Self-energy anomaly of an electric pointlike dipole in three-dimensional static spacetimes

TL;DR

This paper computes the self-energy anomaly of a pointlike electric dipole in a 2+1 dimensional static curved spacetime, linking it to quantum fluctuations and conformal anomalies in an effective two-dimensional field theory.

Contribution

It introduces a method to reduce the self-energy anomaly calculation to a conformal anomaly problem in an effective scalar field theory in two dimensions.

Findings

Derived an explicit expression for the self-energy anomaly.

Connected the anomaly to quantum fluctuations and conformal anomalies.

Applicable to asymptotically flat spacetimes with black-hole-like metrics.

Abstract

We calculate the self-energy anomaly of a pointlike electric dipole located in a static $(2+1)$-dimensional curved spacetime. The energy functional for this problem is invariant under an infinite-dimensional (gauge) group of transformations parameterized by one scalar function of two variables. We demonstrate that the problem of the calculation of the self-energy anomaly for a pointlike dipole can be reduced to the calculation of quantum fluctuations of an effective two-dimensional Euclidean quantum field theory. We reduced the problem in question to the calculation of the conformal anomaly of an effective scalar field in two dimensions and obtained an explicit expression for the self-energy anomaly of an electric dipole in an asymptotically flat, regular $(2+1)$-dimensional spacetime which may have electrically neutral black-hole-like metrics with regular Killing horizon.