Non-abelian fermionic T-duality in supergravity

Abstract

Field transformation rules of the standard fermionic T-duality require fermionic isometries to anticommute, which leads to complexification of the Killing spinors and results in complex valued dual backgrounds. We generalize the field transformations to the setting with non-anticommuting fermionic isometries and show that the resulting backgrounds are solutions of double field theory. Explicit examples of non-abelian fermionic T-dualities that produce real backgrounds are given. Some of our examples can be bosonic T-dualized into usual supergravity solutions, while the others are genuinely non-geometric.Comparison with alternative treatment based on sigma models on supercosets shows consistency.

Poisson-Lie T-plurality for dressing cosets

“…Then we may also find the PL T -plurality for super-dressing cosets. This may contain the fermionic T -duality as a specific case, and may give a non-Abelian extension of the fermionic T -duality (see [88,89] for related recent studies).…”

JT gravity from non-Abelian T-duality

“…The idea of extending the Abelian dualisation procedure to the case of backgrounds enjoying commuting superisometries was introduced in [46,47] and further developed in [48][49][50][51][52][53][54] -see also [55] for previous related work and [56] for a review. In recent years, it has led to various non-Abelian generalisations, formulated in terms of BRST techniques [57], super Poisson-Lie symmetry [58][59][60][61][62][63][64][65], Double Field Theory formalism [66][67][68][69], as well as manifestly supersymmetric generalizations of the NATD technique of de la Ossa and Quevedo [70][71][72][73][74][75][76],…”