Abstract
By numerically investigating the conservation law of the supercurrent, we confirm the restoration of supersymmetry in Sugino's lattice formulation of the two-dimensional N = ( 2 , 2 ) supersymmetric SU ( 2 ) Yang–Mills theory with a scalar mass term. Subtlety in the case without the scalar mass term, that appears to ruin perturbative power counting, is also pointed out.
Highlights
Nonperturbative study of supersymmetric gauge theory is of great general interest but in the context of lattice formulation, no compelling evidence of supersymmetry has been observed so far
Spacetime lattice is generally irreconcilable with supersymmetry and one must fine-tune coefficients of relevant and marginal operators so that supersymmetric Ward-Takahashi (WT) identities are restored in the continuum limit. (An important exception is the four-dimensional N = 1 supersymmetric Yang-Mills theory (SYM) [1]; see Ref. [2] for a lot of effort went into numerical study of this system; see Ref. [3] for a recent attempt.) Recently, for two- and three-dimensional extended supersymmetric gauge theories, lattice formulations that require no fine tuning have been proposed [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]
Our result strongly indicates that the proposed scenario for the supersymmetry restoration is valid and the target continuum theory (i.e., the two-dimensional N = (2, 2) SU(2) SYM with a soft supersymmetry breaking mass term) is realized in the continuum limit of the present lattice model
Summary
Nonperturbative study of supersymmetric gauge theory is of great general interest but in the context of lattice formulation, no compelling evidence of supersymmetry has been observed so far. Spacetime lattice is generally irreconcilable with supersymmetry and one must fine-tune coefficients of relevant and marginal operators so that supersymmetric Ward-Takahashi (WT) identities are restored in the continuum limit. The expected WT identity takes the form of a partially conserved supercurrent (“PCSC”) relation in which the breaking term is proportional to the square of the scalar mass. Our result strongly indicates that the proposed scenario for the supersymmetry restoration is valid and the target continuum theory (i.e., the two-dimensional N = (2, 2) SU(2) SYM with a soft supersymmetry breaking mass term) is realized in the continuum limit of the present lattice model
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