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.

46 pages, LaTeX

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Cited by in corpus (12)

• Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping
• Complex Langevin Simulations of Zero-dimensional Supersymmetric Quantum Field Theories
• SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings
• Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual
• Tracy-Widom distribution as instanton sum of 2D IIA superstrings
• New critical behavior in a supersymmetric double-well matrix model
• One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings
• Complex Langevin Dynamics and Supersymmetric Quantum Mechanics
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings
• Probing Non-perturbative Supersymmetry Breaking through Lattice Path Integrals
• Simple Models in Supersymmetric Quantum Mechanics on a Graph