 Award ID(s):
 1914412
 NSFPAR ID:
 10345758
 Date Published:
 Journal Name:
 SciPost Physics
 Volume:
 11
 Issue:
 3
 ISSN:
 25424653
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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A bstract Pure gravity in AdS 3 is a theory of boundary excitations, most simply expressed as a constrained free scalar with an improved stress tensor that is needed to match the BrownHenneaux central charge. Excising a finite part of AdS gives rise to a static gauge NambuGoto action for the boundary graviton. We show that this is the $$ T\overline{T} $$ T T ¯ deformation of the infinite volume theory, as the effect of the improvement term on the deformed action can be absorbed into a field redefinition. The classical gravitational stress tensor is reproduced order by order by the $$ T\overline{T} $$ T T ¯ trace equation. We calculate the finite volume energy spectrum in static gauge and find that the trace equation imposes sufficient constraints on the ordering ambiguities to guarantee agreement with the lightcone gauge prediction. The correlation functions, however, are not completely fixed by the trace equation. We show how both the gravitational action and the $$ T\overline{T} $$ T T ¯ deformation allow for finite improvement terms, and we match these to the undetermined total derivative terms in Zamolodchikov’s point splitting definition of the $$ T\overline{T} $$ T T ¯ operator.more » « less

null (Ed.)A bstract The $$ T\overline{T} $$ T T ¯ deformation can be formulated as a dynamical change of coordinates. We establish and generalize this relation to curved spaces by coupling the undeformed theory to 2d gravity. For curved space the dynamical change of coordinates is supplemented by a dynamical Weyl transformation. We also sharpen the holographic correspondence to cutoff AdS 3 in multiple ways. First, we show that the action of the annular region between the cutoff surface and the boundary of AdS 3 is given precisely by the $$ T\overline{T} $$ T T ¯ operator integrated over either the cutoff surface or the asymptotic boundary. Then we derive dynamical coordinate and Weyl transformations directly from the bulk. Finally, we reproduce the flow equation for the deformed stress tensor from the cutoff geometry.more » « less

null (Ed.)Abstract We prove duality results for residual intersections that unify and complete results of van Straten,Huneke–Ulrich and Ulrich, and settle conjectures of van Straten and Warmt. Suppose that I is an ideal of codimension g in a Gorenstein ring,and {J\subset I} is an ideal with {s=g+t} generators such that {K:=J:I} has codimension s . Let {{\overline{I}}} be the image of I in {{\overline{R}}:=R/K} . In the first part of the paper we prove, among other things, that under suitable hypotheses on I , the truncated Rees ring {{\overline{R}}\oplus{\overline{I}}\oplus\cdots\oplus{\overline{I}}{}^{t+1}} is a Gorenstein ring, and that the modules {{\overline{I}}{}^{u}} and {{\overline{I}}{}^{t+1u}} are dualto one another via the multiplication pairing into {{{\overline{I}}{}^{t+1}}\cong{\omega_{\overline{R}}}} . In the second part of the paper we study the analogue of residue theory, and prove that, when {R/K} is a finitedimensional algebra over a field of characteristic 0 and certain other hypotheses are satisfied, the socle of {I^{t+1}/JI^{t}\cong{\omega_{R/K}}} is generated by a Jacobian determinant.more » « less

Pure threedimensional gravity is a renormalizable theory with twofree parameters labelled by
andG $G$ .As a consequence, correlation functions of the boundary stress tensor inAdS\Lambda $\Lambda $ are uniquely fixed in terms of one dimensionless parameter, which is thecentral charge of the Virasoro algebra. The same argument implies thatAdS_3 ${}_{3}$ gravity at a finite radial cutoff is a renormalizable theory, but nowwith one additional parameter corresponding to the cutoff location. Thistheory is conjecturally dual to a_3 ${}_{3}$ deformedCFT, assuming that such theories actually exist. To elucidate this, westudy the quantum theory of boundary gravitons living on a cutoff planarboundary and the associated correlation functions of the boundary stresstensor. We compute stress tensor correlation functions to twoloop order(T\overline{T} $T\overline{T}$ being the loop counting parameter), extending existing tree levelresults. This is made feasible by the fact that the boundary gravitonaction simplifies greatly upon making a judicious field redefinition,turning into the NambuGoto action. After imposing Lorentz invariance,the correlators at this order are found to be unambiguous up to a singleundetermined renormalization parameter.G $G$ 
A bstract We obtain microstates accounting for the GibbonsHawking entropy in dS 3 , along with a subleading logarithmic correction, from the solvable T $$ \overline{T} $$ T ¯ + Λ 2 deformation of a seed CFT with sparse light spectrum. The microstates arise as the dressed CFT states near dimension ∆ = c/ 6, associated with the HawkingPage transition; they dominate the real spectrum of the deformed theory. We exhibit an analogue of the HawkingPage transition in de Sitter. Appropriate generalizations of the T $$ \overline{T} $$ T ¯ + Λ 2 deformation are required to treat modeldependent local bulk physics (subleading at large central charge) and higher dimensions. These results add considerably to the already strong motivation for the continued pursuit of such generalizations along with a more complete characterization of T $$ \overline{T} $$ T ¯ type theories, building from existing results in these directions.more » « less