N=1 Super Yang-Mills Theory in Ito Calculus

TL;DR

This paper applies stochastic quantization with Ito calculus to N=1 supersymmetric Yang-Mills theory in 4 and 10 dimensions, preserving supersymmetry and gauge invariance, and explores implications for the IIB matrix model.

Contribution

It formulates the Langevin equation for N=1 SYM in superfield formalism using Ito calculus, preserving symmetries and extending to 10 dimensions, including the IIB matrix model.

Findings

Langevin equations preserve supersymmetry and gauge invariance.

Equilibrium limit reproduces gauge-invariant observables.

Extension to 10D includes Majorana-Weyl spinors and links to IIB matrix model.

Abstract

The stochastic quantization method is applied to N = 1 supersymmetric Yang-Mills theory, in particular in 4 and 10 dimensions. In the 4 dimensional case, based on Ito calculus, the Langevin equation is formulated in terms of the superfield formalism. The stochastic process manifestly preserves both the global N = 1 supersymmetry and the local gauge symmetry. The expectation values of the local gauge invariant observables in SYM_4 are reproduced in the equilibrium limit. In the superfield formalism, it is impossible in SQM to choose the so-called Wess-Zumino gauge in such a way to gauge away the auxiliary component fields in the vector multiplet, while it is shown that the time development of the auxiliary component fields is determined by the Langevin equations for the physical component fields of the vector multiplet in an '' almost Wess-Zumino gauge ''. The physical component expressions of the superfield Langevin equation are naturally extended to the 10 dimensional case, where the spinor field is Majorana-Weyl. By taking a naive zero volume limit of the SYM_10, the IIB matirx model is studied in this context.