Embedding nonlinear sigma model into super-Yang–Mills theory

Abstract

Anomalous dimensions of high-twist Wilson operators have a nontrivial scaling behavior in the limit when their Lorentz spin grows exponentially with the twist. To describe the corresponding scaling function in planar N = 4 SYM theory, we analyze an integral equation recently proposed by Freyhult, Rej and Staudacher and argue that at strong coupling it can be casted into a form identical to the thermodynamical Bethe Ansatz equations for the nonlinear O(6) sigma model. This result is in a perfect agreement with the proposal put forward by Alday and Maldacena within the dual string description, that the scaling function should coincide with the energy density of the nonlinear O(6) sigma model embedded into AdS 5 × S 5 .

Resurgence of the cusp anomalous dimension

“…Closely related examples are the generalized scaling function, proposed in [49], and the generalized cusp anomalous dimension (or equivalently the quark-antiquark potential), studied in [50][51][52][53][54]. As studied in [33,[55][56][57], the strong coupling analysis of the generalized scaling function is almost in parallel with the cusp anomalous dimension, and thus it is a good exercise to see its resurgent aspect along the line in this paper. The analysis of the generalized cusp anomalous dimension will be much more involved.…”

“…This was first discussed by Alday and Maldacena in the dual string consideration [36]. Then in [33][34][35], the relation was embedded into N = 4 SYM. In particular, in [35], the mass gap m O(6) is exactly related to the solution to the BES equation by 28) JHEP09 (2015)138 where f 1 (t) is the same function appearing in the BES solution.…”

“…To resolve the Borel resummation problem, we need non-perturbative corrections. In a series of works [22,[33][34][35], it turned out that the cusp anomalous dimension should receives the following non-perturbative corrections 5) where Γ (0) cusp (g) is the perturbative contribution above and Λ 2 is a non-perturbative scale, related to the 't Hooft coupling as follows Λ 2 = σ Γ( 3 4 ) Γ( 5 4 ) (2πg) 1/2 e −2πg .…”

The generalised scaling function: A note

“…Note added: An interesting paper [16] appears today in the web archives. It seems to have some goals and equations similar to ours, although coming more directly from the approach [12], and giving the leading strong coupling behaviour of f 3 (g) in agreement with us and confirming f 2 (g) = 0 as in [12], and f 1 (g) as in [14].…”

Quantum dispersion relations for the Ad S 4 × ℂ ℙ 3 $$ Ad{S}_4\times \mathrm{\mathbb{C}}{\mathrm{\mathbb{P}}}^3 $$ GKP string

“…Indeed, the Bethe equations analysis reveals that the model has a gap and such modes acquire an exponentially small mass, non-perturbatively. This parallels what occurs to the scalars of the O(6) sigma model emerging in AdS 5 × S 5 in the Alday-Maldacena limit [12,57]. Apart from that, there is no direct identification between the dispersion relations of massless fields of the superstring description and the non-perturbative modes of integrability.…”