Holographic Ward identities for symmetry breaking in two dimensions
  We investigate symmetry breaking in two-dimensional field theories which have a holographic gravity dual. Being at large N, the Coleman theorem does not hold and Goldstone bosons are expected. We consider the minimal setup to describe a conserved current and a charged operator, and we perform holographic renormalization in order to find the correct Ward identities describing symmetry breaking. This involves some subtleties related to the different boundary conditions that a vector can have in the three-dimensional bulk. We establish which is the correct prescription that yields, after renormalization, the same Ward identities as in higher dimensions. 
Riccardo Argurio, Gaston Giribet, Andrea Marzolla, Daniel Naegels, J.   Anibal Sierra-Garcia
hep-th