Poisson-Lie T-plurality for dressing cosets

Abstract

The Poisson-Lie T-plurality is an equivalence of string theories on various cosets $\mathcal{D}/\tilde{G}$, $\mathcal{D}/\tilde{G}'$, $\cdots$, where $\mathcal{D}$ is a Drinfel'd double and $\tilde{G}$, $\tilde{G}'$, $\cdots$ are maximal isotropic subgroups. This can be extended to the equivalence for dressing cosets, i.e., $F\backslash\mathcal{D}/\tilde{G}$, $F\backslash\mathcal{D}/\tilde{G}'$, $\cdots$, where $F$ is an isotropic subgroup of $\mathcal{D}$. We explore this extended Poisson-Lie T-plurality, clarifying the relation between several previous approaches. We propose a gauged sigma model for a general gauge group $F$ and obtain the formula for the metric and the B-field on the dressing coset. Using this formula and an ansatz for the dilaton, we show that the Poisson-Lie T-plurality for dressing cosets (with spectator fields) is a symmetry of double field theory. The formula for the R-R field strength is also proposed such that the equations of motion for the NS-NS fields are transformed covariantly. In addition, we provide specific examples of the PL T-plurality for dressing cosets.