Super Weyl invariance: BPS equations from heterotic worldsheets

TL;DR

This paper demonstrates how heterotic string worldsheet analysis can directly derive spacetime BPS equations, linking worldsheet supersymmetry conditions to target space geometry and gauge field equations.

Contribution

It provides a novel derivation of heterotic BPS equations from the worldsheet perspective using (2,0) supersymmetry and anomaly cancellation.

Findings

Heterotic BPS conditions emerge from worldsheet anomaly cancellation.

Conformal balance and Hermitean Yang-Mills equations are derived at one loop.

The approach connects worldsheet supersymmetry with spacetime BPS equations.

Abstract

It is well-known that the beta functions on a string worldsheet correspond to the target space equations of motion, e.g. the Einstein equations. We show that the BPS equations, i.e. the conditions of vanishing supersymmetry variations of the space-time fermions, can be directly derived from the worldsheet. To this end we consider the RNS-formulation of the heterotic string with (2,0) supersymmetry, which describes a complex torsion target space that supports a holomorphic vector bundle. After a detailed account of its quantization and renormalization, we establish that the cancellation of the Weyl anomaly combined with (2,0) finiteness implies the heterotic BPS conditions: At the one loop level the geometry is required to be conformally balanced and the gauge background has to satisfy the Hermitean Yang-Mills equations.