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

Abstract

We compute non-extremal three-point functions of scalar operators in N = 4 super Yang-Mills at tree-level in g YM and at finite N c , using the operator basis of the restricted Schur characters. We make use of the diagrammatic methods called quiver calculus to simplify the three-point functions. The results involve an invariant product of the generalized Racah-Wigner tensors (6j symbols). Assuming that the invariant product is written by the Littlewood-Richardson coefficients, we show that the non-extremal threepoint functions satisfy the large N c background independence; correspondence between the string excitations on AdS 5 × S 5 and those in the LLM geometry.

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…”

Oscillating multiple giants

“…This term comes from (∆ + ij ) 2 which roughly corresponds to Tr (ZZWŽŽW ). 9 We can also explain the powers of Nc in (3.3) from the fact that D removes fields and adds fields. 10 The author thanks an anonymous referee of JHEP for correcting mistakes in the previous version and emphasizing this point.…”

“…8 Since the -loop dilatation operator D should remove at most fields and add fields, we arrive at the ansatz of P ,m in (3.4). 9 Let us revisit the commutation relations in section 2.2. Now we impose…”

“…This correspondence continues to non-BPS operators in both of the O(N 2 c ) and O(N c ) cases. For the former case, an isomorphism between non-BPS states was conjectured between the LLM geometry and N = 4 SYM [5][6][7][8][9]. For the latter case, non-BPS states around the giant graviton are less well-understood.…”

Multi-matrix correlators and localization

“…1 The coherent states (3.7) have a more natural connection to such geometries [15]. A worthwhile exercise would be to study correlators of single trace chiral primaries in the background of heavy coherent states corresponding to both giant gravitons or bubbling geometries; see [45] for some finite N results. The holographic renomalization techniques of [46] are also applicable in these cases, but it would be interesting to develop more efficient computational techniques in supergravity along the lines of [47].…”