Non-perturbative string theory from AdS/CFT

Abstract

The large N expansion of giant graviton correlators is considered. Giant gravitons are described using operators with a bare dimension of order N. In this case the usual 1/N expansion is not applicable and there are contributions to the correlator that are non-perturbative in character. By writing the (square of the) correlators in terms of the hypergeometric function 2 F 1 (a, b; c; 1), we are able to rephrase the 1/N expansion of the correlator as a semiclassical expansion for a Schrödinger equation. In this way we are able to argue that the 1/N expansion of the correlator is Borel summable and that it exhibits a parametric Stokes phenomenon as the angular momentum of the giant graviton is varied. 1 robert@neo.phys.wits.ac.za

Structure constants in $$ \mathcal{N} $$ = 4 SYM at finite coupling as worldsheet g-function

“…This provides an expression analytic in spin and makes it straightforward to take the large spin limit. As a result, we found 39) with log S ≡ log S + γ E . Importantly, the result does not contain a term proportional to (log S) 2 .…”

“…The spectrum of small deformations of determinant operators was analyzed using various approaches [6][7][8][9][10][11][12][13][14][15][16][17][18][19] including integrability [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. However, not much work has been done on correlation functions 3 except in the protected BPS sector [37][38][39] and in the free field limit, where various interesting structures were found using algebraic [40], combinatorial [41][42][43] and coherent state [44] approaches. In this paper, we first develop two new methods, one based on the large N collective fields and the other based on direct Wick contractions, to study the perturbative correlation functions of determinant operators efficiently.…”

“…It was proposed in [45], based on topological arguments in orbifold theories and free-field computations, that the determinant operators in N = 4 SYM correspond to the maximal Giant Graviton in AdS 5 ×S 5 , which is a D3-brane extended in a S 3 subspace in S 5 and particle-like in AdS. The proposal was later tested by various weak and strong coupling computations [6,7,[10][11][12][13][14][15][16][17][18][19][37][38][39].…”

“…In principle, one should be able to prove this equality by expressing Néelx| in terms of Néel0| and the action of global symmetry generators S3 and S+. However, we will not attempt it in this paper 39. Note that in the twisted translated frame, the two-point function of determinants (4.9) reads D1D2 = 2g 2 κ 2 N N !…”

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

“…Finally, we hope to find a clear understanding of the AdS/CFT correspondence of the operators with huge anomalous dimensions, including giant gravitons [56,57] and the fluctuation in the LLM geometry [43,58,59]. Some correlation functions have been studied such as three giants [60][61][62], two giants and one single-trace [63][64][65][66][67][68][69][70].…”