Non-Abelian U -duality for membranes

A truncation of the SL(5) Exceptional Field Theory that allows to describe spacetimes of the form M 4 × M 7 with the 4-form flux on M 4 is constructed. The resulting theory is used to test the recently proposed tri-vector generalisation of Yang-Baxter deformations applied to the AdS 4 × S 7 solution of d = 11 supergravity. We present two new supergravity solutions corresponding to non-abelian non-unimodular tri-vector deformations of AdS 4 × S 7 .

Section: Jhep05(2020)113mentioning

confidence: 99%

Non-abelian tri-vector deformations in d = 11 supergravity

Bakhmatov

Gubarev

Musaev

2020

“…A key point of [20,21] was that the EDA can be realised by a generalised Leibniz parallelisation for the exceptional tangent bundle T G ⊕ ∧ 2 T G thus echoing the set up of Poisson-Lie T-duality and allowing this framework to be used to generate solutions using the ideas of generalised Scherk-Schwarz reductions. Some features of the geometry, and the membrane interpretation, were then given in [22], while a classification of all possible EDAs for the case of n = 3 was made in [23].…”

Section: Jhep09(2020)151mentioning

confidence: 99%

“…those with mixed four-dimensional and sevendimensional indices. Using the dictionary reproduced in full in appendix A.3, we can, as in [22], work out the geometry giving rise to the Exceptional Drinfeld Algebra…”

Section: Jhep09(2020)151mentioning

confidence: 99%

Exploring exceptional Drinfeld geometries

Blair

Thompson

Zhidkova

2020

We explore geometries that give rise to a novel algebraic structure, the Exceptional Drinfeld Algebra, which has recently been proposed as an approach to study generalised U-dualities, similar to the non-Abelian and Poisson-Lie generalisations of T-duality. This algebra is generically not a Lie algebra but a Leibniz algebra, and can be realised in exceptional generalised geometry or exceptional field theory through a set of frame fields giving a generalised parallelisation. We provide examples including “three-algebra geometries”, which encode the structure constants for three-algebras and in some cases give novel uplifts for CSO(p, q, r) gaugings of seven-dimensional maximal supergravity. We also discuss the M-theoretic embedding of both non-Abelian and Poisson-Lie T-duality.

“…The non-perturbative generalisation of Poisson-Lie T-duality to a U-duality version in M-theory, or more conservatively as a solution-generating mechanism of 11-dimensional supergravity, has long been an open problem, which was recently addressed in [17,18] and further elaborated on in [19][20][21]. Building on the interpretation of PLTD and Drinfel'd doubles within Double Field Theory (DFT), [17,18,[22][23][24] used Exceptional Field Theory (ExFT)/Exceptional Generalised Geometry to propose a natural generalisation of the Drinfel'd double for dualities along four spacetime dimensions.…”

Section: Jhep01(2021)020mentioning

confidence: 99%

E6(6) exceptional Drinfel’d algebras

Malek

Sakatani

Thompson

2021

Self Cite

The exceptional Drinfel’d algebra (EDA) is a Leibniz algebra introduced to provide an algebraic underpinning with which to explore generalised notions of U-duality in M-theory. In essence, it provides an M-theoretic analogue of the way a Drinfel’d double encodes generalised T-dualities of strings. In this note we detail the construction of the EDA in the case where the regular U-duality group is E6(6). We show how the EDA can be realised geometrically as a generalised Leibniz parallelisation of the exceptional generalised tangent bundle for a six-dimensional group manifold G, endowed with a Nambu-Lie structure. When the EDA is of coboundary type, we show how a natural generalisation of the classical Yang-Baxter equation arises. The construction is illustrated with a selection of examples including some which embed Drinfel’d doubles and others that are not of this type.