Integrable Deformation of the AdS 5 × S 5 Superstring Action

Abstract:We discuss the resummation of the strong coupling asymptotic expansion of the dressing phase of the AdS 5 × S 5 superstring. The dressing phase proposed by Beisert, Eden and Staudacher can be recovered from a modified Borel-Ecalle resummation of this asymptotic expansion only by completing it with new, non-perturbative and exponentially suppressed terms that can be organized into different sectors labelled by an instanton-like number. We compute the contribution to the dressing phase coming from the sum over all the instanton sectors and show that it satisfies the homogeneous crossing symmetry equation. We comment on the semiclassical origin of the non-perturbative terms from the world-sheet theory point of view even though their precise explanation remains still quite mysterious.

Section: Jhep01(2017)055supporting

confidence: 60%

Resurgence of the dressing phase for AdS5 × S5

Arutyunov

Dorigoni

Savin

2017

“…In this paper, we will concentrate on the standard q-deformation of the AdS 5 ×S 5 superstring constructed in [45]. A serious problem is that the metric introduced in [46] is singular.…”

Section: Introductionmentioning

confidence: 99%

“…Just after that, a standard q-deformed AdS 5 ×S 5 superstring action has been constructed with a linear R-operator of Drinfeld-Jimbo type [42][43][44] satisfying the modified classical Yang-Baxter equation [45]. Then the metric (in the string frame) and NS-NS two-form have been determined [46].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Landau-Lifshitz sigma models from q-deformed AdS5×S5 superstrings

Kameyama

Yoshida

2014

Abstract:We consider bosonic subsectors of the q-deformed AdS 5 ×S 5 superstring action and study the classical integrable structure of anisotropic Landau-Lifshitz sigma models (LLSMs) derived by taking fast-moving string limits. The subsectors are 1) deformed AdS 3 × S 1 and 2) R × deformed S 3 . The cases 1) and 2) lead to a time-like warped SL(2) LLSM and a squashed S 3 LLSM, respectively. For each of them, we construct an infinite number of non-local conserved charges and show a quantum affine algebra at the classical level. Furthermore, a pp-wave like limit is applied for the case 1). The resulting system is a null-like warped SL(2) LLSM and exhibits a couple of Yangians through non-local gauge transformations associated with Jordanian twists.

“…Two of the most well-studied deformations are associated to q deformations of the isometry algebra psu 2,2|4 . These are the η deformation [1,2] and the λ deformation [3]. The former is a deformation of the Green-Schwarz type IIB superstring [4][5][6][7] written as a sigma model on the supercoset [8,9] PSU 2,2|4 SO 1,4 × SO 5 , (…”

Section: Introductionmentioning

confidence: 99%

“…The η deformation of the AdS 5 ×S 5 superstring [1,2] generalises a certain integrable deformation of the principal chiral model [10,11] and of the symmetric space sigma model [12], often referred to as Yang-Baxter sigma models due to their explicit dependence on a nonsplit solution of the modified classical Yang-Baxter equation. The model depends on two parameters: an overall coupling h, which plays the role of the effective string tension, and the deformation parameter η.…”

Section: Introductionmentioning

confidence: 99%

Poisson-Lie duals of the η deformed symmetric space sigma model

Hoare

Seibold

2017

Poisson-Lie dualising the η deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated λ deformed model. In this paper we investigate when the η deformed model can be dualised with respect to a subgroup G 0 of G. Starting from the first-order action on the complexified group and integrating out the degrees of freedom associated to different subalgebras, we find it is possible to dualise when G 0 is associated to a subDynkin diagram. Additional U 1 factors built from the remaining Cartan generators can also be included. The resulting construction unifies both the Poisson-Lie dual with respect to G and the complete abelian dual of the η deformation in a single framework, with the integrated algebras unimodular in both cases. We speculate that extending these results to the path integral formalism may provide an explanation for why the η deformed AdS 5 × S 5 superstring is not one-loop Weyl invariant, that is the couplings do not solve the equations of type IIB supergravity, yet its complete abelian dual and the λ deformed model are.