approach to the two-dimensional \(\sigma\) model with a topological charge
Christian Torrero, Oleg Borisenko, Vladimir Kushnir, Bartolome Alles Salom, Alessandro Papa
Thu, 17:50, Seminar Room E -- Parallels 8E (Slides)

Based on character decomposition, a dual transformation is introduced leading to two formulations of the theory which should allow for a removal/softening of the sign problem in the original version. Very preliminar numerical results are commented and remaining problems discussed.

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Studying and removing effects of fixed topology in a quantum mechanical model
Arthur Dromard, Marc Wagner
Thu, 18:10, Seminar Room E -- Parallels 8E (Slides)

At small lattice spacing, or when using e.g. overlap fermions, lattice QCD simulations tend to become stuck in a single topological sector. Physical observables then differ from their full QCD counterparts by 1/V corrections. Brower et al. and Aoki et al. have derived equations by means of a saddle point approximation, to determine and to remove these corrections. We extend these equations and apply them to a simple toy model, a quantum mechanical particle on a circle in a square well potential at fixed topology. This model can be solved numerically up to arbitrary precision and allows to explore effects arising due to fixed topology. We investigate the range of validity and accuracy of the above mentioned equations to remove such fixed topology effects. We also speculate about implications regarding fixed topology simulations in QCD.

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Non-\(\gamma_{5}\)hermiticity minimal doubling fermion
Syo Kamata, Hidekazu Tanaka
Fri, 14:00, Seminar Room F -- Parallels 9F (Slides)

A non-\(\gamma_{5}\)hermiticity lattice fermion has a serious problem called sign problem. In finite density system, a fermion determinant always has a complex phase because lattice actions have a chemical potential term which breaks \(\gamma_{5}\)hermiticity. Therefore it is trouble to estimate observable in strong density region. In this talk, we will talk about whether we can estimate observables using non-\(\gamma_{5}\)hermiticity fermion or not. We constructed two-dimensional \(\gamma_{5}\)hermiticity fermions based on minimal doubling fermion. The fermions preserve chiral symmetry but break discrete symmetry. Firstly, we estimate eigenvalue distributions. And we determine if or not such the fermions are appropriate for use in practical calculations. Next, we investigate the parity-broken phase called Aoki phase for a non-\(\gamma_{5}\)hermiticity fermion by using the Gross-Neveu model. And we will discuss a generalization to higher dimension system.

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Lattice QCD with Staggered Wilson Fermions: An Exploratory Numerical Investigation
David Adams, Dániel Nógrádi, Andriy Petrashyk, Christian Zielinski
Fri, 14:20, Seminar Room F -- Parallels 9F (Slides)

Results on the computational efficiency of 2-flavor staggered Wilson fermions compared to usual Wilson fermions in quenched lattice QCD simulations are reported. The computations are done for two lattices, \(12^3 \times 32\) and \(16^3 \times 32\), at \(\beta=6\), using the Chroma/QDP software for lattice QCD. We determine, as a function of the pion mass, the condition number of the lattice fermion matrix in the conjugate gradient computation of the quark propagator for both staggered Wilson and usual Wilson fermions. The condition number is found to be less by a factor of more than 3 for staggered Wilson fermions on both our lattices; this factor has only a mild dependence on the pion mass. Combining this with computations of the number of floating point operations per lattice site for matrix-vector multiplication with the lattice fermion matrices, we derive a theoretical estimate that staggered Wilson fermions are almost 6 times more efficient than usual Wilson fermions (without preconditioning for either of them). We compare this to a direct measurement of the efficiency in terms of CPU time for the quark propagator calculations, which shows an efficiency factor of around 4.5 (4) on our larger (smaller) lattice. That this is less than the theoretical estimate can be explained, at least partly, by implementation details of the staggered Wilson fermions, which we expect can be improved.

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Non-perturbative fermion mass generation in Wilson lattice QCD
Roberto Frezzotti, Giancarlo Rossi
Fri, 14:40, Seminar Room F -- Parallels 9F (Slides)

Based on theoretical arguments and numerical evidence we argue that a phenomenon of dynamical mass generation for fermions, driven by the Wilson term, occurs in lattice QCD with Wilson quarks. The potential implications of this remark for the construction of a renormalizable field theory where a hierarchy of particle masses naturally arises from interactions are discussed in a simple model.

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Quantum Mechanics à la Langevin and Supersymmetry
Stam Nicolis
Fri, 15:00, Seminar Room F -- Parallels 9F (Slides)

We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The full action, at the classical level, is invariant under N=1 SUSY, under periodic boundary conditions or when the fields vanish at the boundaries. Under antiperiodic boundary conditions for the fermions, supersymmetry is broken by a boundary term, unless the fermions vanish there. We define combinations that scale appropriately, as the lattice spacing is taken to zero and the lattice size to infinity and provide evidence, by numerical simulations, that the correlation functions of the auxiliary field do satisfy Wick's theorem. We show, in particular, that simulations can be carried out using a purely bosonic action.

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Cyclic Leibniz rule: a formulation of supersymmetry on lattice
Hiroto So, Mitsuhiro Kato
Fri, 15:20, Seminar Room F -- Parallels 9F (Slides)

For the purpose of constructing supersymmetric(SUSY) theories on lattice, we propose a new type relation on lattice -cyclic Leibniz rule(CLR)- which is slightly different from an ordinary Leibniz rule. Actually, we find that the CLR can enlarge the number of SUSYs from N=1 to N=2 in the quantum-mechanical model.

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Phase transitions in the three-dimensional Z(N) models
Volodymyr Chelnokov, Oleg Borisenko, Gennaro Cortese, Mario Gravina, Alessandro Papa, Ivan Surzhikov
Fri, 16:30, Seminar Room E -- Parallels 10E (Slides)

Phase transitions in zero-temperature 3-d Z(N) lattice gauge theories are studied. We use a cluster algorithm defined for the dual formulation of the models. We also attempt to explain the nature of the intermediate continuously symmetric phase, which appears for \(N > 5\). The critical indices are calculated. The results obtained are used to study scaling of critical points with N as well as scaling of finite-temperature critical points with \(N_T\).

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A study of massive gauge theories on the lattice (I)
Pilar Hernandez
Fri, 16:50, Seminar Room E -- Parallels 10E (Slides)

We consider the lattice formulation of an SU(2) massive gauge theory, which can be interpreted as a gauge plus scalar field theory. Starting from the symmetry properties and the assumption of the existence of a continuum limit within a Higgs phase, we conjecture the structure of the Wilsonian effective theory. Based on this analysis, we define a line of constant physics and study via numerical simulations the existence of such a scaling region.

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A study of massive gauge theories on the lattice (part II)
Michele Della Morte
Fri, 17:10, Seminar Room E -- Parallels 10E (Slides)

Does Yang-Mills theory describe quantum gravity?
Masanori Hanada, Yoshifumi Hyakutake, Goro Ishiki, Jun Nishimura
Fri, 17:30, Seminar Room E -- Parallels 10E

The strongest version of the gauge/gravity duality conjecture relates the 1/N correction to super Yang-Mills theory and the quantum correction to superstring theory. We test this conjecture by studying the D0-brane matrix quantum mechanics and the black zero-brane in type IIA superstring theory.

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Rotating lattice
Arata Yamamoto, Yuji Hirono
Fri, 17:50, Seminar Room E -- Parallels 10E (Slides)

We formulate lattice QCD in rotating frames to study the physics of QCD matter under rotation. We construct the lattice QCD action with the rotational metric and apply it to the Monte Carlo simulation. As the first application, we calculate the angular momenta of gluons and quarks in the rotating QCD vacuum. This new framework is useful to analyze various rotation-related phenomena in QCD.

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Continuum limit of the index of the staggered overlap Dirac operator
Reetabrata Har, Yiyang Jia, Christian Zielinski, David Adams
Poster Session

An analytic calculation of the continuum limit of the index of the staggered overlap Dirac operator is presented.

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Critical properties of 3D Z(N) lattice gauge theories at finite temperature
Alessandro Papa, Oleg Borisenko, Volodymyr Chelnokov, Gennaro Cortese, Mario Gravina, Ivan Surzhikov
Poster Session

The phase structure of three-dimensional Z(N>4) lattice gauge theories at finite temperature is investigated. Using the dual formulation of the models and a cluster algorithm we locate the critical points of the two transitions, determine various critical indices and compute average action and specific heat. Results are consistent with two transitions of infinite order, belonging to the universality class of two-dimensional Z(N) vector spin models.

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A method of analytic continuation for computing the hadronic vacuum polarization function
Karl Jansen, Xu Feng, Grit Hotzel, Shoji Hashimoto, Marcus Petschlies, Dru Renner
Poster Session

We describe a method to make use of continuous photon momenta to analyze the hadronic vacuum polarization function bridging smoothly between the space-like and time-like regions. We show at the example of the leading-order QCD correction to the muon anomalous magnetic moment that this approach can provide a valuable alternative method for calculations of physical quantities where the hadronic vacuum polarization function enters.

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Lattice study of the Schwinger model at fixed topology
Christopher Czaban, Marc Wagner
Poster Session

At small lattice spacing QCD simulations are expected to become stuck in a single topological sector. Observables evaluated in a fixed topological sector differ from their counterparts in full QCD, i.e. at unfixed topology, by volume dependent corrections. We investigate these corrections in the two-flavor Schwinger model, which is in several aspects similar to QCD, using Wilson fermions. We also try to remove these corrections by suitable extrapolations to infinite volume.

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