Super Non-Abelian T-Duality

Abstract

We analyse super non-Abelian T-duality for principal chiral models, symmetric space sigma models, and semi-symmetric space sigma models for general Lie supergroups. This includes T-duality along both bosonic and fermionic directions. Specifically, super non-Abelian T-duality exchanges the Maurer-Cartan equations with the equations of motion thus mapping integrable models into integrable models. This, in turn, allows us to construct the T-dual Lax connections. As a prime example, we analyse the OSpp1|2q principal chiral model, and whilst the target superspace of this model is a three-dimensional supergravity background, we argue that its super non-Abelian T-dual falls outside the class of such backgrounds.

JT gravity from non-Abelian T-duality

“…Dualising the left sector of the OSp(1|2) L × OSp(1|2) R isometry group, one lands on a dual geometry whose isometries are reduced to the non-dualised right sector. However, as noted in [74], the supervielbeins of the dual model no longer satisfy supergravity constraints, though the background still exhibits manifest supersymmetry. The situation does not improve upon dualising only the maximal bosonic subgroup of OSp(1|2) L -analogous results would be obtained by performing dualisation in the right sector OSp(1|2) R .…”

“…In [74], the application of super NATD (SNATD) has been worked out in detail for the Principal Chiral Model (PCM) on OSp(1|2). This model describes a N = 1 supersymmetric generalisation of AdS 3 (sAdS 3 ), and allows for a consistent description as a supermanifold satisfying the torsion constraints of 3D superspace [79][80][81].…”

“…On the other hand, integrating out the gauge fields we obtain the T-dual sigma model in which the Lagrange multipliers play the role of background coordinates. Its action can be written in the form [74,76]…”

“…For the sAdS 3 model, SNATD was developed in [74,75] dualising either the full left sector OSp(1|2) L of the isometry group, or on its maximal bosonic subgroup SL(2, R) L . It turns out that the dual model has no longer the interpretation of a supergravity background in 3D superspace, as one lands on a dual sigma model which does not satisfy the supergravity torsion constraints.…”

“…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],…”