Ginsparg-Wilson Formulation of 2D N = (2,2) SQCD with Exact Lattice Supersymmetry

Abstract

In this paper, we introduce the overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, to the matter sector of two-dimensional N = (2, 2) lattice supersymmetric QCD (SQCD) with preserving one of the supercharges. It realizes the exact chiral flavor symmetry on the lattice, to make possible to define the lattice action for general number of the flavors of fundamental and anti-fundamental matter multiplets and for general twisted masses. Furthermore, superpotential terms can be introduced with exact holomorphic or anti-holomorphic structure on the lattice. We also consider the lattice formulation of matter multiplets charged only under the central U(1) (the overall U(1)) of the gauge group G = U(N ), and then construct lattice models for gauged linear sigma models with exactly preserving one supercharge and their chiral flavor symmetry.

Anomaly and sign problem in N=(2,2) SYM on polyhedra: Numerical analysis

“…In particular, for low-dimensional gauge theories with extended supersymmetries, lattice models could avoid fine-tuning for the continuum limit due to partially preserved supercharges. In [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21], the lattice supersymmetric gauge models preserving one or two supercharges are proposed based on the discretized topologically twisted gauge theories (for relations among several lattice formulations, see [22,23,24,25,26]). Since the supersymmetries are partially preserved in the models, the numerical simulation can be carried out on the basis similar to lattice QCD [27,28,29,30,31,32,33,34].…”

O(a) improvement of 2D N=(2,2Hanada1, Kadoh2, Matsuura3 et al. 2018Nuclear Physics B7030View full textAdd to dashboardCite

“…The theory is obtained from the four-dimensional N = 1 supersymmetric Yang-Mills theory by the dimensional reduction. In fact, the gaugino fields with/without bars signify four-dimensional chirality and the indices L and R two-dimensional chirality [17]. The covariant derivatives and the field strengths are defined by…”

“…For two-dimensional theories, the parameter fine tuning problems can be circumvented by keeping a part of the supersymmetry algebra (one or two supercharges and U(1) or SU(2) R-symmetry) at discretized level [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Encouraged by this development, several groups have been trying lattice simulations of two-dimensional super Yang-Mills theories [21,22,23,24,25], 5 including the maximally supersymmetric theory relevant for the gauge/gravity duality [26,27,28,29].…”

Two dimensional super QCD on a lattice

“…In [14] and [15] these formulations were extended using orbifold methods to the case of theories incorporating fermions transforming in the fundamental representation of the gauge group. These methods yield quiver gauge theories containing fields that transform as bi-fundamentals under a product gauge group U(N c ) × U(N f ).…”