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

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.

1+25 pages, 2 tables. Discussion improved, references added. Version accepted for publication in JHEP

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Cited by in corpus (3)

• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• A Monte Carlo Approach to the Worldline Formalism in Curved Space
• Worldline Path Integrals for Gauge Fields and Quantum Computing