MS Seminar (Mathematics - String Theory)

Speaker: David Berenstein (UC Santa Barbara)
Title: Extremal chiral ring states in AdS/CFT are described by free fermions
Date: Wed, Jul 29, 2015, 13:15 - 14:45
Place: Seminar Room A
Related File: 1450.pdf
Abstract: Half BPS states (operators) in N=4 SYM are famously described by free fermions both at weak and strong coupling. I describe a set of conjectures for a preferred class of states in more general conformal field theories that can be tested in supergravity for when such a free fermion description might arise and some motivation for it applying generally. The states in question belong to the chiral ring of a supersymmetric conformal field theory that extremize an additional U(1) charge for fixed dimension and can be reduced to multi-traces of a composite matrix field, which is equivalent to using Young tableaux (Schur polynomials) as a basis. The main conjecture asserts that if the Young tableaux are orthogonal — for which evidence is provided in various cases — then the set of extremal three point functions of traces to order 1/N are determined up to a single constant. The conjecture is extended further by providing an exact norm for the Schur basis and this norm arises from a set of free fermions for a generalized oscillator algebra.