Dual vector multiplet coupled to dualN=1supergravity in 10D

Abstract

We couple in superspace a dual vector multiplet $({C}_{{m}_{1}\dots{}{m}_{7}},{\ensuremath{\lambda}}^{\ensuremath{\alpha}})$ to the dual version of $N=1$ supergravity $(e_{m}{}^{a},\ensuremath{\psi}_{m}{}^{\ensuremath{\alpha}},{M}_{{m}_{1}\dots{}{m}_{6}},{\ensuremath{\chi}}_{\ensuremath{\alpha}},\ensuremath{\Phi})$ in ten dimensions. The 7-form field $C$ has its 8-form field strength $H$ dual to the 2-form field strength $F$ of the conventional vector multiplet. To simplify the computation, we use so-called beta-function-favored superspace constraints for dual supergravity developed for $\ensuremath{\beta}$-function computations. As in a more conventional constraint set, the $H$-Bianchi identity must have the form $N\ensuremath{\wedge}F$, where $N$ is the 7-form field strength in dual supergravity. The potential anomaly for the dual vector multiplet can be cancelled for the particular gauge group $U(1{)}^{496}$ by the Green-Schwarz mechanism. As a by-product, we also give the globally supersymmetric Abelian Dirac-Born-Infeld interactions for the dual vector multiplet for the first time.