Dressing phases ofAdS3/CFT2

Abstract

This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractWe determine the all-loop dressing phases of the AdS 3 /CFT 2 integrable system related to type IIB string theory on AdS 3 ×S 3 ×T 4 by solving the recently found crossing relations and studying their singularity structure. The two resulting phases present a novel structure with respect to the ones appearing in AdS 5 /CFT 4 and AdS 4 /CFT 3 . In the strongly-coupled regime, their leading order reduces to the universal Arutyunov-Frolov-Staudacher phase as expected. We also compute their sub-leading order and compare it with recent one-loop perturbative results, and comment on their weak-coupling expansion.

Resurgence of the dressing phase for AdS5 × S5

“…Similar results about non-perturbative sectors of the dressing phase might be expected also for the case of q-deformed theories [37]- [43] and for lower dimensional examples of AdS/CFT, like for instance for AdS 3 /CFT 2 , see e.g. [44]- [46]. Furthermore similar type of methods can be applied also to different observables within the context of AdS/CFT correspondence, for example it was realized in [47] that the hydrodynamic gradient series for the strongly coupled N = 4 super Yang-Mills plasma is only an asymptotic expansion leading to the works [48]- [50] dealing with resurgence and resummation issues in the fluid context of AdS 5 /CFT 4 .…”

Towards the All-Loop WorldsheetSMatrix forAdS3×S3×TBorsato1, Sax2, Sfondrini3 et al. 2014Phys. Rev. Lett.Self Cite8521750View full textAdd to dashboardCite

“…while on the latter one should exchange a p ↔ b p , flipping the sign of M. We then see that whole massive module is invariant under relabeling L ↔ R, resulting in a Z 2 left-right (LR) symmetry [17,19]. The two massless psuð1j1Þ 4 c:e: modules have a fermionic highest weight, and up to a change of basis they can equivalently be given by ϱ L ⊗ρ L or ϱ R ⊗ρ R [37], provided that all representation parameters satisfy a pāp ¼ b pbp , i.e., that M vanishes.…”

“…[13], the presence of flat directions in this background gives rise to massless string modes, which, at first sight, cannot be analysed using integrability methods. Classically, this was addressed only recently [16], while so far quantum integrability of the worldsheet theory was probed only for massive modes [17][18][19][20][21]; see however Ref. [22] for a description of massless modes in the weakly coupled spin chain.…”

“…This facilitates our treatment and distinguishes it from the relativistic case [23]-in particular, no ad hoc scaling limit needs to be taken. The more technical details of our analysis will be presented elsewhere [30].…”

The AdS n × S n × T 10−2n BMN string at two loops

“…For the massive sector of AdS 3 ×S 3 ×T 4 the one-loop phases were determined in [40][41][42]. There are two distinct phases, labeled with respect to the underlying symmetry groups as LL and LR (or equivalently RR and RL).…”