Effect of quantum fluctuations on topological excitations and central charge in supersymmetric theories

TL;DR

This paper investigates how quantum fluctuations influence topological excitations and central charges in supersymmetric theories, revealing dimension-dependent effects and the stabilizing role of holomorphy in four dimensions.

Contribution

It introduces a general method to analyze quantum effects on BPS states and central charges using superfield supercurrents and superspace dilatation techniques.

Findings

Quantum fluctuations alter the spectrum and profile of topological excitations in lower dimensions.

The supercharge algebra remains classically intact despite quantum effects, with anomalies in the central charge operator.

Holomorphy in four dimensions stabilizes BPS spectra against quantum corrections.

Abstract

The effect of quantum fluctuations on Bogomol'nyi-Prasad-Sommerfield (BPS)-saturated topological excitations in supersymmetric theories is studied. Focus is placed on a sequence of topological excitations that derive from the same classical soliton or vortex in lower dimensions and it is shown that their quantum characteristics, such as the spectrum and profile, differ critically with the dimension of spacetime. In all the examples examined the supercharge algebra retains its classical form although short-wavelength fluctuations may modify the operator structure of the central charge, yielding an anomaly. The central charge, on taking the expectation value, is further affected by long-wavelength fluctuations, and this makes the BPS-excitation spectra only approximately calculable in some low-dimensional theories. In four dimensions, in contrast, holomorphy plays a special role in stabilizing the BPS-excitation spectra against quantum corrections. The basic tool in our study is the superfield supercurrent, from which the supercharge algebra with a central extension is extracted in a supersymmetric setting. A general method is developed to determine the associated superconformal anomaly by considering dilatation directly in superspace.