Killing Spinors for the Bosonic String

TL;DR

This paper derives the effective action for the bosonic string with Yang-Mills fields up to order alpha', showing it admits Killing spinor equations that imply the equations of motion, hinting at a hidden pseudo-supersymmetry.

Contribution

It introduces a method to obtain the bosonic string effective action ensuring the existence of Killing spinor equations, revealing potential pseudo-supersymmetry in the bosonic string.

Findings

Effective action derived up to order alpha' in general dimensions.

Killing spinor equations lead to equations of motion.

Evidence of hidden pseudo-supersymmetry in bosonic string.

Abstract

We obtain the effective action for the bosonic string with arbitrary Yang-Mills fields, up to the \alpha' order, in general dimensions. The form of the action is determined by the requirement that the action admit well-defined Killing spinor equations, whose projected integrability conditions give rise to the full set of equations of motion. The success of the construction suggests that the hidden "pseudo-supersymmetry" associated with the Killing spinor equations may be a property of the bosonic string itself.