Spontaneous supersymmetry breaking in large-N matrix models with slowly varying potential

Abstract

We construct a class of matrix models, where supersymmetry (SUSY) is spontaneously broken at the matrix size N infinite. The models are obtained by dimensional reduction of matrix-valued SUSY quantum mechanics. The potential of the models is slowly varying, and the large-N limit is taken with the slowly varying limit.First, we explain our formalism, introducing an external field to detect spontaneous SUSY breaking, analogously to ordinary (bosonic) symmetry breaking. It is observed that SUSY is possibly broken even in systems in less than one-dimension, for example, discretized quantum mechanics with a finite number of discretized time steps. Then, we consider spontaneous SUSY breaking in the SUSY matrix models with slowly varying potential, where the external field is turned off after the large-N and slowly varying limit, analogously to the thermodynamic limit in statistical systems. On the other hand, without taking the slowly varying limit, in the SUSY matrix model with a double-well potential whose SUSY is broken due to instantons for finite N , a number of supersymmetric behavior is explicitly seen at large N . It convinces us that the instanton effect disappears and the SUSY gets restored in the large-N limit.

Tracy-Widom distribution as instanton sum of 2D IIA superstrings

“…F (1, s), except an unimportant additive constant. 7 The same result is obtained in a continuum formulation of the gauge theory [33,34]. 8 Methods of trans-series and resurgence have been recently investigated in matrix models [37][38][39][40] and in quantum field theory [41][42][43][44].…”

“…there is no phase transition any longer in the double scaling limit. 7 That issue is discussed in the context of trans-series and resurgence in [35,36]. 8 • In the double scaling limit of our model, aspects of nonperturbative SUSY breaking for the region s > 0 carry over to the region s < 0 where SUSY is broken at the classical level.…”

“…by filling fraction (ν + , ν − ), 2 and transition between the phases (I) and (II) is of the third order [7,8]. As discussed in [10][11][12], various correlation functions of the two-dimensional type IIA superstring theory compactified on R × S 1 at the selfdual radius, with the string coupling g s and the Liouville coupling ω (multiplied by the tachyon operator), coincide with their counterparts in this matrix model through the identification g s = N −1 and 4ω = µ 2 − 2, in the double scaling limit…”

“…Although various matrix models have been investigated as nonperturbative formulations of superstring/M theory [1][2][3][4][5][6], it is still difficult to elucidate whether these models do break SUSY and derive our four-dimensional world. In this situation, a simple double-well SUSY matrix model had been recently considered in [7,8], and its connection to two-dimensional type IIA superstring theory [9] on a nontrivial Ramond-Ramond background had been explored from the viewpoint of symmetries [10] and from direct comparison of scattering amplitudes at the tree and one-loop orders [11]. Interestingly, in a double scaling limit that realizes the type IIA superstring theory, instanton effects of the matrix model survive and break the SUSY spontaneously [12].…”

Spontaneous Supersymmetry Breaking, Localization and Nicolai Mapping in Matrix Models

“…Section 5 is devoted to summarize the results and discuss future directions. This chapter is mainly based on the two papers (Kuroki & Sugino, 2010;2011).…”