[HEG] No Shift, Sherlock: No Shift Symmetries in AdS/CFT

Who: Jose Calderon Infante (Caltech)
Title: No Shift, Sherlock: No Shift Symmetries in AdS/CFT
Abstract: The absence of global symmetries is a long-standing conjecture about theories of quantum gravity. In this talk, I will discuss how continuous global shift symmetries in AdS quantum gravity seem to be forbidden from a purely CFT perspective. First, I will discuss that a continuous global shift symmetry in AdS maps onto the presence of a marginal operator that spans a conformal manifold along which the CFT does not change at all. This raises the question of whether a local, unitary CFT can exhibit such a property. I will present progress towards an argument against this possibility. A crucial assumption on the CFT is the presence of the stress tensor, which is dual to the graviton in the bulk. To see this more clearly, I will also describe how the argument fails in the dual theory of a massless free scalar in AdS, namely the generalized free field theory of a marginal operator. Finally, I will ask whether this type of argument could lead to a bound on how much the shift symmetry must be broken, unfortunately finding a negative answer.