Geometric Formulation of Generalized Root-TT[over ¯] Deformations.

We develop a generic geometric formalism that incorporates both TT[over ¯]-like and root-TT[over ¯]-like deformations in arbitrary dimensions. This framework applies to a wide family of stress-energy tensor perturbations and encompasses various well-known field theories. Building upon the recently proposed correspondence between Ricci-based gravity and TT[over ¯]-like deformations, we further extend this duality to include root-TT[over ¯]-like perturbations.

Quantum spectral curve of the N=6 supersymmetric Chern-Simons theory.

Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N=6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model.

The Bethe ansatz and the Tzitzéica-Bullough-Dodd equation.

The theory of classically integrable nonlinear wave equations and the Bethe ansatz systems describing massive quantum field theories defined on an infinite cylinder are related by an important mathematical correspondence that still lacks a satisfactory physical interpretation. In this paper, we shall extend this link to the case of the classical and quantum versions of the Tzitzéica-Bullough-Dodd model.