Integrable Field Theories with an Interacting Massless Sector

Abstract: Integrability techniques have played a major role in the study the AdS/CFT correspondence, providing an accurate description of different string theoretic observables beyond the weak or strong coupling perturbation theory. However, the case of string on certain $AdS_3$ backgrounds provided new challenges in the form of massless excitations. Difficulties in incorporating these into the integrable description have led to disagreements concerning the energy of massive physical states. In general integrable theories, massless and massive sectors can generally be treated separately. We know this cannot be the case in $AdS_3$, but a full TBA description of the interaction between the sectors is yet to be found. Surprisingly, such a description can found in a family of integrable field theories — homogeneous sine-Gordon models. Here, one can take a double scaling limit of the adjustable parameters and zoom into a regime described by a TBA where the massless sector does not decouple and contributes to the energy of massive particles at the same order as for which the Bethe ansatz would suffice in a massive theory.

HEP - theorymathematical physicsexactly solvable and integrable systems

Audience: researchers in the topic

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London Integrability Journal Club

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