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Journal of High Energy Physics

, 2017:124 | Cite as

Exactly marginal deformations from exceptional generalised geometry

  • Anthony Ashmore
  • Maxime Gabella
  • Mariana Graña
  • Michela Petrini
  • Daniel Waldram
Open Access
Regular Article - Theoretical Physics

Abstract

We apply exceptional generalised geometry to the study of exactly marginal deformations of \( \mathcal{N} \) = 1 SCFTs that are dual to generic AdS5 flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries.

Our analysis holds for any \( \mathcal{N} \) = 2 AdS5 flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.

Keywords

AdS-CFT Correspondence Flux compactifications 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Anthony Ashmore
    • 1
    • 2
  • Maxime Gabella
    • 3
  • Mariana Graña
    • 4
  • Michela Petrini
    • 5
  • Daniel Waldram
    • 6
  1. 1.Merton CollegeUniversity of OxfordOxfordU.K.
  2. 2.Mathematical InstituteUniversity of OxfordOxfordU.K.
  3. 3.Institute for Advanced StudyPrincetonU.S.A.
  4. 4.Institut de Physique Théorique, CEA/SaclayGif-sur-YvetteFrance
  5. 5.Sorbonne Université, UPMC Paris 05, UMR 7589, LPTHEParisFrance
  6. 6.Department of PhysicsImperial College LondonLondonU.K.

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