Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies

TL;DR

This paper extends simplified path integral techniques to N=1 supersymmetric quantum mechanics, enabling efficient computation of type-A trace anomalies for Dirac fermions in various dimensions.

Contribution

It introduces a supersymmetric extension of simplified path integrals, improving calculations of trace anomalies in curved spaces.

Findings

Successfully computed trace anomalies up to 16 dimensions.

Demonstrated efficiency gains in perturbative calculations.

Extended the simplified path integral framework to supersymmetric models.

Abstract

Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals. The latter require a precise regularization to deal with the derivative interactions arising from the nonlinear kinetic term. Recently, for maximally symmetric spaces, simplified path integrals have been developed: they allow to trade the nonlinear kinetic term with a purely quadratic kinetic term (linear sigma model). This happens at the expense of introducing a suitable effective scalar potential, which contains the information on the curvature of the space. The simplified path integral provides a sensible gain in the efficiency of perturbative calculations. Here we extend the construction to models with N = 1 supersymmetry on the worldline, which are applicable to the first quantized description of a Dirac fermion. As an application we use the simplified worldline path integral to compute the type-A trace anomaly of a Dirac fermion in d dimensions up to d = 16.