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 [J. J. Fernández-Melgarejo et al., 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. Since our approach is based on $U$-duality, we can also determine the 11D uplifts of the mixed-symmetry potential, unlike the $T$-duality-covariant approach known in the literature. We also study the field strengths of the mixed-symmetry potentials.