Abstract
We determine the bosonic part of the superstring sigma model Lagrangian on η-deformed AdS5 × S5, and use it to compute the perturbative world-sheet scattering matrix of bosonic particles of the model. We then compare it with the large string tension limit of the q-deformed S-matrix and find exact agreement.
Highlights
Giving a string theory on a TsT-transformed background [4, 5]
The deformation parameter q can be an arbitrary complex number, but in physical applications is typically taken to be either real or a root of unity. Since these quantum group deformations modify the dispersion relation and the scattering matrix, to solve the corresponding model by means of the mirror Thermodynamic Bethe Ansatz (TBA), for a recent review see [10], one has to go through the entire procedure of first deriving the TBA equations for the ground state and extending them to include excited states
The aim of the present work is to compute the 2 → 2 scattering matrix for the ηdeformed model in the limit of large string tension g and to compare the corresponding result with the known q-deformed S-matrix found from quantum group symmetries, unitarity and crossing [6, 8]
Summary
To fix the light-cone gauge and compute the scattering matrix, it is advantageous to use the Hamiltonian formalism. The solution for the Hamiltonian is still given by eq (2.16) of the review [24], with the only difference that the components of the metric are deformed and that Hx has the B-field contribution. Where the shorthand notation pyy ≡ pyiyi, pzz ≡ pzizi was used After this is done the quartic Hamiltonian is (1 + κ2) (z2z 2 − y2y 2) + 2. To render invariance under su(2) subalgebras manifest, one can introduce two-index notation for the world-sheet fields. In terms of two-index fields the quartic Hamiltonian becomes H4 = H4G + H4W Z, where H4G is the contribution coming from the spacetime metric and H4W Z from the B-field. Note that we have used the Virasoro constraint C1 in order to express x− in terms of the two index fields.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
