Eur. Phys. J. C (2012) 72: 1853
https://doi.org/10.1140/epjc/s10052-011-1853-5

Regular Article - Theoretical Physics

Killing spinors for the bosonic string and Kaluza–Klein theory with scalar potentials

¹ Zheijiang Institute of Modern Physics Department of Physics, Zheijiang University, Hangzhou, 310027, China
² China Economics and Management Academy, Central University of Finance and Economics, Beijing, 100081, China
³ Institute for Advanced Study, Shenzhen University, Nanhai Ave 3688, Shenzhen, 518060, China
⁴ School of Physics, Korea Institute for Advanced Study, Seoul, 130-722, Korea

^* e-mail: zlwang@kias.re.kr

Received: 27 October 2011
Revised: 8 December 2011
Published online: 3 January 2012

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 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.