arXiv subjects

Simon Catterall

Publications and source records attributed to Simon Catterall.

At least 91 records · Page 5Linked to original sources

arXiv2012

Investigating the sign problem for two-dimensional $\mathcal{N}=(2,2)$ and $\mathcal{N}=(8,8)$ lattice super Yang--Mills theories

Recently there has been some controversy in the literature concerning the existence of a fermion sign problem in the $\mathcal{N}=(2,2)$ supersymmetric Yang--Mills (SYM) theories on the lattice. In this work, we address this issue by conducting Monte Carlo simulations not only for $\mathcal{N}=(2,2)$ but also for $\mathcal{N}=(8,8)$ SYM in two dimensions for the U(N) theories with N=2, using the new ideas derived from topological twisting followed by geometric discretization. Our results from simulations provide the evidence that these theories do {\it not} suffer from a sign problem as the continuum limit is approached. These results thus boost confidence that these new lattice formulations can be used successfully to explore the nonperturbative aspects of the four-dimensional $\mathcal{N}=4$ SYM theory.

hep-lat↗

arXiv2011

Supersymmetric gauge theories on the lattice: Pfaffian phases and the Neuberger 0/0 problem

Recently a class of supersymmetric gauge theories have been successfully implemented on the lattice. However, there has been an ongoing debate on whether lattice versions of some of these theories suffer from a sign problem, with independent simulations for the ${\cal N} = (2, 2)$ supersymmetric Yang-Mills theories in two dimensions yielding seemingly contradictory results. Here, we address this issue from an interesting theoretical point of view. We conjecture that the sign problem observed in some of the simulations is related to the so called Neuberger 0/0 problem, which arises in ordinary non-supersymmetric lattice gauge theories, and prevents the realization of Becchi-Rouet-Stora-Tyutin symmetry on the lattice. After discussing why we expect a sign problem in certain classes of supersymmetric lattice gauge theories far from the continuum limit, we argue that these problems can be evaded by use of a non-compact parametrization of the gauge link fields.

hep-lat↗

arXiv2011

On the sign problem in 2D lattice super Yang--Mills

In recent years a new class of supersymmetric lattice theories have been proposed which retain one or more exact supersymmetries for non-zero lattice spacing. Recently there has been some controversy in the literature concerning whether these theories suffer from a sign problem. In this paper we address this issue by conducting simulations of the N=(2, 2) and N=(8, 8) supersymmetric Yang--Mills theories in two dimensions for the U(N) theories with N=2,3,4, using the new twisted lattice formulations. Our results provide evidence that these theories do not suffer from a sign problem in the continuum limit. These results thus boost confidence that the new lattice formulations can be used successfully to explore non-perturbative aspects of four-dimensional N=4 supersymmetric Yang--Mills theory.

hep-lat↗

arXiv2011

de Sitter gravity from lattice gauge theory

We investigate a lattice model for Euclidean quantum gravity based on discretization of the Palatini formulation of General Relativity. Using Monte Carlo simulation we show that while a naive approach fails to lead to a vacuum state consistent with the emergence of classical spacetime, this problem may be evaded if the lattice action is supplemented by an appropriate counter term. In this new model we find regions of the parameter space which admit a ground state which can be interpreted as (Euclidean) de Sitter space.

hep-lat↗

arXiv2011

Systematic Errors of the MCRG Method

We present a Monte Carlo Renormalisation Group (MCRG) study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two-lattice matching technique we measure the running of the coupling and the anomalous mass dimension. We find slow running of the coupling, compatible with an infrared fixed point. Assuming this running is negligible we find a vanishing anomalous dimension, gamma=-0.03(13), however without this assumption our uncertainty in the running of the coupling leads to a much larger range of allowed values, -0.6 < gamma < 0.6. We discuss the systematic errors affecting the current analysis and possible improvements.

hep-ph↗

arXiv2011

MCRG Minimal Walking Technicolor

We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two-lattice matching technique we measure the running of the coupling and the anomalous mass dimension. We find slow running of the coupling, compatible with an infrared fixed point. Assuming this running is negligible we find a vanishing anomalous dimension, gamma=-0.03(13), however taking this source of systematic error into account gives a much larger range of allowed values, -0.6 < gamma < 0.6. We also attempt to measure the anomalous mass dimension using the stability matrix method. We discuss the systematic errors affecting the current analysis and possible improvements.

hep-ph↗

arXiv2011

Perturbative renormalization of lattice N=4 super Yang-Mills theory

We consider N=4 super Yang-Mills theory on a four-dimensional lattice. The lattice formulation under consideration retains one exact supersymmetry at non-zero lattice spacing. We show that this feature combined with gauge invariance and the large point group symmetry of the lattice theory ensures that the only counterterms that appear at any order in perturbation theory correspond to renormalizations of existing terms in the bare lattice action. In particular we find that no mass terms are generated at any finite order of perturbation theory. We calculate these renormalizations by examining the fermion and auxiliary boson self energies at one loop and find that they all exhibit a common logarithmic divergence which can be absorbed by a single wavefunction renormalization. This finding implies that at one loop only a fine tuning of the finite parts is required to regain full supersymmetry in the continuum limit.

hep-th↗

arXiv2010

Twisted lattice supersymmetry and applications to AdS/CFT

I review recent approaches to constructing supersymmetric lattice theories focusing in particular on the concept of topological twisting. The latter technique is shown to expose a nilpotent, scalar supersymmetry which can be implemented exactly in the lattice theory. Using these ideas a lattice action for $\mathcal{N}=4$ super Yang-Mills in four dimensions can be written down which is gauge invariant, free of fermion doublers and respects one out of a total of 16 continuum supersymmetries. It is shown how these exact symmetries together with the large point group symmetry of the lattice strongly constrain the possible counterterms needed to renormalize the theory and hence determine how much residual fine tuning will be needed to restore all supersymmetries in the continuum limit. We report on progress to study these renormalization effects at one loop. We go on to give examples of applications of these supersymmetric lattice theories to explore the connections between gauge theories and gravity.

hep-lat↗

arXiv2010

MCRG Minimal Walking Technicolor

We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two lattice matching technique recently advocated and exploited in [arXiv:0907.0919], we measure the running of the coupling and the anomalous mass dimension.

hep-ph↗

arXiv2010

Three dimensional lattice gravity as supersymmetric Yang-Mills theory

We argue that a certain twisted supersymmetric Yang-Mills theory in three dimensions with gauge group SU(2) possesses a set of topological observables whose expectation values can be computed in a related Chern Simons theory. This Chern Simons theory has been proposed as a definition of three dimensional Euclidean quantum gravity. Since the YM theory admits a discretization which preserves the values of topological observables we conjecture that it can be used as a non-perturbative definition of the quantum gravity theory.

hep-lat↗

arXiv2010

Gauge theory duals of black hole - black string transitions of gravitational theories on a circle

We study the black hole - black string phase transitions of gravitational theories compactified on a circle using the holographic duality conjecture. The gauge theory duals of these theories are maximally supersymmetric and strongly coupled 1 + 1 dimensional SU(N) Yang-Mills theories compactified on a circle, in the large $N$ limit. We perform the strongly coupled finite temperature gauge theory calculations on a lattice, using the recently developed exact lattice supersymmetry methods based on topological twisting and orbifolding. The spatial Polyakov line serves as relevant order parameter of the confinement - deconfinement phase transitions in the gauge theory duals.

hep-th↗

arXiv2010

First Results from Lattice Simulation of the PWMM

We present results of lattice simulations of the Plane Wave Matrix Model (PWMM). The PWMM is a theory of supersymmetric quantum mechanics that has a well-defined canonical ensemble. We simulate this theory by applying rational hybrid Monte Carlo techniques to a naive lattice action. We examine the strong coupling behaviour of the model focussing on the deconfinement transition.

hep-th↗

arXiv2010

Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills

We report on the results of numerical simulations of $SU(N)$ lattice Yang Mills with two flavors of (light) Wilson fermion in the adjoint representation. We analytically and numerically address the question of center symmetry realization on lattices with $Γ$ sites in each direction in the large-$N$ limit. We show, by a weak coupling calculation that, for massless fermions, center symmetry realization is independent of $Γ$, and is unbroken. Then, we extend our result by conducting simulations at non zero mass and finite gauge coupling. Our results indicate that center symmetry is intact for a range of fermion mass in the vicinity of the critical line on lattices of volume $2^4$. This observation makes it possible to compute infinite volume physical observables using small volume simulations in the limit $N\to\infty$, with possible applications to the determination of the conformal window in gauge theories with adjoint fermions.

hep-lat↗

arXiv2010

Supersymmetric lattices

Discretization of supersymmetric theories is an old problem in lattice field theory. It has resisted solution until quite recently when new ideas drawn from orbifold constructions and topological field theory have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theory in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local and free of doublers and in the case of Yang-Mills theories also possess exact gauge invariance. In principle they form the basis for a truly non-perturbative definition of the continuum supersymmetric field theory. In this talk these ideas are reviewed with particular emphasis being placed on ${\cal N}=4$ super Yang-Mills theory.

hep-lat↗

arXiv2010

A model for semantic integration of business components

Today, reusable components are available in several repositories. These last are certainly conceived for the reusing However, this re-use is not immediate; it requires, in the fact, to pass through some essential conceptual operations, among them in particular, research, integration, adaptation, and composition. We are interested in the present work to the problem of semantic integration of heterogeneous Business Components. This problem is often put in syntactical terms, while the real stake is of semantic order. Our contribution concerns a model proposal for Business components integration as well as resolution method of semantic naming conflicts, met during the integration of Business Components.

cs.SE↗

arXiv2010

Topological gravity on the lattice

In this paper we show that a particular twist of $\mathcal{N}=4$ super Yang-Mills in three dimensions with gauge group SU(2) possesses a set of classical vacua corresponding to the space of flat connections of the {\it complexified} gauge group $SL(2,C)$. The theory also contains a set of topological observables corresponding to Wilson loops wrapping non-trivial cycles of the base manifold. This moduli space and set of topological observables is shared with the Chern Simons formulation of three dimensional gravity and we hence conjecture that the Yang-Mills theory gives an equivalent description of the gravitational theory. Unlike the Chern Simons formulation the twisted Yang-Mills theory possesses a supersymmetric and gauge invariant lattice construction which then provides a possible non-perturbative definition of three dimensional gravity.

hep-lat↗

arXiv2009

Supersymmetric lattices - a brief introduction

Recently, new theoretical ideas have allowed the construction of lattice actions which are explicitly invariant under one or more supersymmetries. These theories are local and free of doublers and in the case of Yang-Mills theories also possess exact gauge invariance. In this talk these ideas are reviewed with particular emphasis being placed on ${\cal N}=4$ super Yang-Mills theory.

hep-lat↗

arXiv2009

Probes of nearly conformal behavior in lattice simulations of minimal walking technicolor

We present results from high precision, large volume simulations of the lattice gauge theory corresponding to minimal walking technicolor. We find evidence that the pion decay constant vanishes in the infinite volume limit and that the dependence of the chiral condensate on quark mass m_q is inconsistent with spontaneous symmetry breaking. These findings are consistent with the all-orders beta function prediction as well as the Schroedinger functional studies that indicate the existence of a nontrivial infrared fixed point.

hep-lat↗