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General solutions in Chern-Simons gravity and $T \bar T$-deformations

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arxiv 1912.13330 v2 pith:XPXAZSUO submitted 2019-12-31 hep-th

classification hep-th
keywords boundarychern-simonsconditionsfindformalismgeneralgravityprinciple
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We find the most general solution to Chern-Simons AdS$_3$ gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $T \bar T$-deformation.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. QG from SymQRG: AdS$_3$/CFT$_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow

    hep-th 2024-12 conditional novelty 7.0 of 10

    A framework called SymQRG identifies 3D quantum gravity as the symmetry-preserving RG flow of 2D CFTs, realized discretely by U_q(SL(2,R)) 6j symbols.

  2. On topological defects in Chern-Simons theory

    hep-th 2024-12 conditional novelty 7.0 of 10

    R-matrix solutions of the modified classical Yang-Baxter equation define non-invertible topological surface defects in non-Abelian Chern-Simons theory, with semigroup fusion.

  3. Boundary Quantum Field Theories Perturbed by ${\rm T}\bar{\rm T}$: Towards a Form Factor Program

    hep-th 2025-01 reject novelty 6.0 of 10

    The paper constructs deformed boundary minimal form factors for T anti-T perturbed theories and rewrites the sinh-Gordon Dirichlet minimal form factor in the same block form, but the central solution formula has a sign error.

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