11 research outputs found
BRST treatment of zero modes for the worldline formalism in curved space
One-loop quantities in QFT can be computed in an efficient way using the
worldline formalism. The latter rests on the ability of calculating 1D path
integrals on the circle. In this paper we give a systematic discussion for
treating zero modes on the circle of 1D path integrals for both bosonic and
supersymmetric nonlinear sigma models, following an approach originally
introduced by Friedan. We use BRST techniques and place a special emphasis on
the issue of reparametrization invariance. Various examples are extensively
analyzed to verify and test the general set-up. In particular, we explicitly
check that the chiral anomaly, which can be obtained by the semiclassical
approximation of a supersymmetric 1D path integral, does not receive higher
order worldline contributions, as implied by supersymmetry.Comment: 37 pages, no figures; misprints correcte
Dimensional regularization for N=1supersymmetric sigma models and the worldline formalism
We generalize the worldline formalism to include spin 1/2 fields coupled to
gravity. To this purpose we first extend dimensional regularization to
supersymmetric nonlinear sigma models in one dimension. We consider a finite
propagation time and find that dimensional regularization is a manifestly
supersymmetric regularization scheme, since the classically supersymmetric
action does not need any counterterm to preserve worldline supersymmetry. We
apply this regularization scheme to the worldline description of Dirac fermions
coupled to gravity. We first compute the trace anomaly of a Dirac fermion in 4
dimensions, providing an additional check on the regularization with finite
propagation time. Then we come to the main topic and consider the one-loop
effective action for a Dirac field in a gravitational background. We describe
how to represent this effective action as a worldline path integral and compute
explicitly the one- and two-point correlation functions, i.e. the spin 1/2
particle contribution to the graviton tadpole and graviton self-energy. These
results are presented for the general case of a massive fermion. It is
interesting to note that in the worldline formalism the coupling to gravity can
be described entirely in terms of the metric, avoiding the introduction of a
vielbein. Consequently, the fermion--graviton vertices are always linear in the
graviton, just like the standard coupling of fermions to gauge fields
Worldline formalism in a gravitational background
We analyze the worldline formalism in the presence of a gravitational
background. In the worldline formalism a path integral is used to quantize the
worldline coordinates of the particles. Contrary to the simpler cases of scalar
and vector backgrounds, external gravity requires a precise definition of the
ultraviolet regularization of the path integral. Taking into account the UV
regularization, we describe the first quantized representation of the one-loop
effective action for a scalar particle. We compute explicitly the contribution
to the graviton tadpole and self-energy to test the validity of the method. The
results obtained by usual field theoretical Feynman diagrams are reproduced in
an efficient way. Finally, we comment on the technical problems related to the
factorization of the zero mode from the path integral on the circle.Comment: 18 pages, 5 figures, LaTeX; references adde