Quantum Corrections to Generic Branes: DBI, NLSM, and More

TL;DR

This paper develops a covariant method to compute one-loop quantum corrections for hypersurfaces in higher-dimensional spacetimes, unifying various models like DBI and sigma models, and clarifying their symmetry properties.

Contribution

It introduces a manifestly covariant approach to quantum corrections applicable to a wide class of brane theories, unifying different models under a single framework.

Findings

Derived explicit one-loop corrections maintaining covariance.

Unified corrections for DBI, NLSM, and related models.

Confirmed physical equivalence of different computational approaches.

Abstract

We study quantum corrections to hypersurfaces of dimension $d+1>2$ embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results.