“Short” spinning strings and structure of quantumAdS5×S5spectrum

Abstract

Using information from the marginality conditions of vertex operators for the AdS 5 ×S 5 superstring, we determine the structure of the dependence of the energy of quantum string states on their conserved charges and the string tension ∼ √ λ. We consider states on the leading Regge trajectory in the flat space limit which carry one or two (equal) spins in AdS 5 or S 5 and an orbital momentum in S 5 , with Konishi multiplet states being particular cases. We argue that the coefficients in the energy may be found by using a semiclassical expansion. By analyzing the examples of folded spinning strings in AdS 5 and S 5 as well as three cases of circular two-spin strings we demonstrate the universality of transcendental (zeta-function) parts of few leading coefficients. We also show the consistency with target space supersymmetry with different states belonging to the same multiplet having the same non-trivial part of the energy. We suggest, in particular, that a rational coefficient (found by Basso for the folded string using Bethe Ansatz considerations and which, in general, is yet to be determined by a direct two-loop string calculation) should, in fact, be universal.

Computing three-point functions for short operators

“…Using (1.3), (1.5), (2.3), (2.4) and the AdS/CFT dictionary value g c = π 3/2 /N , we obtain 9) reproducing the result in [28].…”

“…9 The twisted vertices are annihilated by the sixteen supercharges Q A = Q A L − i Q A R and, since they have non-zero momenta, they can be written as the action of those supercharges on another vertex operator V T = {Q A , X}. It is then straightforward to see that…”

“…The next two terms in this series can also be motivated by semi-classical string theory computations [5][6][7][8][9][10], or by analyzing the algebraic curve [11,12], or by a mini-superspace approach on the string world-sheet [13]. To fully solve planar N = 4 SYM it is also necessary to know the three-point functions between local operators.…”

$$ \mathcal{N} $$ = 2 conformal gauge theories at large R-charge: the SU(N) case

“…The naive operators O(a) are not correct to reproduce flat space correlators due to conformal anomalies inducing a peculiar mixing on the sphere [23,25,26]. 8 In general, the matrix model chiral operator O has to be replaced by its normal ordered version defined in : O : [27], i.e.…”

“…1 The idea of a large charge/weak coupling compensation is closely related to the solvability of the BMN limit in AdS/CFT [4,5] and, more generally, to the coherent-state effective theory description of "semiclassical" string states [6,7] and its role in capturing the strong coupling regime [8].…”