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.
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Bastianelli, F., Corradini, O. & Iacconi, L. Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies. J. High Energ. Phys. 2018, 10 (2018). https://doi.org/10.1007/JHEP05(2018)010
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DOI: https://doi.org/10.1007/JHEP05(2018)010