Large spin expansion of semiclassical 3-point correlators in AdS_5 x S^5

TL;DR

This paper computes semiclassical 3-point correlators in AdS_5 x S^5 involving heavy and light states, revealing universal structures and proposing protection of certain coefficients across coupling regimes.

Contribution

It introduces a universal resolution for ambiguities in BPS correlator computations and explores the large spin expansion of correlators with spinning string states.

Findings

Large J expansion matches perturbative gauge theory results.

Ambiguity in BPS correlator computation is resolved by a limiting procedure.

Coefficients of subleading terms are conjectured to be protected across couplings.

Abstract

3-point correlators in AdS_5xS^5 string theory in which two states are "heavy" (have large quantum numbers) and the third is "light" (here chosen as chiral primary scalar) can be computed semiclassically in terms of the "light" vertex operator evaluated on the classical string solution sourced by the two "heavy" operators. We observe that in the case when the "heavy" operators represent BPS states there is an ambiguity in the computation depending on whether the mass shell (or marginality) condition is imposed before or after integration over the world sheet. We show that this ambiguity is resolved in a universal way by defining the BPS correlator as a limit of the one with non-BPS "heavy" states. We consider several examples with "heavy" states represented by folded or circular spinning strings in AdS_5xS^5 that admit a point-like BMN-type limit when one S^5 spin J is much larger than the others. Remarkably, in all of these cases the large J expansion of the 3-point correlator has the same structure as expected in perturbative (tree-level and one-loop) dual gauge theory. We conjecture that, like the leading chiral primary correlator term, the coefficients of the first few subleading terms are also protected, i.e. should be the same at strong and weak coupling.