Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges
TL;DR: In this paper, the authors study the origin of the theory of stress tensor exchanges based on reparametrization modes, that has been used to efficiently compute Virasoro identity blocks at large central charge.
Abstract: 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.
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TL;DR: In this paper, the conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights, and they reside at the bottom corners of memory diamonds, and ascend to generalized currents.
Abstract: Celestial diamonds encode the structure of global conformal multiplets in 2D celestial CFT and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to conformally soft factorization theorems, the bottom corners correspond to conserved charges, and the top corners to conformal dressings. We show that conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights. They reside at the bottom corners of memory diamonds, and ascend to generalized currents. We then identify the top corners of the associated Goldstone diamonds with conformal Faddeev-Kulish dressings and compute the sub-leading conformally soft dressings in gauge theory and gravity which are important for finding nontrivial central extensions. Finally, we combine these ingredients to speculate on 2D effective descriptions for the conformally soft sector of celestial CFT.
54 citations
TL;DR: In this paper, it was shown that the form of this celestial two-point function simply derives from an effective action that also controls infrared divergences in the symplectic structure of General Relativity with asymptotically flat boundary conditions.
Abstract: Infrared divergences in perturbative gravitational scattering amplitudes have been recently argued to be governed by the two-point function of the supertranslation Goldstone mode on the celestial sphere. We show that the form of this celestial two-point function simply derives from an effective action that also controls infrared divergences in the symplectic structure of General Relativity with asymptotically flat boundary conditions. This effective action finds its natural place in a path integral formulation of a celestial conformal field theory, as we illustrate by re-deriving the infrared soft factors in terms of celestial correlators. Our analysis relies on a well-posed action principle close to spatial infinity introduced by Compere and Dehouck.
17 citations
TL;DR: Ebert et al. as mentioned in this paper considered T T -type deformations of the (0+1)-dimensional dual to this 2D BF theory and interpreted the deformation as a modification of the BF theory boundary conditions.
Abstract: JT gravity has a first-order formulation as a two-dimensional BF theory, which can be viewed as the dimensional reduction of the Chern-Simons description of 3d gravity. We consider T T -type deformations of the (0+1)-dimensional dual to this 2d BF theory and interpret the deformation as a modification of the BF theory boundary conditions. The fundamental observables in this deformed BF theory, and in its 3d Chern-Simons lift, are Wilson lines and loops. In the 3d Chern-Simons setting, we study modifications to correlators involving boundary-anchored Wilson lines which are induced by a T T deformation on the 2d boundary; results are presented at both the classical level (using modified boundary conditions) and the quantum-mechanical level (using conformal perturbation theory). Finally, we calculate the analogous deformed Wilson line correlators in 2d BF theory below the Hagedorn temperature where the principal series dominates over the discrete series. Copyright S. Ebert et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. Received 06-06-2022 Accepted 06-09-2022 Published 13-10-2022 Check for updates doi:10.21468/SciPostPhys.13.4.096
16 citations
TL;DR: In particular, the flat Liouville action is still off-shell with respect to bulk equations of motion, and simply vanishes in case the latter are imposed as mentioned in this paper, and the Hamiltonian reduction of three-dimensional gravity to a flat-Liouville theory is unrelated.
Abstract: The generating functional of stress tensor correlation functions in two-dimensional conformal field theory is the nonlocal Polyakov action, or equivalently, the Liouville or Alekseev-Shatashvili action. I review its holographic derivation within the AdS$_3$/CFT$_2$ correspondence, both in metric and Chern-Simons formulations. I also provide a detailed comparison with the well-known Hamiltonian reduction of three-dimensional gravity to a flat Liouville theory, and conclude that the two results are unrelated. In particular, the flat Liouville action is still off-shell with respect to bulk equations of motion, and simply vanishes in case the latter are imposed. The present study also suggests an interesting re-interpretation of the computation of black hole spectral statistics recently performed by Cotler and Jensen as that of an explicit averaging of the partition function over the boundary source geometry, thereby providing potential justification for its agreement with the predictions of a random matrix ensemble.
11 citations
24 Jan 2022
TL;DR: In this article , the Schwarzian behavior of the gravitational field at null infinity under superrotations is described as an unobservable gauge artifact, and the construction of the gauge-invariant News tensor is discussed.
Abstract: I describe the Schwarzian behavior of the gravitational field at null infinity under superrotations, to be understood as an unobservable gauge artifact. To this end I review the induced geometry of null infinity and the construction of the gauge-invariant News tensor that characterizes gravitational radiation. I discuss potentially important implications for the celestial holography program, suggesting in particular that the uplift of the AdS3/CFT2 correspondence directly relates to the unobservable gauge sector.
9 citations
References
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TL;DR: In this article, it was shown that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of the super Yang-Mills theory in four dimensions.
Abstract: Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of ${\cal N}=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the ${\cal N}=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.
14,084 citations
TL;DR: In this paper, a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory is introduced to obtain certain Green's functions in 3+1-dimensional N = 4 supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory.
11,887 citations
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Abstract: It is shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level. This is done by studying three dimensional gravity with a negative cosmological constant. The asymptotic symmetry group in that case is eitherR×SO(2) or the pseudo-conformal group in two dimensions, depending on the boundary conditions adopted at spatial infinity. In the latter situation, a nontrivial central charge appears in the algebra of the canonical generators, which turns out to be just the Virasoro central charge.
3,072 citations
TL;DR: In this article, a formalism for computing sums over random surfaces which arise in all problems containing gauge invariance (like QCD, three-dimensional Ising model etc.) is developed.
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