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.

Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies / Bastianelli, Fiorenzo; Corradini, Olindo; Iacconi, Laura. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2018:5(2018), pp. 0-21. [10.1007/JHEP05(2018)010]

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

Corradini Olindo
;
2018

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.
2018
3-mag-2018
2018
5
0
21
Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies / Bastianelli, Fiorenzo; Corradini, Olindo; Iacconi, Laura. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2018:5(2018), pp. 0-21. [10.1007/JHEP05(2018)010]
Bastianelli, Fiorenzo; Corradini, Olindo; Iacconi, Laura
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1166780
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