Duality rules for more 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.