Exciting LLM geometries

Abstract

We study excitations of LLM geometries. These geometries arise from the backreaction of a condensate of giant gravitons. Excitations of the condensed branes are open strings, which give rise to an emergent Yang-Mills theory at low energy. We study the dynamics of the planar limit of these emergent gauge theories, accumulating evidence that they are planar N = 4 super Yang-Mills. There are three observations supporting this conclusion: (i) we argue for an isomorphism between the planar Hilbert space of the original N = 4 super Yang-Mills and the planar Hilbert space of the emergent gauge theory, (ii) we argue that the OPE coefficients of the planar limit of the emergent gauge theory vanish and (iii) we argue that the planar spectrum of anomalous dimensions of the emergent gauge theory is that of planar N = 4 super Yang-Mills. Despite the fact that the planar limit of the emergent gauge theory is planar N = 4 super Yang-Mills, we explain why the emergent gauge theory is not N = 4 super Yang-Mills theory. 1 robert@neo.phys.wits.ac.za

Emergent Yang-Mills theory

“…where the second equality is true at large N in the displaced corners limit. Next, a number of studies [50][51][52][53][54][55] have established that when fields that correspond to boxes on a large Young diagram interact, they do so with an effective 't Hooft coupling obtained by replacing N g 2 YM → N eff g 2 YM , with N eff given by the factor of the box that is interacting. For boxes appearing in the ith row of r 1 we should replace…”

Three-point functions in $$ \mathcal{N} $$ = 4 SYM at finite Nc and background independence

“…We study the tree-level three-point functions in the representation basis, and check the background independence conjectured in [43]. Our proof is based on the conjectured relations for the generalized Racah-Wigner tensor in appendix C.…”

“…From (1.1) and (1.2), it is straightforward to show the large N c background independence in N = 4 SYM [43]. The background independence is a conjectured correspondence between the operators with O(N 0 c ) canonical dimensions and those with O(N 2 c ) canonical dimensions, where the latter is constructed from the former by "attaching" a large number of background boxes.…”

“…Let us review the argument on the large-N c background independence [43]. They mapped the N = 4 SYM operators with the O(N 0 c ) canonical dimensions to those with the O(N 2 c ) canonical dimensions by attaching a large number of background boxes.…”

“…However, the overlap between such states and (+ + +r) is suppressed by 1/N c . Second, the hook length of (+ + +r) factorizes as [43] hook where η B is the factor which depends only on B,…”