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

Abstract

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.

7 pages, 4 figures, Proceedings of the XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, California, USA

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Cited by in corpus (10)

• Enumerating Gribov copies on the lattice
• Testing holography using lattice super-Yang--Mills on a 2-torus
• Twisted supersymmetries in lattice $\mathcal{N}=4$ super Yang-Mills theory
• Phase Structure of Lattice N=4 Super Yang-Mills
• Review of Lattice Supersymmetry and Gauge-Gravity Duality
• An object oriented code for simulating supersymmetric Yang--Mills theories
• Lattice formulation of two-dimensional N=(2,2) super Yang-Mills with SU(N) gauge group
• Supersymmetric quiver gauge theories on the lattice
• Two-dimensional $\mathcal{N}=(2,2)$ Lattice Gauge Theories with Matter in Higher Representations
• Eigenvalue spectrum of lattice $\mathcal{N}=4$ super Yang-Mills