On non-supersymmetric conformal manifolds: field theory and holography

Abstract

We discuss the constraints that a conformal field theory should enjoy to admit exactly marginal deformations, i.e. to be part of a conformal manifold. In particular, using tools from conformal perturbation theory, we derive a sum rule from which one can extract restrictions on the spectrum of low spin operators and on the behavior of OPE coefficients involving nearly marginal operators. We then consider conformal field theories admitting a gravity dual description, and as such a large-$N$ expansion. We discuss the relation between conformal perturbation theory and loop expansion in the bulk, and show how such connection could help in the search for conformal manifolds beyond the planar limit. Our results do not rely on supersymmetry, and therefore apply also outside the realm of superconformal field theories.

arXiv comment30 pages, figures. v3: discussion on contribution of graviton exchange extended + minor corrections

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• Holographic Evidence for Non-Supersymmetric Conformal Manifolds
• On the exact quantum scale invariance of three-dimensional reduced QED theories
• Superconformal Models for Graphene and Boundary Central Charges
• The unitary subsector of generalized minimal models
• Conformal Manifolds with Boundaries or Defects
• Discreteness and Integrality in Conformal Field Theory
• Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry
• Thermal order in large N conformal gauge theories
• The Techni-Pati-Salam Composite Higgs
• Geometry of Conformal Manifolds and the Inversion Formula
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• A Nilpotency Index of Conformal Manifolds
• Marginal deformations from type IIA supergravity
• Tri-vector deformations on compact isometries
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• Recursive construction of the operator product expansion in curved space
• Critical properties of three-dimensional many-flavour QEDs
• On SUSY-breaking Moduli Spaces of AdS${}_7$ Vacua and 6D SCFTs
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation