Boost generator in AdS 3 integrable superstrings for general braiding
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Springer
Received: April 15, Revised: July 2, Accepted: July 6, Published: July 30,
2020 2020 2020 2020
Juan Miguel Nieto Garc´ıa, Alessandro Torrielli and Leander Wyss Department of Mathematics, University of Surrey, Guildford, GU2 7XH, U.K.
E-mail: [email protected], [email protected], [email protected] Abstract: In this paper we find a host of boost operators for a very general choice of coproducts in AdS3 -inspired scattering theories, focusing on the massless sector, with and without an added trigonometric deformation. We find that the boost coproducts are exact symmetries of the R-matrices we construct, besides fulfilling the relations of modified Poincar´e-type superalgebras. In the process, we discover an ambiguity in determining the boost coproduct which allows us to derive differential constraints on our R-matrices. In one particular case of the trigonometric deformation, we find a non-coassociative structure which satisfies the axioms of a quasi-Hopf algebra. Keywords: AdS-CFT Correspondence, Integrable Field Theories, Quantum Groups ArXiv ePrint: 2004.02531
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)223
JHEP07(2020)223
Boost generator in AdS3 integrable superstrings for general braiding
Contents 1 Introduction
1
2 Modified Poincar´ e algebra in AdS3 /CFT2
2 5 7 11
4 q-deformed algebra and η-deformation 4.1 Unbraided energy case 4.2 Braided energy case 4.3 Quasi-Hopf algebra and the coassociator
14 15 16 17
5 Conclusions
20
A R-matrix and difference form A.1 Undeformed bosonically braided A.2 Undeformed bosonically unbraided
22 23 24
B Action of the boost generator in the Uq [sl(1|1)] algebra
24
1
Introduction
The existence of integrable structures within the context of the AdS/CFT correspondence [1, 2] has allowed us to use a powerful set of techniques that probe both sides of the correspondence beyond perturbation theory. Integrability is made manifest after we map the spectral problem into that of an effective two-dimensional system which is solvable by Bethe ansatz. The associated asymptotic scattering problem, obtained by considering the system in infinite volume, can be studied in the context of Hopf superalgebras, and the problem is reduced to the construction of irreducible representations. However, the one we encounter in this context is very unconventional and is not entirely understood [3–10]. The AdS3 /CFT2 version of the correspondence has been the focus of some attention in the recent years. This encompasses both the cases of superstrings living on AdS3 × S 3 × S 3 × S 1 and AdS3 × S 3 × T 4 backgrounds. The classical integrability of the string sigma-models associated to these backgrounds was shown in [11, 12] (see also [13, 14]). This has allowed the application of most of the integrability toolbox developed for AdS5 /CFT4 for the infinite volume case, while notably the full (massive + massless) Thermodynamic Bethe Ansatz and the Quantum Spectral Curve analysis still need to be developed. Some exampl
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