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Non-abelian T-duality, Ramond Fields and Coset Geometries

Yolanda Lozano, Eoin 'O Colgain, Konstadinos Sfetsos, Daniel C. Thompson

TL;DR

The paper develops non-abelian T-duality in the presence of Ramond fluxes for backgrounds where the duality group acts with isotropy on coset spaces, enabling a new class of supergravity solutions linked to D-brane near-horizon geometries and standard compactifications. Using a coset reduction framework, it derives RR-field transformation rules via a bi-spinor construction and identifies how the spinor rotation Ω encodes frame changes, with chirality depending on the duality group's dimension. It then provides explicit non-abelian T-duals for AdS3×S3×T4, AdS5×S5, AdS4×CP2×S2, and AdS4×S2×S2×S2, detailing the RR flux rearrangements, dilaton profiles, vanishing NS two-forms, and often non-supersymmetric outcomes. The work highlights fixed-point singularities from isotropy and discusses the implications for AdS/CFT contexts and potential high-spin sector descriptions, while suggesting future derivations via dimensional reduction. Overall, it broadens the toolkit for generating new supergravity solutions through coset non-abelian T-duality and clarifies the associated geometric and supersymmetric structure.

Abstract

We extend previous work on non-abelian T-duality in the presence of Ramond fluxes to cases in which the duality group acts with isotropy such as in backgrounds containing coset spaces. In the process we generate new supergravity solutions related to D-brane configurations and to standard supergravity compactifications.

Non-abelian T-duality, Ramond Fields and Coset Geometries

TL;DR

The paper develops non-abelian T-duality in the presence of Ramond fluxes for backgrounds where the duality group acts with isotropy on coset spaces, enabling a new class of supergravity solutions linked to D-brane near-horizon geometries and standard compactifications. Using a coset reduction framework, it derives RR-field transformation rules via a bi-spinor construction and identifies how the spinor rotation Ω encodes frame changes, with chirality depending on the duality group's dimension. It then provides explicit non-abelian T-duals for AdS3×S3×T4, AdS5×S5, AdS4×CP2×S2, and AdS4×S2×S2×S2, detailing the RR flux rearrangements, dilaton profiles, vanishing NS two-forms, and often non-supersymmetric outcomes. The work highlights fixed-point singularities from isotropy and discusses the implications for AdS/CFT contexts and potential high-spin sector descriptions, while suggesting future derivations via dimensional reduction. Overall, it broadens the toolkit for generating new supergravity solutions through coset non-abelian T-duality and clarifies the associated geometric and supersymmetric structure.

Abstract

We extend previous work on non-abelian T-duality in the presence of Ramond fluxes to cases in which the duality group acts with isotropy such as in backgrounds containing coset spaces. In the process we generate new supergravity solutions related to D-brane configurations and to standard supergravity compactifications.

Paper Structure

This paper contains 16 sections, 131 equations, 2 tables.

Table of Contents

  1. Introduction
  2. General strategy
  3. Non-abelian T-duals in coset spaces
  4. Review of T-duals in group spaces
  5. Non-abelian T-duals in coset spaces via reduction
  6. Examples
  7. Non-abelian T-dual in the D1-D5 near horizon
  8. (No) Supersymmetry of the dual
  9. Non-abelian T-dual in the D3 near horizon
  10. Non-abelian T-dual of AdS4CP2S2
  11. Non-abelian T-dual of $AdS_4 \times S^2 \times S^2 \times S^2$
  12. Concluding remarks
  13. Non-abelian T-dual of AdS4CP3
  14. Geometry and Killing vectors in group and coset spaces
  15. Spinor derivative on $AdS_5\times S^5$ Killing vectors
  16. ...and 1 more sections