We re-examine the black hole solutions in classical theories of dilaton gravity in two dimensions. We consider an arbitrary dilaton potential such that there are black hole solutions asymptotic at infinity to the nearly $\mathrm{AdS}_2$ solutions of JT gravity, and such that the black hole energy and entropy are bounded below. We show that if there is a black hole solution with negative specific heat at some temperature $T$, then at the same temperature there is a black hole solution with lower free energy and positive specific heat. As the temperature is increased from 0 to infinity, the black hole energy and entropy increase monotonically but not necessarily continuously; there can be first order phase transitions, similar to the Hawking-Page transition. These theories can also have solutions corresponding to closed universes.
We study the duality between JT gravity and the double-scaled matrix model including their respective deformations. For these deformed theories we relate the thermal partition function to the generating function of topological gravity correlators that are determined as solutions to the KdV hierarchy. We specialise to those deformations of JT gravity coupled to a gas of defects, which conforms with known results in the literature. We express the (asymptotic) thermal partition functions in a low temperature limit, in which non-perturbative corrections are suppressed and the thermal partition fun…
A large class of two-dimensional dilaton-gravity theories in asymptotically AdS$_2$ spacetimes are holographically dual to a matrix integral, interpreted as an ensemble average over Hamiltonians. Viewing these theories as Jackiw-Teitelboim gravity with a gas of defects, we extend this duality to a broader class of dilaton potentials compared to previous work by including conical defects with small deficit angles. In order to do this we show that these theories are equal to the large $p$ limit of a natural deformation of the $(2,p)$ minimal string theory.
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 $T \bar T$-deformat…
Recently, it has been found that JT gravity, which is a two-dimensional theory with bulk action $ -\frac{1}{2}\int {\mathrm d}^2x \sqrt gϕ(R+2)$, is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action $ -\frac{1}{2}\int {\mathrm d}^2x \sqrt g(ϕR+W(ϕ))$ is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if $…
In this paper we study a black hole phase transition in a generalized JT gravity noticed in arXiv:2006.03494. We investigate the effect of the phase transition on the Euclidean geodesic and holographic two-point function in models with dilaton potential which interpolates two ordinary JT gravities with different cosmological constants. It is noted that there exists a closed geodesic with a new scale at low temperature phase when the potential has a locally negative region. This scale causes several peaks in the two-point function. We also comment on the phase transition of charged black holes.…
We study the $T\bar{T}$ deformation of the chiral bosons and show the equivalence between the chiral bosons of opposite chiralities and the scalar fields at the Hamiltonian level under the deformation. We also derive the deformed Lagrangian of more generic theories which contain an arbitrary number of chiral bosons to all orders. By using these results, we derive the $T\bar{T}$ deformed boundary action of the AdS$_3$ gravity theory in the Chern-Simons formulation. We compute the deformed one-loop torus partition function, which satisfies the $T\bar{T}$ flow equation up to the one-loop order. F…
In this paper, we shed new light onto $T\bar{T}$-deformations by engineering them on 2D surface defects, supporting chiral and antichiral CFT's, in a 4D Chern-Simons bulk. This approach is motivated by various connections between $T\bar{T}$-deformations, gravity and Chern-Simons theory and suggests that the formalism developed in this paper and the gravity picture of $T\bar{T}$-deformations should be closely related.
We study the connection of Moyal deformations of self-dual gravity and self-dual Yang-Mills theory to chiral higher-spin theories, and also to deformations of operator algebras in celestial holography. The relation to Moyal deformations illuminates various aspects of the structure of chiral higher-spin theories. For instance, the appearance of the self-dual kinematic algebra in all the theories considered here leads via the double copy to vanishing tree-level scattering amplitudes. Regarding celestial holography, the Moyal deformation of self-dual gravity was recently shown to lead to the loop…
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 $T\bar{T}$-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 induc…
In this Letter we construct the noncommutative (NC) gravity model on the $θ$-constant NC space-time. We start from the NC $SO(2,3)_\star$ gauge theory and use the enveloping algebra approach and the Seiberg-Witten map to construct the effective NC gravity action. The action and the equations of motion are expanded up to second order in the deformation parameter. The equations of motion show that the noncommutativity plays a role of a source for the curvature and/or torsion. Finally, we calculate the NC corrections to the Minkowski space-time and we show that in the presence of noncommutativity…
Three-dimensional Yang-Mills theory allows for a deformation quadratic in the field strengths which can not be integrated to a local action without auxiliary fields. Yet, its covariant divergence consistently vanishes after iterating the equation, realizing a spin-1 analogue of `minimal massive gravity', which has been dubbed `third way consistent'. In this note, we show that after dualization of the three-dimensional gauge fields, the model possesses a natural action as a Chern-Simons coupled gauged sigma model. In this dual formulation, coupling to matter and to gravity becomes straightforwa…
