String theory in $Ad{{S}_{3}}\times {{S}^{3}}\times {{T}^{4}}$ with mixed flux: semiclassical and 1-loop phase in the S-matrix

Abstract

We present a semiclassical derivation of the tree-level and 1-loop dressing phases in the massive sector of string theory on AdS 3 × S 3 × T 4 supplemented by R-R and NS-NS 3-form fluxes. In analogy with the AdS 5 ×S 5 case, we use the dressing method to obtain scattering solutions for dyonic giant magnons which allows us to determine the semiclassical bound-state S-matrix and its 1-loop correction. We also find that the 1-loop correction to the dyonic giant magnon energy vanishes. Looking at the relation between the bound-state picture and elementary magnons in terms of the fusion procedure we deduce the elementary dressing phases. In both the semiclassical and 1-loop cases we find agreement with recent proposals from finite-gap equations and unitarity cut methods. Further, we find consistency with the finite-gap picture by determining the resolvent for the dyonic giant magnon from the semiclassical bosonic scattering data.

The AdS3× S3× S3× S1worldsheetSmatrix

“…In this paper, we construct an S matrix for the scattering of asymptotic excitations on the string worldsheet, that is compatible with the assumption of quantum integrability, in particular with factorised scattering. In this context the scattering of giant magnons in AdS 3 was originally investigated in [23,24] and more recently in [25]. In this paper we will construct the worldsheet S matrix for the AdS 3 × S 3 × S 3 × S 1 background by studying the off-shell symmetry algebra of the lightcone gauge-fixed string theory.…”

Semiclassical quantization of the mixed-flux AdS3 giant magnon

“…For the mixed-flux AdS 3 × S 3 × T 4 background the direct GS action calculation [58] shows that there is no one-loop correction, c = 0, and the same conclusion can be drawn by considering the worldsheet scattering of giant magnons [55]. Our results are in agreement with the new prescription, although it is not clear that we work in either of the regularisation schemes, as in (4.19) we have an implicit cutoff 8 on the mode numbersk in the magnon's frame.…”

“…Just like in the AdS 5 case, there are a number of semiclassical checks on these string solutions. The 1-loop worldsheet S-matrix has been determined from multi-soliton scattering states in [55] in agreement with the finite-gap calculations of [56]. The 1-loop correction to the magnon energy can also be calculated from the algebraic curve [57], or directly from the GS action [41,58].…”

SL(2, Z) invariant rotating (m, n) strings in $$AdS_3\times S^3$$ A d S 3 × S 3 with mixed flux

“…2 The theory has been shown to be integrable and for a generic value of the parameter q the corresponding tree-level S-matrix for massive BMN-type excitations has been computed. Further computations along the lines of a rotating and pulsating string have been studied, for example, in [20][21][22][23][24][25][26][27][28][29]. In view of the study of superstrings in an Ad S 3 ×S 3 background with mixed flux, it is interesting to investigate further the rotating (m, n) string in an Ad S 3 × S 3 background with mixed three form fluxes.…”