Callisesi, Giulia
(2018)
Simplified worldline path integrals for p-forms and type-A trace anomalies.
[Laurea magistrale], Università di Bologna, Corso di Studio in
Fisica [LM-DM270]
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Abstract
In this work we study a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, in the case of N=2 supersymmetries on the worldline.
This quantum mechanics is generically that of a nonlinear sigma model in one dimension with two supersymmetries (N=2 supersymmetric quantum mechanics), and it is mostly used for describing spin 1 fields and p-forms in first quantisation. Here, we conjecture a simplified path integral defined in terms of a linear sigma model, rather than a nonlinear one. The use of a quadratic kinetic term in the bosonic part of the particle action should
be allowed by the use of Riemann normal coordinates, while a scalar effective potential is expected to reproduce the effects of the curvature. Such simplifications have already been proven to be possible for the cases of N=0 and N=1 supersymmetric quantum mechanics. As a particular application, we employ our construction to give a simplified worldline representation of the one-loop effective action of gauge p-forms on maximally symmetric spaces. We use it to compute the first three Seeley-DeWitt coefficients, denoted by a_(p+1)(d;p), namely a_1(2;0), a_2(4;1) and a_3(6;2), that appear in the calculation of the type-A trace anomalies of conformally invariant p-form gauge potentials in d=2p+2 dimensions. The simplified model describes correctly the first two coefficients, while it seems to fail to reproduce the third one. One possible reason could be that the model is based on a conjecture about the effective potential that has been oversimplified in our analysis. Future work could improve our construction, in order to give a correct description to all orders, or alternatively disprove the possibility of having such a simplification in the full N=2 quantum mechanics.
Abstract
In this work we study a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, in the case of N=2 supersymmetries on the worldline.
This quantum mechanics is generically that of a nonlinear sigma model in one dimension with two supersymmetries (N=2 supersymmetric quantum mechanics), and it is mostly used for describing spin 1 fields and p-forms in first quantisation. Here, we conjecture a simplified path integral defined in terms of a linear sigma model, rather than a nonlinear one. The use of a quadratic kinetic term in the bosonic part of the particle action should
be allowed by the use of Riemann normal coordinates, while a scalar effective potential is expected to reproduce the effects of the curvature. Such simplifications have already been proven to be possible for the cases of N=0 and N=1 supersymmetric quantum mechanics. As a particular application, we employ our construction to give a simplified worldline representation of the one-loop effective action of gauge p-forms on maximally symmetric spaces. We use it to compute the first three Seeley-DeWitt coefficients, denoted by a_(p+1)(d;p), namely a_1(2;0), a_2(4;1) and a_3(6;2), that appear in the calculation of the type-A trace anomalies of conformally invariant p-form gauge potentials in d=2p+2 dimensions. The simplified model describes correctly the first two coefficients, while it seems to fail to reproduce the third one. One possible reason could be that the model is based on a conjecture about the effective potential that has been oversimplified in our analysis. Future work could improve our construction, in order to give a correct description to all orders, or alternatively disprove the possibility of having such a simplification in the full N=2 quantum mechanics.
Tipologia del documento
Tesi di laurea
(Laurea magistrale)
Autore della tesi
Callisesi, Giulia
Relatore della tesi
Scuola
Corso di studio
Indirizzo
Curriculum A: Teorico generale
Ordinamento Cds
DM270
Parole chiave
path integral,supersymmetry,sigma model,worldline,trace anomalies,amplitude transition,p-form,curved space,Riemann normal coordinates,maximally symmetric spaces
Data di discussione della Tesi
14 Dicembre 2018
URI
Altri metadati
Tipologia del documento
Tesi di laurea
(NON SPECIFICATO)
Autore della tesi
Callisesi, Giulia
Relatore della tesi
Scuola
Corso di studio
Indirizzo
Curriculum A: Teorico generale
Ordinamento Cds
DM270
Parole chiave
path integral,supersymmetry,sigma model,worldline,trace anomalies,amplitude transition,p-form,curved space,Riemann normal coordinates,maximally symmetric spaces
Data di discussione della Tesi
14 Dicembre 2018
URI
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