High Energy Theory Seminar

The paradigmatic example of $AdS_4/CFT_3$ relates M-theory on $AdS_4 x S^7$ to the family of maximally supersymmetric 3d CFTs discovered by Aharony, Bergman, Jafferis, and Maldacena (ABJM). I will focus on the stress tensor four point function for these dual theories. On the CFT side, I will show that all maximally supersymmetric 3d CFTs contain a 1d topological sector that includes only 1/2 and 1/4 BPS operators. I will then use matrix model techniques and the ABJM Lagrangian to compute the OPE coefficients of these BPS operators to all orders in 1/N, where N is the rank of the gauge group. On the $AdS_4$ side, I will use Mellin space and the superconformal Ward identity to express the contribution to the four point function from all higher derivative corrections to $AdS_4$ supergravity, in terms of a set of unknown constants. The leading correction is given by the $R^4$ term in the 11d effective action for M-theory. Using the known coefficient for this term, I will fix the corresponding $AdS_4$ expression, extract the 1/2 and 1/4 BPS OPE coefficients, and compare to the ABJM prediction, finding perfect agreement. This is the first check of $AdS_4/CFT_3$ that goes beyond 11d supergravity.