A family of algebras that extends the Lie algebra of the Drinfel'd double is proposed. This allows us to systematically construct the generalized frame fields which realize the proposed algebra by means of the generalized Lie derivative, i.e., $\hat{\mathcal{L}}_{E_A}E_B{}^I = - \mathcal{F}_{A…
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Study of exceptional algebroids in relation to type IIB superstrings.
problem Understanding the structure of exceptional algebroids in type IIB superstring theory.
method Analyzing the local form of IIB-exact exceptional algebroids and deriving possible twists.
result A simple description of Leibniz parallelisable spaces and U-duality.
Geometric formulation of 4D supergravity for mathematicians.
problem Geometric characterization of U-duality group in 4D supergravity.
method Geometric formulation based on Riemannian submersion and symplectic vector bundle.
result Characterization of electromagnetic duality transformations as a short exact sequence of automorphism groups.
The paper integrates supergravity with geometric and symplectic structures.
problem Classical ungauged supergravity's geometric and symplectic integration.
method Implementing Dirac-Schwinger-Zwanziger integrality condition on supergravity.
result Geometric model of supergravity on an oriented four-manifold.
We classify generalised supersymmetric fluxbranes in type II string theory obtained as Kaluza-Klein reductions of the Minkowski space vacuum of eleven-dimensional supergravity. We obtain two families of smooth solutions which contains all the known solutions, new solutions called nullbranes, and solutions interpolating…
We describe principal 3-bundles with adjusted connections using Lie algebras and groupoids.
problem Describing principal 3-bundles with adjusted connections.
method Derived explicit forms of adjustment data for 3-term -algebras, integrated action Lie 3-algebroids to Lie 3-groupoids, and used differential cohomology.
result Explicit description of principal 3-bundles with adjusted connections in terms of differential cohomology.
U-geometry : SL(5)hep-th
Recently Berman and Perry constructed a four-dimensional M-theory effective action which manifests SL(5) U-duality. Here we propose an underlying differential geometry of it, under the name `SL(5) U-geometry' which generalizes the ordinary Riemannian geometry in an SL(5) compatible manner. We introduce a `semi-covarian…
Extends Drinfel'd doubles to include twists and generalizes Lie bialgebroids.
problem Tackles the extension of Drinfel'd doubles and Lie bialgebroids to include twists and generalizes them.
method Introduces a framework of calculus on algebroids and examines compatibility conditions for various algebroid properties.
result Introduces the notion of proto bialgebroids and their Drinfel'd doubles, generalizing both bialgebroids and proto Lie bialgebroids.
Starting from a higher Courant bracket associated to exceptional generalized geometry, we provide a systematic derivation of all types of fluxes and their Bianchi identities for four-dimensional compactifications of M-theory. We show that these fluxes may be understood as generalized Wess-Zumino terms in certain topolo…
We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical data and constraints. In special cases, we recover general relativity with and with…
In this paper we reformulate N=2 supergravity backgrounds arising in type II string theory in terms of quantities transforming under the U-duality group E7(7). In particular we combine the Ramond--Ramond scalar degrees of freedom together with the O(6,6) pure spinors which govern the Neveu-Schwarz sector by considering…
In these lectures we review how the symmetries of gravitational theories may be regarded as originating from those of "Yang-Mills squared". We begin by motivating the idea that certain aspects of gravitational theories can be captured by the product, in some sense, of two distinct Yang-Mills theories, particularly in t…
G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie dualitymath.DG
Unified framework for exceptional and generalised geometry, and Poisson-Lie duality.
problem Unified framework for exceptional and generalised geometry.
method Introducing G-algebroid, generalising Lie and Courant algebroids.
result Classification of 'exact' algebroids and compatibility with supergravity.
We study compactifications of type II theories on SU(2) x SU(2) structure manifolds to six, five and four spacetime dimensions. We use the framework of generalized geometry to describe the NS-NS sector of such compactifications and derive the structure of their moduli spaces. We show that in contrast to SU(3) x SU(3) s…
Study of exceptional algebroids in type IIA string theory.
problem Understanding the structure of algebroids in type IIA string theory.
method Warped compactifications and analysis of local moduli space.
result Local classification of algebroids reveals new scalar deformations and twists.
We discuss the structure of "exceptional generalised geometry" (EGG), an extension of Hitchin's generalised geometry that provides a unified geometrical description of backgrounds in eleven-dimensional supergravity. On a d-dimensional background, as first described by Hull, the action of the generalised geometrical O(d…
Y-algebroids generalize symmetry structures for string/M-theory compactifications.
problem Capturing local symmetry structures for string/M-theory compactifications to various dimensions.
method Define Y-algebroids based on a tensor Y, classify M-exact E7-algebroids, and relate to E7(7)×R^+ generalised geometry.
result Y-algebroids match the generalised tangent space of E7(7)×R^+ generalised geometry, including possible fluxes.
We describe a construction of geometric U-folds compatible with a non-trivial extension of the global formulation of four-dimensional extended supergravity on a differentiable spin manifold. The topology of geometric U-folds depends on certain flat fiber bundles which encode how supergravity fields are globally glued t…
By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in R,C,H,O, it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently…
This thesis proposes a global geometric formulation of Extended Field Theories.
problem Global understanding of Extended Field Theories remains an open problem.
method Introducing an atlas for the principal infinity-bundle, unifying metric and higher gauge field.
result Global abelian T-duality and Poisson-Lie T-duality are automatically recovered.