Quantum Corrections to Central Charges and Supersymmetric Casimir Energy in AdS₃/CFT₂

Authors: Arash Arabi Ardehali, Finn Larsen, James T. Liu, Phillip Szepietowski

Preprint number: UUITP-56/18

We study the Casimir energy of bulk fields in AdS₃ and its relation to subleading terms in the central charge of the dual CFT₂. Computing both sides of the standard CFT₂ relation E=−c/12 independently we show that this relation is not necessarily satisfied at the level of individual bulk supergravity states, but in theories with sufficient supersymmetry it is restored at the level of bulk supermultiplets. Assuming at least (0,2) supersymmetry, we improve the situation by relating quantum corrections to the central charge and the supersymmetric Casimir energy which in turn is related to an index. These relations adapt recent progress on the AdS₅/CFT₄ correspondence to AdS₃/CFT₂ holography. We test our formula successfully in several examples, including the (0,4) MSW theory describing classes of 4D black holes and the large (4,4) theory that is interesting for higher spin holography. We also make predictions for the subleading central charges in several recently proposed (2,2) dualities where the CFT₂ is not yet well-understood.