Generalized Dualities and Supergroups

Abstract

Using a recently developed formulation of double field theory in superspace, the graviton, $B$-field, gravitini, dilatini, and Ramond-Ramond bispinor are encoded in a single generalized supervielbein. Duality transformations are encoded as orthosymplectic transformations, extending the bosonic $O(D,D)$ duality group, and these act on all constituents of the supervielbein in an easily computable way. We first review conventional non-abelian T-duality in the Green-Schwarz superstring and describe the dual geometries in the language of double superspace. Since dualities are related to super-Killing vectors, this includes as special cases both abelian and non-abelian fermionic T-duality. We then extend this approach to include Poisson-Lie T-duality and its generalizations, including the generalized coset construction recently discussed in arXiv:1912.11036. As an application, we construct the supergeometries associated with the integrable $\lambda$ and $\eta$ deformations of the $Ad{S}_5\times S^5$ superstring. The deformation parameters $\lambda$ and $\eta$ are identified with the possible one-parameter embeddings of the supergravity frame within the doubled supergeometry. In this framework, the Ramond-Ramond bispinors are directly computable purely from the algebraic data of the supergroup.

85 pages, published version

References in corpus (89)

• Double Field Theory
• Generalized metric formulation of double field theory
• A new maximally supersymmetric background of IIB superstring theory
• Background independent action for double field theory
• On integrability of the Yang-Baxter $\si$-model
• Foundations of the AdS_5 x S^5 Superstring. Part I
• Timelike T-Duality, de Sitter Space, Large $N$ Gauge Theories and Topological Field Theory
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• On classical q-deformations of integrable sigma-models
• The gauge algebra of double field theory and Courant brackets
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Duality Twists, Orbifolds, and Fluxes
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Double Field Theory and N=4 Gauged Supergravity
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• $E_{11}$, SL(32) and Central Charges
• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• On non-abelian T-dual geometries with Ramond fluxes
• T-Duality, Space-time Spinors and R-R Fields in Curved Backgrounds
• Double Field Theory of Type II Strings
• Stringy differential geometry, beyond Riemann
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• An Integrable Deformation of the AdS5 x S5 Superstring
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• WZW-Poisson manifolds
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Abelian Yang-Baxter Deformations and TsT transformations
• Integrable Deformations of Strings on Symmetric Spaces
• Non-abelian T-duality, Ramond Fields and Coset Geometries
• Spacetimes for λ-deformations
• Maximally supersymmetric solutions of ten- and eleven-dimensional supergravities
• Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory
• The effective action of Double Field Theory
• T-Duality in the Green-Schwarz Formalism, and the Massless/Massive IIA Duality Map
• Poisson-Lie T-Duality in Double Field Theory
• Doubled aspects of generalised dualities and integrable deformations
• Ramond-Ramond Cohomology and O(D,D) T-duality
• SO(d,d) Transformations of Ramond-Ramond Fields and Space-time Spinors
• Supergravity background of lambda-deformed model for AdS2 x S2 supercoset
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• E11, generalised space-time and IIA string theory
• Generalized gravity from modified DFT
• On non-abelian T-duality and deformations of supercoset string sigma-models
• U-duality extension of Drinfel'd double
• Poisson-Lie U-duality in Exceptional Field Theory
• Weyl invariance for generalized supergravity backgrounds from the doubled formalism
• Beyond E11
• Local $\beta$-deformations and Yang-Baxter sigma model
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Superspace with manifest T-duality from type II superstring
• T-duality in Ramond-Ramond backgrounds
• 4-dimensional Chern-Simons theory and integrable field theories
• A master exceptional field theory
• Green-Schwarz superstring on doubled-yet-gauged spacetime
• On supersymmetric E11 exceptional field theory
• Ramond-Ramond gauge fields in superspace with manifest T-duality
• Natural curvature for manifest T-duality
• Dressing cosets and multi-parametric integrable deformations
• Poisson-Lie T-dual sigma models on supermanifolds
• T-duality of the Green-Schwarz superstring
• Double supergeometry
• Integrable $\mathcal{E}$-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
• Exploring Exceptional Drinfeld Geometries
• Exploring Fermionic T-duality
• Superstring in doubled superspace
• Canonical pure spinor (Fermionic) T-duality
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• E${}_{7(7)}$ Exceptional Field Theory in Superspace
• Fermionic T-duality: A snapshot review
• On current algebras, generalised fluxes and non-geometry
• Non-abelian U-duality at work
• String cosmology from Poisson-Lie T-dual sigma models on supermanifolds
• On non-abelian U-duality of 11D backgrounds
• Theory of Superdualities and the Orthosymplectic Supergroup
• Super Non-Abelian T-Duality
• Consistent Truncations and Dualities
• All maximal gauged supergravities with uplift
• Exploring the geometry of supersymmetric double field theory
• Superfield T-duality rules
• Aspects of Quantum Fermionic T-duality
• Type II Double Field Theory in Superspace
• Fermionic T-duality in fermionic double space
• Fermionic T-duality of DFT
• Plane Wave Type II${}^{\ast }$ String Backgrounds
• Notes on Ramond-Ramond spinors and bispinors in double field theory
• Poisson-Lie T-plurality for dressing cosets

Cited by in corpus (2)

• A hierarchy of WZW models related to super Poisson-Lie T-duality
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations