Poisson–Lie T-plurality for dressing cosets

Abstract

Abstract The Poisson–Lie T-plurality is an equivalence of string theories on various cosets $\mathcal {D}/\tilde{G},\ \mathcal {D}/\tilde{G}^{\prime },\ldots$, where $\mathcal {D}$ is a Drinfel’d double and $\tilde{G}$, $\tilde{G}^{\prime },\ldots$ are maximal isotropic subgroups. This can be extended to the equivalence for dressing cosets, i.e., $F\backslash \mathcal {D}/\tilde{G},\ F\backslash \mathcal {D}/\tilde{G}^{\prime },\ldots$, 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 (PL) T-plurality for dressing cosets (with spectator fields) is a symmetry of double field theory. The formula for the Ramond–Ramond field strength is also proposed such that the equations of motion for the Neveu–Schwarz–Neveu–Schwarz fields are transformed covariantly. In addition, we provide specific examples of the PL T-plurality for dressing cosets.