Juan Miguel Nieto Garcia, Alessandro Torrielli (2020)Norms and scalar products for AdS3, In: Journal of Physics A: Mathematical and Theoretical53(14)145401
We compute scalar products and norms of Bethe vectors in the massless sector of AdS3 integrable superstring theories, by exploiting the general difference form of the S-matrix of massless excitations in the pure Ramond-Ramond case, and the difference form valid only in the BMN limit in the mixedflux case. We obtain determinant-like formulas for the scalar products, generalising a procedure developed in previous literature for standard R-matrices to the present non-conventional situation. We verify our expressions against explicit calculations using Bethe vectors for chains of small length, and perform some computer tests of the exact formulas as far as numerical accuracy sustains us. This should be the first step towards the derivation of integrable form-factors and correlation functions for the AdS3 S-matrix theory.
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.
We obtain the ratio of semiclassical partition functions for the extension under mixed flux of the minimal surfaces subtending a circumference and a line in Euclidean AdS3 × S3 × T4.We reduce the problem to the computation of a set of functional determinants. If the Ramond-Ramond flux does not vanish, we find that the contribution of the B-field is comprised in the conformal anomaly. In this case, we successively apply the Gel’fand-Yaglom method and the Abel-Plana formula to the flat-measure determinants. To cancel the resultant infrared divergences, we shift the regularization of the sum over half-integers depending on whether it corresponds to massive or massless fermionic modes.We show that the result is compatible with the zeta-function regularization approach. In the limit of pure Neveu-Schwarz-Neveu-Schwarz flux we argue that the computation trivializes. We extend the reasoning to other surfaces with the same behavior in this regime.