Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCorrelation functions in finite temperature CFT and black hole singularities
71
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We compute thermal 2-point correlation functions in the black brane $AdS_5$ background dual to 4d CFTs at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.
rate research
Read More
We study 2-point and 3-point functions in CFT at finite temperature for large dimension operators using holography. The 2-point function leads to a universal formula for the holographic free energy in $d$ dimensions in terms of the $c$-anomaly coefficient. By including $alpha$ corrections to the black brane background, one can reproduce the leading correction at strong coupling. In turn, 3-point functions have a very intricate structure, exhibiting a number of interesting properties. In simple cases, we find an analytic formula, which reduces to the expected expressions in different limits. When the dimensions satisfy $Delta_i= Delta_j+ Delta_k$, the thermal 3-point function satisfies a factorization property. We argue that in $d>2$ factorization is a reflection of the semiclassical regime.
We present a new exact black hole solution in three dimensional Einstein gravity coupled to a single scalar field. This is one of the extended solutions of the BTZ black hole and has in fact $textrm{AdS}_3$ geometries both at the spatial infinity and at the event horizon. An explicit derivation of Virasoro algebras for $textrm{CFT}_2$ at the two boundaries is shown to be possible `{a} la Brown and Henneauxs calculation. If we regard the scalar field as a running coupling in the dual two dimensional field theory, and its flow in the bulk as the holographic renormalization group flow, our black hole should interpolate the two $textrm{CFT}_2$ living at the infinity and at the horizon. Following the Hamilton-Jacobi analysis by de Boer, Verlinde and Verlinde, we calculate the central charges $c_{textrm{UV}}$ and $c_{textrm{IR}}$ for the $textrm{CFT}_2$ on the infinity and the horizon, respectively. We also confirm that the inequality $c_{textrm{IR}} < c_{textrm{UV}}$ is satisfied, which is consistent with the Zamolodchikovs c-theorem.
We study the behavior of black hole singularities across the Hawking-Page phase transitions, uncovering the possible connection between the physics inside and outside the horizon. We focus on the case of spacelike singularities in Einstein-scalar theory which are of the Kasner form. We find that the Kasner exponents are continuous and non-differentiable during the second order phase transitions, while discontinuous in the first order phase transitions. We give some arguments on the universality of this behavior. We also discuss possible observables in the dual field theory which encode the Kasner exponents.
The macroscopic entropy and the attractor equations for BPS black holes in four-dimensional N=2 supergravity theories follow from a variational principle for a certain `entropy function. We present this function in the presence of R^2-interactions and non-holomorphic corrections. The variational principle identifies the entropy as a Legendre transform and this motivates the definition of various partition functions corresponding to different ensembles and a hierarchy of corresponding duality invariant inverse Laplace integral representations for the microscopic degeneracies. Whenever the microscopic degeneracies are known the partition functions can be evaluated directly. This is the case for N=4 heterotic CHL black holes, where we demonstrate that the partition functions are consistent with the results obtained on the macroscopic side for black holes that have a non-vanishing classical area. In this way we confirm the presence of a measure in the duality invariant inverse Laplace integrals. Most, but not all, of these results are obtained in the context of semiclassical approximations. For black holes whose area vanishes classically, there remain discrepancies at the semiclassical level and beyond, the nature of which is not fully understood at present.
The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N=2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
