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.
Highlights
The AdS/CFT correspondence allows the study of a wide class of superconformal field theories in four dimensions, many of which are realised as the world-volume theories of D3-branes at conical singularities of Calabi-Yau manifolds
In this paper we have used exceptional generalised geometry to analyse exactly marginal deformations of N = 1 SCFTs that are dual to AdS5 backgrounds in type II or elevendimensional supergravity
Marginal deformations are determined by imposing F-term conditions on operators of conformal dimension three and quotienting by the complexified global symmetry group
Summary
The AdS/CFT correspondence allows the study of a wide class of superconformal field theories in four dimensions, many of which are realised as the world-volume theories of D3-branes at conical singularities of Calabi-Yau manifolds. Our specific examples will focus on type IIB geometries, the same analysis applies to generic N = 2 AdS5 solutions of type IIB or eleven-dimensional supergravity This generalised geometric description of the internal geometry translates naturally to quantities in the dual field theory, which is useful when analysing marginal deformations. The exactly marginal deformations are a symplectic quotient of the marginal deformations by the isometry group of the internal manifold This corresponds to the global symmetry group of the dual field theory. If the original SCFT has a global symmetry G that is broken by the generic deformation W = hiOi, the conformal manifold, near the original theory, is given by the quotient of the space of marginal couplings by the complexified broken global symmetry group. Since this will be relevant for the gravity dual, we stress that the only obstruction to having exactly marginal deformations is the one-loop constraint (2.7)
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