Penrose limits and spin chains in the GJV/CS-SYM duality

Abstract

We examine Penrose limits of the duality proposed by Guarino, Jafferis and Varela between a type IIA massive background of the type of a warped, squashed $AdS_4\times S^6$, and a 2+1 dimensional IR fixed point of ${\cal N}=8$ super Yang-Mills deformed by Chern-Simons terms to ${\cal N}=2$ supersymmetry. One type of Penrose limit for closed strings corresponds to a large charge closed spin chain, and another, for open strings on giant graviton D-branes, corresponds to an open spin chain on sub-determinant operators. For the first limit, we find that like in the ABJM case, there are functions $f_a(λ)$ that interpolate between the perturbative and nonperturbative (string) regions for the magnon energy. For the second, we are unable to match the gravity result with the expected field theory result, making this model more interesting than ones with more supersymmetry.

48 pages, 1 figure; typos corrected, references added