On the Virasoro six-point identity block and chaos

We study the origin of the recently proposed effective theory of stress tensor exchanges based on reparametrization modes, that has been used to efficiently compute Virasoro identity blocks at large central charge. We first provide a derivation of the nonlinear Alekseev-Shatashvili action governing these reparametrization modes, and argue that it should be interpreted as the generating functional of stress tensor correlations on manifolds related to the plane by conformal transformations. In addition, we demonstrate that the rules previously prescribed with the reparametrization formalism for computing Virasoro identity blocks naturally emerge when evaluating Feynman diagrams associated with stress tensor exchanges between pairs of external primary operators. We make a few comments on the connection of these results to gravitational theories and holography.

Section: Introductionmentioning

confidence: 91%

“…We start by reviewing the prescriptions for computing Virasoro identity blocks within the reparametrization formalism, following [2,4,25]. Ultimately, our goal will be to derive these rules from Feynman diagrams describing stress tensor exchanges between external primary operators.…”

Section: Jhep05(2021)029mentioning

confidence: 99%

Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges

Nguyen

2021

“…Similar but richer solutions of nested AdS2 throats arise as BPS solutions of four-dimensional N = 2 supergravity [40]. Microscopic considerations of such macroscopic configurations have been considered, for instance, in [27,[41][42][43][44][45]. where z = r − 1.…”

Section: Constraints From the Null Energy Conditionmentioning

confidence: 99%

Constructing AdS2 flow geometries

Anninos

Galante

2021

We consider two-dimensional geometries flowing away from an asymptotically AdS2 spacetime. Macroscopically, flow geometries and their thermodynamic properties are studied from the perspective of dilaton-gravity models. We present a precise map constructing the fixed background metric from the boundary two-point function of a nearly massless matter field. We analyse constraints on flow geometries, viewed as solutions of dimensionally reduced theories, stemming from energy conditions. Microscopically, we construct computationally tractable RG flows in SYK-type models at vanishing and non-vanishing temperature. For certain regimes of parameter space, the flow geometry holographically encoding the microscopic RG flow is argued to interpolate between two (near) AdS2 spacetimes. The coupling between matter fields and the dilaton in the putative bulk is also discussed. We speculate on microscopic flows interpolating between an asymptotically AdS2 spacetime and a portion of a dS2 world.

“…See also ref [62]. for an application to two-dimensional six-point global blocks for stress tensor exchanges, and ref [63].…”

mentioning

confidence: 99%

Towards Feynman rules for conformal blocks

Hoback

Parikh

2021

We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.