Counterterms, Holonomy and Supersymmetry

TL;DR

This paper explores how supergravity counterterms relate to supersymmetry preservation in string theory, showing that Killing spinor structures can persist despite holonomy deformations caused by perturbative corrections.

Contribution

It demonstrates that Killing spinor structures remain consistent with perturbed equations even when holonomy is deformed by supergravity counterterms.

Findings

Killing spinors can persist despite holonomy deformation.

Supergravity counterterms influence supersymmetry in string vacua.

Integrability conditions remain consistent with effective field equations.

Abstract

The divergence structure of supergravity has long been a topic of concern because of the theory's non-renormalizability. In the context of string theory, where perturbative finiteness should be achieved, the supergravity counterterm structures remain nonetheless of importance because they still occur, albeit with finite coefficients. The leading nonvanishing supergravity counterterms have a particularly rich structure that has a bearing on the preservation of supersymmetry in string vacua in the presence of perturbative string corrections. Although the holonomy of such manifolds is deformed by the corrections, a Killing spinor structure nevertheless can persist. The integrability conditions for the existence of such Killing spinors remarkably remain consistent with the perturbed effective field equations.