arXiv subjects
Publications and source records attributed to Georg Bergner.
We provide evidence for partial deconfinement -- the deconfinement of a SU($M$) subgroup of the SU($N$) gauge group -- by using lattice Monte Carlo simulations. We take matrix models as concrete examples. By appropriately fixing the gauge, we observe that the $M\times M$ submatrices deconfine. This gives direct evidence for partial deconfinement at strong coupling. We discuss the applications to QCD and holography.
The mass anomalous dimension is determined in SU(2) gauge theory coupled to $N_f$ fermions in the adjoint representation for $N_f = 2$, $3/2$, $1$ and $1/2$, where half-integer flavor numbers correspond to Majorana fermions. The numerical method is based on gradient flow. The results show near-conformal behavior for $N_f = 2$, $3/2$ and $1$. Particular emphasis is placed on $N_f = 2$, which is relevant for a strongly interacting extension of the Standard Model and has been studied in several previous investigations. We check whether the method is able to resolve discrepancies in earlier results for this theory. Overall, the method based on the gradient flow delivers reliable results in qualitative agreement with previously known numerical data.
In this article we summarize our efforts in simulating Yang-Mills theories coupled to matter fields transforming under the fundamental and adjoint representations of the gauge group. In the context of composite Higgs scenarios, gauge theories with mixed representation fields have been suggested to describe the fundamental interactions well beyond the electroweak unification scale, and they are also closely related to supersymmetric QCD. In addition, they are studied as deformations of theories with pure adjoint matter in the context of adiabatic continuity. We provide some first results for bare parameter tuning and interdependence of the two representations. We also investigate how the chiral symmetry breaking or a conformal scenario can be realized and checked in such theories.
In $\mathcal{N}=1$ supersymmetric Yang-Mills theory, regularised on a space-time lattice, in addition to the breaking by the gluino mass term, supersymmetry is broken explicitly by the lattice regulator. In addition to the parameter tuning in the theory, the supersymmetric Ward identities can be used as a tool to investigate lattice artefacts as well as to check whether supersymmetry can be recovered in the chiral and continuum limits. In this paper we present the numerical results of an analysis of the supersymmetric Ward identities for our available gauge ensembles at different values of the inverse gauge coupling $β$ and of the hopping parameter $κ$. The results clearly indicate that the lattice artefacts vanish in the continuum limit, confirming the restoration of supersymmetry.
We present a preliminary study of the pion, kaon and D-meson masses and decay constants in isosymmetric QCD, as well as a preliminary result for the light-quark renormalized mass. The analysis is based on the gauge ensembles produced by ETMC with $N_f=2+1+1$ flavours of Wilson-clover twisted mass quarks, spanning a range of lattice spacings from $\sim0.10$ to $0.07$ fm and include configurations at the physical pion point on lattices with linear size up to $L~\sim~5.6$~fm
We summarize our investigations of several aspects of $\mathcal{N}=1$ supersymmetric Yang-Mills (SYM) theory. We present our final results for SU(3) $\mathcal{N}=1$ SYM simulated with Wilson fermions. We also discuss the first test of the simulations of the theory with overlap gluinos. Finally, we present some recent progresses concerning the phase structure of the compactified theory on $R^3\times S^1$.
We study the bosonic matrix model obtained as the high-temperature limit of two-dimensional maximally supersymmetric SU($N$) Yang-Mills theory. So far, no consensus about the order of the deconfinement transition in this theory has been reached and this hinders progress in understanding the nature of the black hole/black string topology change from the gauge/gravity duality perspective. On the one hand, previous works considered the deconfinement transition consistent with two transitions which are of second and third order. On the other hand, evidence for a first order transition was put forward more recently. We perform high-statistics lattice Monte Carlo simulations at large $N$ and small lattice spacing to establish that the transition is really of first order. Our findings flag a warning that the required large-$N$ and continuum limit might not have been reached in earlier publications, and that was the source of the discrepancy. Moreover, our detailed results confirm the existence of a new partially deconfined phase which describes non-uniform black strings via the gauge/gravity duality. This phase exhibits universal features already predicted in quantum field theory.
We compute the renormalization group flow of the mass anomalous dimension in adjoint QCD with $N_{f}=1$, $3/2$, and 2 Dirac fermions, using the gradient flow. Preliminary results are in agreement with at least a near-conformal scenario in all cases. At the largest flavor numbers we obtain the strongest indication for an IR conformal fixed point scenario. Moreover, we provide results for the thermal phase transitions in SU(3) supersymmetric Yang-Mills theory. We find hints for a connection between chiral and center symmetries in terms of a single first order phase transition where chiral symmetry is restored and center symmetry gets broken.
The realization of center and chiral symmetries in $\mathcal{N}=1$ super Yang-Mills theory (SYM) is investigated on a four-dimensional Euclidean lattice by means of Monte Carlo methods. At zero temperature this theory is expected to confine external fundamental charges and to have a non-vanishing gaugino condensate, which breaks the non-anomalous Z$_{2\textrm{N}_{c}}$ chiral symmetry. In previous studies at finite temperatures, the phase transitions corresponding to deconfinement and chiral restoration were observed to occur at roughly the same critical temperature for SU(2) gauge group. We find further evidences for this observation from new measurements at smaller lattice spacings using the fermion gradient flow, and we discuss the agreement of our findings with conjectures from superstring theory. The implementation of the gradient flow technique allows us also to estimate, for the first time, the condensate at zero temperatures and zero gaugino mass with Wilson fermions.
The physical particles in supersymmetric Yang-Mills theory (SYM) are bound states of gluons and gluinos. We have determined the masses of the lightest bound states in SU(3) $\mathcal{N}=1$ SYM. Our simulations cover a range of different lattice spacings, which for the first time allows an extrapolation to the continuum limit. Our results show the formation of a supermultiplet of bound states, which provides a clear evidence for unbroken supersymmetry.
We have calculated the masses of bound states numerically in N = 1 supersymmetric Yang-Mills theory with gauge group SU(2). Using the suitably optimised variational method with an operator basis consisting of smeared Wilson loops and mesonic operators, we are able to obtain the masses of the ground states and first excited states in the scalar, pseudoscalar and spin-1/2 sectors. Extrapolated to the continuum limit, the corresponding particles appear to be approximately mass degenerate and to fit into the predicted chiral supermultiplets. The extended operator basis including both glueball-like and mesonic operators leads to improved results compared to earlier studies, and moreover allows us to investigate the mixing content of the physical states, which we compare to predictions in the literature.
We consider the heavy-dense limit of QCD at finite fermion density in the canonical formulation and approximate it by a 3-state Potts model. In the strong coupling limit, the model is free of the sign problem. Away from the strong coupling, the sign problem is solved by employing a cluster algorithm which allows to average each cluster over the Z(3) sectors. Improved estimators for physical quantities can be constructed by taking into account the triality of the clusters, that is, their transformation properties with respect to Z(3) transformations.
{We present the results of a numerical investigation of SU(2) gauge theory with $N_f=3/2$ flavours of fermions, corresponding to 3 Majorana fermions, which transform in the adjoint representation of the gauge group. At two values of the gauge coupling, the masses of bound states are considered as a function of the PCAC quark mass. The scaling of bound states masses indicates an infrared conformal behaviour of the theory. We obtain estimates for the fixed-point value of the mass anomalous dimension $γ^*$ from the scaling of masses and from the scaling of the mode number of the Wilson-Dirac operator.
Composite operators of bare fermion fields evolved along a trajectory on field space by means of flow equations are multiplicatively renormalized. Therefore, even in the case of Wilson fermions, the renormalization of expectation values of fermion operators can be drastically simplified on the lattice. We measure the gluino condensate in $\mathcal{N}$=1 supersymmetric Yang-Mills theory at non-zero temperatures by means of the gradient flow. The non-vanishing expectation value of the gluino condensate up to a certain critical temperature is a signal of chiral symmetry breaking, in agreement with theoretical conjectures on the vacuum structure of the theory. Furthermore, the deconfinement phase transition seems to occur close to this critical temperature, meaning that in $\mathcal{N}$=1 SYM the phases of broken chiral symmetry and of confinement would coincide.
In $\mathcal{N}$=1 supersymmetric Yang-Mills theory the superpartner of the gluon is the gluino, which is a spin 1/2 Majorana particle in the adjoint representation of the gauge group. Combining three gluinos, it is possible to form colour neutral bound states, analogous to baryons in QCD. The correlation functions of the corresponding baryonic operators contain a contribution represented by a `sunset diagram', and in addition, unlike in QCD, another contribution represented by a `spectacle diagram'. We present first results from an implementation and calculation of these objects, obtained from numerical simulations of supersymmetric Yang-Mills theory.
This talk is an overview of our recent investigations of supersymmetric and near conformal gauge theories. We have studied extensively $\mathcal{N}=1$ super Yang-Mills theory, most recently with the gauge group SU(3). In addition we have investigated theories that show indications for a conformal behavior at an infrared fixed point. We have included a mixed fundamental and adjoint fermion action setup in our studies. I will explain how this is related to the investigation of supersymmetric QCD on the lattice and present some first studies of the main obstacles that need to be addressed in the investigation of this theory.
This work is a step towards merging the ideas that arise from semi-classical methods in continuum QFT with analytic/numerical lattice field theory. In this context, we consider Yang-Mills theories coupled to fermions in the adjoint representation. These theories have the remarkable property that confinement and discrete chiral symmetry breaking can persist at weak coupling on small (non-thermal) $\mathbb R^3 \times S^1$. This work presents a lattice investigation of Yang-Mills with one adjoint Majorana fermion, $\mathcal N=1$ super Yang-Mills, and opens the prospect to understand a number of non-perturbative phenomena, such as the mechanism of confinement, mass gap, chiral and center symmetry realizations both in lattice and continuum analytically. We study the compactification of this theory on the lattice with periodic and thermal boundary conditions. We provide numerical evidence for the conjectured absence of the phase transitions with periodic boundary conditions for sufficiently light lattice fermions (stability of center-symmetry), suppression of the chiral transition, and also provide a diagnostic for abelian vs. non-abelian confinement, based on per-site Polyakov loop eigenvalue distribution functions. In numerical and perturbative investigations we identify the role of the lattice artefacts that become relevant in the very small radius regime, and resolve some puzzles in the naive comparison between continuum and lattice.
In numerical investigations of supersymmetric Yang-Mills theory on a lattice, the supersymmetric Ward identities are valuable for finding the critical value of the hopping parameter and for examining the size of supersymmetry breaking by the lattice discretisation. In this article we present an improved method for the numerical analysis of supersymmetric Ward identities, which takes into account the correlations between the various observables involved. We present the first complete analysis of supersymmetric Ward identities in $\mathcal{N}=1$ supersymmetric Yang-Mills theory with gauge group SU(3). The results show that lattice artefacts scale to zero as $O(a^2)$ towards the continuum limit in agreement with theoretical expectations.