Weyl Connections and their Role in Holography - Archive ouverte HAL
Article Dans Une Revue Physical Review D Année : 2020

Weyl Connections and their Role in Holography

Robert G. Leigh
  • Fonction : Auteur

Résumé

It is a well-known property of holographic theories that diffeomorphism invariance in the bulk space-time implies Weyl invariance of the dual holographic field theory in the sense that the field theory couples to a conformal class of background metrics. The usual Fefferman-Graham formalism, which provides us with a holographic dictionary between the two theories, breaks explicitly this symmetry by choosing a specific boundary metric and a corresponding specific metric ansatz in the bulk. In this paper, we show that a simple extension of the Fefferman-Graham formalism allows us to sidestep this explicit breaking; one finds that the geometry of the boundary includes an induced metric and an induced connection on the tangent bundle of the boundary that is a Weyl connection (rather than the more familiar Levi-Civita connection uniquely determined by the induced metric). Properly invoking this boundary geometry has far-reaching consequences: the holographic dictionary extends and naturally encodes Weyl-covariant geometrical data, and, most importantly, the Weyl anomaly gains a clearer geometrical interpretation, cohomologically relating two Weyl-transformed volumes. The boundary theory is enhanced due to the presence of the Weyl current, which participates with the stress tensor in the boundary Ward identity.

Dates et versions

hal-02147978 , version 1 (05-06-2019)

Identifiants

Citer

Luca Ciambelli, Robert G. Leigh. Weyl Connections and their Role in Holography. Physical Review D, 2020, 101 (8), pp.086020. ⟨10.1103/PhysRevD.101.086020⟩. ⟨hal-02147978⟩
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