Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping

Abstract

In the previous work, it was shown that, in supersymmetric (matrix) discretized quantum mechanics, inclusion of an external field twisting the boundary condition of fermions enables us to discuss spontaneous breaking of supersymmetry (SUSY) in the path-integral formalism in a well-defined way. In the present work, we continue investigating the same systems from the points of view of localization and Nicolai mapping. The localization is studied by changing of integration variables in the path integral, which is applicable whether or not SUSY is explicitly broken. We examine in detail how the integrand of the partition function with respect to the integral over the auxiliary field behaves as the auxiliary field vanishes, which clarifies a mechanism of the localization. In SUSY matrix models, we obtain a matrix-model generalization of the localization formula. In terms of eigenvalues of matrix variables, we observe that eigenvalues' dynamics is governed by balance of attractive force from the localization and repulsive force from the Vandermonde determinant. The approach of the Nicolai mapping works even in the presence of the external field. It enables us to compute the partition function of SUSY matrix models for finite N (N is the rank of matrices) with arbitrary superpotential at least in the leading nontrivial order of an expansion with respect to the small external field. We confirm the restoration of SUSY in the large-N limit of a SUSY matrix model with a double-well scalar potential observed in the previous work.

45 pages, no figure; v2 references added; v3 discussions for general T moved to appendix, references added, typos fixed, version to be published in Nuclear Physics B

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Cited by in corpus (12)

• Complex Langevin Simulations of Zero-dimensional Supersymmetric Quantum Field Theories
• Universal form of the Nicolai map
• SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings
• New critical behavior in a supersymmetric double-well matrix model
• Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual
• Tracy-Widom distribution as instanton sum of 2D IIA superstrings
• Supersymmetric double-well matrix model as two-dimensional type IIA superstring on RR background
• 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
• Simple Models in Supersymmetric Quantum Mechanics on a Graph