Killing Spinors for the Bosonic String and the Kaluza-Klein Theory with Scalar Potentials

TL;DR

This paper derives Killing spinor equations for bosonic string theory with a unique scalar potential and demonstrates how Kaluza-Klein theory can be gauged to produce charged Killing spinors and AdS spacetimes, including explicit solutions.

Contribution

It introduces well-defined Killing spinor equations for the bosonic string with the conformal anomaly term and shows how to gauge Kaluza-Klein theory to obtain charged spinors and AdS solutions.

Findings

Conformal anomaly term is the only scalar potential compatible with Killing spinors.

Gauging Kaluza-Klein theory yields a scalar potential with an AdS maximum.

Constructed explicit solutions in these gauged theories.

Abstract

The paper consists mainly of two parts. In the first part, we obtain well-defined Killing spinor equations for the low-energy effective action of the bosonic string with the conformal anomaly term. We show that the conformal anomaly term is the only scalar potential that one can add into the action that is consistent with the Killing spinor equations. In the second part, we demonstrate that the Kaluza-Klein theory can be gauged so that the Killing spinors are charged under the Kaluza-Klein vector. This gauging process generates a scalar potential with a maximum that gives rise to an AdS spacetime. We also construct solutions of these theories.