Spectrum-generating Symmetries for BPS Solitons

TL;DR

This work identifies a nonlinear, spectrum-generating symmetry for fundamental BPS solitons in supergravity, extending the standard global symmetry $G$ by a trombone scaling that changes masses while keeping moduli fixed. The authors construct an active $SL(2,\mathbb{Z})$ for Type IIB in $D=10$ by compensating $SL(2,\mathbb{Z})$ transformations with a Borel-trombone pair, yielding a discrete group that acts transitively on the BPS charge lattice. They show this active symmetry is distinct from the gauged U-duality $G(\mathbb{Z})$, which preserves masses, and provide a group-theoretical interpretation of the BPS spectrum as cosets $SL(2,\mathbb{Z})/\mathbb{Z}$ (and its higher-dimensional analogues via Iwasawa decomposition). The paper also discusses lower-dimensional extensions and analyzes potential quantum anomalies, arguing that while the trombone symmetry is vulnerable in general, BPS backgrounds may retain the active spectrum-generating structure, with non-BPS sectors remaining susceptible to anomalies. Overall, the active $G(\mathbb{Z})$ multiplet concept offers a robust framework for organizing BPS states and clarifies the role of scaling symmetries in dualities and spectrum generation.

Abstract

We show that there exist nonlinearly realised duality symmetries that are independent of the standard supergravity global symmetries, and which provide active spectrum-generating symmetries for the fundamental BPS solitons. The additional ingredient, in any spacetime dimension, is a single scaling transformation that allows one to map between BPS solitons with different masses. Without the inclusion of this additional transformation, which is a symmetry of the classical equations of motion, but not the action, it is not possible to find a spectrum-generating symmetry. The necessity of including this scaling transformation highlights the vulnerability of duality multiplets to quantum anomalies. We argue that fundamental BPS solitons may be immune to this threat.