AdS2/CFT1 AT FINITE DENSITY AND HOLOGRAPHIC ASPECTS OF 2D BLACK HOLES

Abstract

In the present thesis, we study various models of 2D dilaton gravity known as JT gravity coupled with non-trivial gauge interactions. In particular, we investigate the effects of the non-trivial gauge couplings on the thermal properties of black holes and wormholes in two dimensions and compute various physical observables like entropy, free energy, etc. Further, we examine the possibilities of the Hawking-Page transition and wormhole to black hole phase transition in two dimensions. In addition, we also study the transformation properties of boundary stress-energy tensor under the diffeomorphism and U(1) gauge transformation and hence compute the central charge associated with the 1D boundary theory. To begin with, we first construct the model of JT gravity coupled with Abelian (U(1)) and SU(2) Yang-Mills (YM) fields using the compactification of 5D gravitational theory. We obtain the vacuum and black hole solutions associated with the 2D model perturbatively, treating the gauge couplings as the expansion parameters. We find that the interpolating vacuum solution asymptotes to AdS2 in the IR and Lifshitz2 in the UV, which we identify as the thermal radiation background for our analysis. On the other hand, the charged 2D black hole solution asymptotes to Lifshitz2 geometry. Our analysis on thermal stability reveals the existence of a first order phase transition at T ∼ T0 such that for T < T0 the thermal radiation dominates. On the other hand, as we increase the temperature of the system T ∼ T2(> T0), a globally stable black hole emerges, which clearly indicates the onset of the Hawking-Page (HP) transition in 2D gravity models. Next, we construct a model of JT gravity that uncovers the phase transition between the Euclidean wormhole and the black hole phase at finite charge density and/or chemical potential. In the low temperature regime, the charged wormhole solution dominates the system, while, on the other hand, as we increase the temperature, the wormhole phase undergoes a first order phase transition into a pair of black holes at finite chemical potential. Moreover, the Free energy (density) and ii the total charge of the system suffer a discontinuous change at the critical point (T = T0). We finally conjectured that the boundary theory dual to the aforementioned model of JT gravity could be a two-site (uncoupled) complex SYK model with finite chemical potential. In the third example, we propose a diffeomorphism invariant action of the JT gravity coupled with U(1) gauge fields that contain all the possible 2-derivative as well as 4-derivative interactions. We compute the vacuum and black hole solutions of 2D gravity in the perturbative regime, where we consider the couplings associated with the higher derivative interactions as the expansion parameters. We find that the vacuum solution in the UV limit is dominated by the Lifshitz2 geometry with dynamical exponent (z = 7 3 ). On the other hand, the Ricci scalar blows up in the deep IR limit due to the presence of higher derivative interactions in the theory. We compute the holographic stress-energy tensor and obtain the central charge associated with the 1D boundary theory. Our analysis reveals that the central charge depends on the negative power of the coupling associated with the 4-derivative interactions. We further explore the thermal properties of 2D black holes in the presence of quartic interactions. To be specific, we compute the Wald entropy associated with the 2D black holes and interpret its near-horizon divergence in terms of the density of states. Then, we investigate the properties of the 2D black hole in the near-horizon limit and calculate the associated central charge. We find that the near-horizon CFT may be recast as a 2D Liouville theory with higher derivative corrections using suitable coordinate transformations. We study the vacuum structure and invariant properties of the generalized Liouville theory and obtain the Weyl anomaly associated with it. In the final example, we construct a model of 2D dilaton gravity by compactifying the four dimensional Einstein gravity coupled with the ModMax Lagrangian. We perform the perturbative analysis to find out the vacuum solutions of the theiii ory, which reduce to AdS2 in the absence of ModMax interactions. We further compute the holographic central charge associated with the 1D boundary theory up to quadratic order in the gauge couplings. We finally obtain the ModMax corrected 2D black hole solutions and explore their extremal limits.