Keywords: Quantum Field Theory Yang-Mills theory Bethe Ansatz Conformal Field Theory Integrability

**non-perturbative Quantum Field Theory**, with particular emphasys on the integrable and conformal methods. . In the years, I have contributed to the follwing fields:

- Conformal Field Theory

- Integrable Models: Quantum inverse scattering, Algebraic and
Thermodynamic Bethe ansatz, finite size effects and NLIE
(non-linear integral equations)

- Lattice Field Theories (1982-86)

**Present interests**(2007-11)

**Finite size effects in integrable field theories**- The exact approach to finite volume effects in 2D quantum field theories through NLIE's deducible from Bethe Ansatz has revealed to be one of the most effective ways to investigate the structure of energy levels.**Integrability in gauge-string duality**- The dilation operators in Yang-Mills theories, linked by gauge/string (AdS/CFT) duality to energy levels of semicalssical strings propagating on AdS curved spaces, can be remapped into integrable Hamiltonians of spin chains. New opportunities of shading light on AdS/CFT correspondence emerge from this observation.

**Entanglemet Entropy in conformal and integrable theories**- This fascinating and subtly conceptual subject finds applications in many areas ranging from information theory to condensed matter physics, to the physics of evaporation of black holes.

**Finite size and boundary effects in integrable theories**- These effects find applications ranging from the theory of strongly correlated electrons in condensed matter physics to the world-sheet dynamics of strings propagating on curved spaces. They are governed by non-linear integral equations (NLIE). Here we illustrate the main results obtained and the ongoing projects on this topic:*sine-Gordon - sinh-Gordon through analytic continuation*- the goal of this ongoing project is the reconstruction of the scaling functions governing the finite size effects in the sinh-Gordon integrable model as analytic continuation of a subset of those present in the sine-Gordon model. The delicate mechanisms leading to the disappearance of some states (solitons and higher bound states) allow to foresee the roadmap towards extension of these results to models of great physical relevance, like e.g. sigma models on non-compact spaces, crucial in the understanding of the AdS/CFT correspondence.*NLIE for integrable deformations of sigma-models*- at the quantum level, many integrable sigma models allow for some deformations of the parameter of the target space in such a way to stay integrable. The prototypical example is the so called sausage model, a deformation of the O(3) sigma-model. The goal is to deepen the integrability of such class of models though the NLIE (non-linear integral equation) approach.**Entanglement Entropy (EE) in conformal and integrable systems**- This subject, that has undergone a dramatic increase of interest after the appearance of a fundamental paper by Cardy and Calabrese, presents delicate questions on finite size and boundary effects, as well as stimulating applications to black hole physics.*Exact entanglement entropy of the XYZ model and its sine-Gordon limit*- The exact expression for the Von Neumann entropy for an infinite bipartition of the XYZ spin ½ model has been obtained, by connecting its reduced density matrix to the corner transfer matrix of the eight vertex model. Then, the anisotropic scaling limit of the XYZ chain has been considered, yielding the 1+1 dimensional sine-Gordon model. The formula for the entanglement entropy of the latter has the structure of a dominant logarithmic term plus a constant, in agreement with what is generally expected for a massive quantum field theory. [1]*Essential singular behaviour in entanglement entropy of the XYZ spin chian*[2] - The Renyi entropy of the one-dimensional XYZ spin-1/2 chain in the entirety of its phase diagram is explored. The model has several quantum critical lines corresponding to rotated XXZ chains in their paramagnetic phase, and four tri-critical points where these phases join. Two of these points are described by a conformal field theory and close to them the entropy scales as the logarithm of its mass gap. The other two points are not conformal and the entropy has a peculiar singular behavior in their neighbors, characteristic of an essential singularity. At these non-conformal points the model undergoes a discontinuous transition, with a level crossing in the ground state and a quadratic excitation spectrum. The entanglement entropy is proposed as an efficient tool to determine the discontinuous or continuous nature of a phase transition also in more complicated models.*Correlation Length and Unusual Corrections to the Entanglement Entropy*[3] - We study analytically the corrections to the leading terms in the Renyi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise to different contributions (with different exponents) and thus violate a simple scaling argument. In the specific, we look at the entanglement entropy of a bipartite XYZ spin-1/2 chain in its ground state. When the system is divided into two semi-infinite half-chains, we have an analytical expression of the Renyi entropy as a function of a single mass parameter. In the scaling limit, we show that the entropy as a function of the correlation length formally coincides with that of a bulk Ising model. This should be compared with the fact that, at criticality, the model is described by a c=1 Conformal Field Theory and the corrections to the entropy due to finite size effects show exponents depending on the compactification radius of the theory. We will argue that there is no contradiction between these statements. If the lattice spacing is retained finite, the relation between the mass parameter and the correlation length generates new subleading terms in the entropy, whose form is path-dependent in phase-space and whose interpretation within a field theory is not available yet. These contributions arise as a consequence of the existence of stable bound states and are thus a distinctive feature of truly interacting theories, such as the XYZ chain.