Davide Fioravanti

TBA and Y-system for planar

Abstract We conjecture the set of asymptotic Bethe Ansatz equations for the mirror model of the AdS 4 × CP 3 string theory, corresponding to the planar N = 6 superconformal Chern–Simons gauge theory in three dimensions. Hence, we derive the (vacuum energy) thermodynamic Bethe Ansatz equations and the Y-system describing the direct AdS 4 / CFT 3 string theory.

Large spin corrections in

Abstract Anomalous dimension and higher conserved charges in the sl ( 2 ) sector of N = 4 SYM for generic spin s and twist L are described by using a novel kind of non-linear integral equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-linear (finite range) integral terms, appearing in the NLIE and in the dimension formula, go to zero as s → ∞ . Therefore they can be neglected at least up to the O ( s 0 ) order, thus implying a linear integral equation (LIE) and a linear dimension/charge formula respectively, likewise the ‘thermodynamic’ (i.e. infinite spin) case. Importantly, these non-linear terms go faster than any inverse logarithm power ( ln s ) − n , n > 0 , thus extending the linearity validity.

{\cal N}=4

A generalization of the Yang–Baxter algebra is found in quantizing the monodromy matrix of two (m)KdV equations discretized on a space lattice. This braided Yang–Baxter equation still ensures that the transfer matrix generates operators in involution which form the Cartan sub-algebra of the braided quantum group. Representations diagonalizing these operators are described through relying on an easy generalization of algebraic Bethe ansatz techniques. The conjecture that this monodromy matrix algebra leads, in the cylinder continuum limit, to a perturbed minimal conformal field theory description is analysed and supported.

SYM sl(2): still a linear integral equation

With the aim of exploring a massive family of models, the nonlinear integral equation for a quantum system consisting of left and right KdV equations coupled on the cylinder is derived from an integrable lattice field theory. The eigenvalues of the energy and of the transfer matrix (and of all the other local integrals of motion) are expressed in terms of the corresponding solutions of the nonlinear integral equation. The family of models turns out to correspond to the Φ(1,3) perturbation of Conformal Field Theories. The analytic and asymptotic behaviours of the transfer matrix are studied and given.

A braided Yang–Baxter algebra in a theory of two coupled lattice quantum KdV: algebraic properties and ABA representations

Quantum monodromy matrices coming from a theory of two coupled (m)KdV equations are modified in order to satisfy the usual Yang–Baxter relation. As a consequence, a general connection between braided and unbraided (usual) Yang–Baxter algebras is derived and also analysed.

Exact conserved quantities on the cylinder II: off-critical case

Recently, it was shown that the spectrum of anomalous dimensions and other important observables in N = 4 SYM are encoded into a simple nonlinear Riemann-Hilbert problem: the P\mu-system or Quantum Spectral Curve. In this letter we present the P\mu-system for the spectrum of the ABJM theory. This may be an important step towards the exact determination of the interpolating function h(\lambda) characterising the integrability of the ABJM model. We also discuss a surprising symmetry between the P\mu-system equations for N = 4 SYM and ABJM.

From the braided to the usual Yang-Baxter relation

Abstract We present a construction of a Virasoro symmetry of the sine-Gordon (SG) theory. It is a dynamical one and has nothing to do with the space–time Virasoro symmetry of 2D CFT. Although it is clear how it can be realized directly in the SG field theory, we are rather concerned here with the corresponding N -soliton solutions. We present explicit expressions for their infinitesimal transformations and show that they are local in this case. Some preliminary stages about the quantization of the classical results presented in this paper are also given.

The Quantum Spectral Curve of the ABJM theory

We propose an alternative description of the spectrum of local fields in the classical limit of the integrable quantum field theories. It is close to similar constructions used in the geometrical treatment of W-gravities. Our approach provides a systematic way of deriving the null-vectors that appear in this construction. We present explicit results for the case of the A_1^{1}-(m)KdV and the A_2^{2}-(m)KdV hierarchies, different classical limits of 2D CFTs. In the former case our results coincide with the classical limit of the construction of Babelon, Bernard and Smirnov.Some hints about quantization and off-critical treatment are also given.Abstract We propose an alternative description of the spectrum of local fields in the classical limit of the integrable quantum field theories. It is close to similar constructions used in the geometrical treatment of W -gravities [17] . Our approach provides a systematic way of deriving the null-vectors that appear in this construction. We present explicit results for the case of the A1(1)-(m)KdV and the A2(2)-(m)KdV hierarchies, different classical limits of 2D CFTs. In the former case our results coincide with the classical limit of the construction [3] . Some hints about quantization and off-critical treatment are also given.

Hidden Virasoro Symmetry of (Soliton Solutions of) the Sine Gordon Theory

Abstract The knowledge of non usual and sometimes hidden symmetries of (classical) integrable systems provides a very powerful setting-out of solutions of these models. Primarily, the understanding and possibly the quantisation of intriguing symmetries could give rise to deeper insight into the nature of field spectrum and correlation functions in quantum integrable models. With this perspective in mind we will propose a general framework for discovery and investigation of local, quasi-local and non-local symmetries in classical integrable systems. We will pay particular attention to the structure of symmetry algebra and to the role of conserved quantities. We will also stress a nice unifying point of view about KdV hierarchies and Toda field theories with the result of obtaining a Virasoro algebra as exact symmetry of sine-Gordon model.

ON THE NULL-VECTORS IN THE SPECTRA OF THE 2D INTEGRABLE HIERARCHIES

This review is devoted to collecting some results on the high spin expansion of (minimal) anomalous dimension. Thanks to the recent rationale on integrability, planar 𝒩=4 super Yang-Mills theory (or its AdS5×S5 string counterpart) represents a very practicable field. Here the attention will be restricted to its sector of twist operators, although the analysis tools are quite general (in integrable theories). Some structures and ideas turn out to be general also for other sectors or gauge theories.