Abstract
c. We compute Virasoro blocks in the heavy-light, large c limit, extending our previous results by determining perturbative 1=c corrections. We obtain explicit closed-form expressions for both the ‘semi-classical’ h 2 =c 2 and ‘quantum’ hL=c 2 corrections to the vacuum block, and we provide integral formulas for general Virasoro blocks. We comment on the interpretation of our results for thermodynamics, discussing how monodromies in Euclidean time can arise from AdS calculations using ‘geodesic Witten diagrams’. We expect that only non-perturbative corrections in 1=c can resolve the singularities associated with the information paradox.
Highlights
Conformal block, computed at large central charge c in the limit hH ∝ c hL
We comment on the interpretation of our results for thermodynamics, discussing how monodromies in Euclidean time can arise from AdS calculations using ‘geodesic Witten diagrams’
In the remainder of this introduction we will discuss how our discussion relates to the black hole information paradox, and we provide a summary of the results
Summary
The black hole information paradox has many guises. In its most visceral and pressing form, it requires understanding the correct description of physics near black hole horizons, and in particular, the question of whether the semi-classical description can survive as a good approximation while simultaneously allowing for unitary evolution [15,16,17,18]. For a CFT living on a compact space with finite central charge and at a finite temperature, correlators cannot decay exponentially for all times, as this would signal loss of information concerning a perturbation to the thermal density matrix We add another layer to the story by studying the correlators of light operators in the background of a heavy pure state. We expect that unitarity can only be restored by nonperturbative effects in 1/c, and in particular that perturbative 1/c corrections should not violate the thermal periodicity tE → tE + β of the large c heavy-light correlators These expectations are primarily based on the expectation that 1/c corrections correspond to loop effects around the infinite c gravity saddle, which is an AdS black hole background with fixed Euclidean-time periodicity, and such corrections should at most produce perturbative corrections to β. The case of both global and Virasoro blocks can be given a parallel treatment, which suggests that the Euclidean-time monodromies of the 1/c corrections are likely to disappear in the full correlators
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