Lifting flat directions in lattice supersymmetry

We present a procedure to improve the lattice definition of $\mathcal N = 4$ supersymmetric Yang--Mills theory. The lattice construction necessarily involves U(1) flat directions, and we show how these can be lifted without violating the exact lattice supersymmetry. The basic idea is to modify the equations of motion of an auxiliary field, which determine the moduli space of the system. Applied to numerical calculations, the resulting improved lattice action leads to dramatically reduced violations of supersymmetric Ward identities and much more rapid approach to the continuum limit

Parallel software for lattice N=4 supersymmetric Yang--Mills theory

We present new parallel software, SUSY LATTICE, for lattice studies of four-dimensional $\mathcal N = 4$ supersymmetric Yang--Mills theory with gauge group SU(N). The lattice action is constructed to exactly preserve a single supersymmetry charge at non-zero lattice spacing, up to additional potential terms included to stabilize numerical simulations. The software evolved from the MILC code for lattice QCD, and retains a similar large-scale framework despite the different target theory. Many routines are adapted from an existing serial code, which SUSY LATTICE supersedes. This paper provides an overview of the new parallel software, summarizing the lattice system, describing the applications that are currently provided and explaining their basic workflow for non-experts in lattice gauge theory. We discuss the parallel performance of the code, and highlight some notable aspects of the documentation for those interested in contributing to its future development.Comment: Code available at https://github.com/daschaich/sus

Finite-temperature study of eight-flavor SU(3) gauge theory

We present new lattice investigations of finite-temperature transitions for SU(3) gauge theory with Nf=8 light flavors. Using nHYP-smeared staggered fermions we are able to explore renormalized couplings $g^2 \lesssim 20$ on lattice volumes as large as $48^3 \times 24$. Finite-temperature transitions at non-zero fermion mass do not persist in the chiral limit, instead running into a strongly coupled lattice phase as the mass decreases. That is, finite-temperature studies with this lattice action require even larger $N_T > 24$ to directly confirm spontaneous chiral symmetry breaking.Comment: Contribution to the Sakata Memorial KMI Workshop on "Origin of Mass and Strong Coupling Gauge Theories" (SCGT15), 3--6 March 2015, Nagoya Universit

Hybrid Monte Carlo Simulation of Graphene on the Hexagonal Lattice

We present a method for direct hybrid Monte Carlo simulation of graphene on the hexagonal lattice. We compare the results of the simulation with exact results for a unit hexagonal cell system, where the Hamiltonian can be solved analytically.Comment: 5 pages, 4 figure

Scale-dependent mass anomalous dimension from Dirac eigenmodes

We investigate the eigenmodes of the massless Dirac operator to extract the scale-dependent fermion mass anomalous dimension gamma_m(mu). By combining simulations on multiple lattice volumes, and when possible several gauge couplings, we are able to measure the anomalous dimension across a wide range of energy scales. The method that we present is universal and can be applied to any lattice model of interest, including both conformal or chirally broken systems. We consider SU(3) lattice gauge theories with Nf=4, 8 and 12 light or massless fermions. The 4-flavor model behaves as expected for a QCD-like system and demonstrates that systematic effects are manageable in practical lattice calculations. Our 12-flavor results are consistent with the existence of an infrared fixed point, at which we predict the scheme-independent mass anomalous dimension gamma_m^*=0.32(3). For the 8-flavor model we observe a large anomalous dimension across a wide range of energy scales. Further investigation is required to determine whether Nf=8 is chirally broken and walking, or if it possesses a strongly-coupled conformal fixed point.Comment: Version to be published in JHE

Improved Lattice Renormalization Group Techniques

We compute the bare step-scaling function $s_b$ for SU(3) lattice gauge theory with $N_f = 12$ massless fundamental fermions, using the non-perturbative Wilson-flow-optimized Monte Carlo Renormalization Group two-lattice matching technique. We use a short Wilson flow to approach the renormalized trajectory before beginning RG blocking steps. By optimizing the length of the Wilson flow, we are able to determine an $s_b$ corresponding to a unique discrete $\beta$ function, after a few blocking steps. We carry out this study using new ensembles of 12-flavor gauge configurations generated with exactly massless fermions, using volumes up to $32^4$. The results are consistent with the existence of an infrared fixed point (IRFP) for all investigated lattice volumes and number of blocking steps. We also compare different renormalization schemes, each of which indicates an IRFP at a slightly different value of the bare coupling, as expected for an IR-conformal theory.Comment: 31st International Symposium on Lattice Field Theory, Lattice201

How scaling of the disturbance set affects robust positively invariant sets for linear systems

This paper presents new results on robust positively invariant (RPI) sets for linear discrete-time systems with additive disturbances. In particular, we study how RPI sets change with scaling of the disturbance set. More precisely, we show that many properties of RPI sets crucially depend on a unique scaling factor which determines the transition from nonempty to empty RPI sets. We characterize this critical scaling factor, present an efficient algorithm for its computation, and analyze it for a number of examples from the literature