Lattice $$ \mathcal{N} $$ = 4 super Yang-Mills at strong coupling

In this paper we present results from numerical simulations of $$ \mathcal{N} $$ N = 4 super Yang-Mills for two color gauge theory over a wide range of ’t Hooft coupling 0 < λ ≤ 30 using a supersymmetric lattice action [1]. Numerical study of this lattice theory has been stymied until recently by both sign problems and the occurrence of lattice artifact phases at strong coupling. We have recently developed a new action that appears capable of solving both problems. The resulting action possesses just SU(2) rather than U(2) gauge symmetry. By explicit computations of the fermion Pfaffian we present evidence that the theory possesses no sign problem and exists in a single phase out to arbitrarily strong coupling. Furthermore, preliminary work shows that the logarithm of the supersymmetric Wilson loop varies as the square root of the ’t Hooft coupling λ for large λ in agreement with holographic predictions.

Accurate simulation of the finite density lattice Thirring model

We present a study of the finite density lattice Thirring model in 1+1 dimensions using the world-line/fermion-bag algorithm. The model has features similar to QCD and provides a test case for exploring the accuracy of various methods of solving sign problems. In the massless limit and with open boundary conditions we show that the sign problem is an artifact of the auxiliary field approach and is completely eliminated in the fermion bag approach. With periodic boundary conditions the sign problem is mild in the fermion bag method. We present accurate results for various quantities in the model that can be used as a benchmark for comparison with other methods of solving sign problems.