Pseudo-Duality

TL;DR

This paper explores pseudo-duality groups acting on fields and couplings in supergravity theories, revealing their structure and relation to string theory dualities, and identifies specific symmetry groups in compactified string models.

Contribution

It identifies the pseudo-duality groups in supergravity and string theories, extending the understanding of symmetries beyond proper dualities and providing evidence for their specific group structures.

Findings

Pseudo-duality groups act on equations of motion in scalar and vector field systems.

The pseudo-duality group for certain supergravities is identified as Sp(56;Z)×D.

In string compactifications, the pseudo-duality group contains the conjectured heterotic and type II duality groups.

Abstract

Proper symmetries act on fields while pseudo-symmetries act on both fields and coupling constants. We identify the pseudo-duality groups that act as symmetries of the equations of motion of general systems of scalar and vector fields and apply our results to $N=2,4$ and $8$ supergravity theories. We present evidence that the pseudo-duality group for both the heterotic and type II strings toroidally compactified to four dimensions is $Sp(56;\Z)\times D$, where $D$ is a certain subgroup of the diffeomorphism group of the scalar field target space. This contains the conjectured heterotic $S\times T$ or type II $U$ proper duality group as a subgroup.