Duality rules for more mixed-symmetry potentials

TL;DR

This paper investigates T- and S-duality transformations of mixed-symmetry gauge potentials in type II supergravities, simplifying their rules through redefinitions and connecting them with $E_{11}$ predictions.

Contribution

It determines and simplifies the T- and S-duality rules for mixed-symmetry potentials, aligning them with $E_{11}$ conjecture predictions.

Findings

Redefinition of potentials simplifies duality rules.

Identification of potentials with $E_{11}$-predicted components.

Discussion of field strengths of mixed-symmetry potentials.

Abstract

T- and S-duality rules among the gauge potentials in type II supergravities are studied. In particular, by following the approach of arXiv:1909.01335, we determine the T- and S-duality rules for certain mixed-symmetry potentials, which couple to supersymmetric branes with tension $T\propto g_s^{-n}$ ($n\leq 4$). Although the T-duality rules are rather intricate, we find a certain redefinition of potentials which considerably simplifies the duality rules. After the redefinition, potentials are identified with components of the T-duality-covariant potentials, which have been predicted by the $E_{11}$ conjecture. We also discuss the field strengths of the mixed-symmetry potentials.