Wrapping interactions and the genus expansion of the 2-point function of composite operators

Abstract

We perform a systematic analysis of wrapping interactions for a general class of theories with color degrees of freedom, including N=4 SYM. Wrapping interactions arise in the genus expansion of the 2-point function of composite operators as finite size effects that start to appear at a certain order in the coupling constant at which the range of the interaction is equal to the length of the operators. We analyze in detail the relevant genus expansions, and introduce a strategy to single out the wrapping contributions, based on adding spectator fields. We use a toy model to demonstrate our procedure, performing all computations explicitly. Although completely general, our treatment should be particularly useful for applications to the recent problem of wrapping contributions in some checks of the AdS/CFT correspondence

Four-loop perturbative Konishi from strings and finite size effects for multiparticle states

“…They scatter diagonally on each other and are described by holes in the NLIE [47,48]. By expanding the NLIE equation in a similar manner we did for the sinh-Gordon TBA system we were able to confirm our formulas (30,31) for this special case. Moreover, by analyzing more complicated states we have gained some hints to the generalization for non-diagonal scatterings.…”

RG stability of integrable fishnet models

“…The results are potentially useful from the integrability viewpoint. As we explain in section 4.3, our re-summation procedure has a natural interpretation from the perspective of [10], but computes quantities that involve nontrivial finite size corrections in the planar limit [21]. where C denotes the Catalan constant, in which both real branches simultaneously exist.…”

“…From the spin chain perspective, nevertheless, the amplitudes computed correspond to operators with wrapping effects [21] of arbitrarily high order. Consequently, despite they are the simplest nontrivial operators one can compute in the theory, the authors expect that the results of this section can serve as a guiding principle when extending compact spin integrability results beyond the reach of Asymptotic Bethe Ansatz.…”

Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT

“…The understanding of the conjectured integrability has steadily advanced towards the inclusion of finite-size effects (wrapping effects) [99][100][101][102]. This ambitious program included the development of an infinite set of coupled integral equations called Thermodynamic Bethe ansatz (TBA) [100,[103][104][105][106][107][108] (also in [109,110]) which are solvable in some cases for scattering amplitudes [111] and cusped Wilson lines [112][113][114].…”