Pin(d,d) covariance of pure spinor equations for supersymmetric vacua and Non-Abelian T-duality

Abstract

In a supersymmetric compactification of Type II supergravity, preservation of $\mathcal{N}=1$ supersymmetry in four dimensions requires that the structure group of the generalized tangent bundle $TM\oplus T^{\ast }M$ of the six dimensional internal manifold $M$ is reduced from $SO(6,6)$ to $SU(3)\times SU(3)$. This topological condition on the internal manifold implies existence of two globally defined compatibe pure spinors ${\Phi }_1$ and ${\Phi }_2$ of non-vanishing norm. Furthermore, these pure spinors should satisfy certain first order differential equations. In this paper, we show that Non-Abelian T-duality (NATD) is a solution generating transformation for these pure spinor equations. We first show that the pure spinor equations are covariant under $Pin(d,d)$ transformations. Then, we use the fact NATD is generated by a coordinate dependent $Pin(d,d)$ transformation. The key point is that the flux produced by this transformation is the same as the geometric flux associated with the isometry group, with respect to which one implements NATD. We demonstrate our method by studying NATD of certain solutions of Type IIB supergravity with $SU(2)$ isometry and $SU(3)$ structure.

arXiv commentminor corrections, references added

References in corpus (61)

• Target Space Duality in String Theory
• Double Field Theory
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Superstrings with Intrinsic Torsion
• New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls
• Generalized structures of N=1 vacua
• The gauge algebra of double field theory and Courant brackets
• A scan for new N=1 vacua on twisted tori
• Double Field Theory and N=4 Gauged Supergravity
• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• On non-abelian T-dual geometries with Ramond fluxes
• Double Field Theory of Type II Strings
• On Non-Abelian Duality
• Gauged Double Field Theory
• Supersymmetric D-branes and calibrations on general N=1 backgrounds
• Non-abelian T-duality, Ramond Fields and Coset Geometries
• Type IIB Supergravity Solutions with AdS${}_5$ From Abelian and Non-Abelian T Dualities
• Green-Schwarz Strings in TsT-transformed backgrounds
• Supersymmetric sources, integrability and generalized-structure compactifications
• Non-Abelian T-duality and the AdS/CFT correspondence:new N=1 backgrounds
• The effective action of Double Field Theory
• Supersymmetry and non-Abelian T-duality in type II supergravity
• Poisson-Lie T-Duality in Double Field Theory
• Doubled aspects of generalised dualities and integrable deformations
• Generalized Calabi-Yau manifolds
• Non-Abelian T-duality and consistent truncations in type-II supergravity
• N=1 geometries for M-theory and type IIA strings with fluxes
• Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory
• On supersymmetric solutions of type IIB supergravity with general fluxes
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• An alternative IIB embedding of F(4) gauged supergravity
• Double Field Theory, T-Duality, and Courant Brackets
• Comments on T-dualities of Ramond-Ramond Potentials
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Type II Strings and Generalized Calabi-Yau Manifolds
• Lunin-Maldacena Deformations With Three Parameters
• Gravity duals to deformed SYM theories and Generalized Complex Geometry
• The $Ad{S}_5$ non-Abelian T-dual of Klebanov-Witten as a $\mathcal{N}=1$ linear quiver from M5-branes
• G-structures and Flavouring non-Abelian T-duality
• Quantum correction to generalized T-dualities
• New supersymmetric flux vacua with intermediate SU(2) structure
• non-Abelian T-duality, G2-structure Rotation and Holographic Duals of N=1 Chern-Simons Theories
• Generalized structures of ten-dimensional supersymmetric solutions
• Flux backgrounds from Twists
• ${\alpha }^{\prime }$-corrected Poisson-Lie T-duality
• New $\mathcal{N}=1$ supersymmetric $Ad{S}_5$ backgrounds in Type IIA supergravity
• Dualising the Baryonic Branch: Dynamic SU(2) and confining backgrounds in IIA
• New Type IIB Backgrounds and Aspects of Their Field Theory Duals
• Generalized Dualities and Higher Derivatives
• Holographic Flows in non-Abelian T-dual Geometries
• The first ${\alpha }^{\prime }$-correction to homogeneous Yang-Baxter deformations using $O(d,d)$
• Polyvector deformations in eleven-dimensional supergravity
• Yang-Baxter Deformation as an O(d,d) Transformation
• Non-Abelian T-duality as a Transformation in Double Field Theory
• Non-abelian T-folds
• $O(d,d)$ transformations preserve classical integrability
• Duality Twisted Reductions of Double Field Theory of Type II Strings
• An Algebraic Classification of Solution Generating Techniques
• Supergravity solution-generating techniques and canonical transformations of $\sigma$-models from $O(D,D)$