Related papers: Integrable Boundaries and Universal TBA Functional…

Finite temperature correlation functions in integrable quantum field theories are formulated only in terms of the usual, temperature-independent form factors, and certain thermodynamic filling fractions which are determined from the…

We consider Abelian topological quantum field theories (TQFTs) in 3d and show that gaugings of invertible global symmetries naturally give rise to additive codes. These codes emerge as nonanomalous subgroups of the 1-form symmetry group,…

Based on properties of the universal R-matrix, we derive universal Baxter TQ-relations for quantum integrable systems with (diagonal) open boundaries associated with $U_{q}(\widehat{sl_{2}})$. The Baxter TQ-relations for the open XXZ-spin…

We show how a lattice approach can be used to derive Thermodynamic Bethe Ansatz (TBA) equations describing all excitations for boundary flows. The method is illustrated for a prototypical flow of the tricritical Ising model by considering…

The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…

For an arbitrary semisimple Frobenius manifold we construct Hodge integrable hierarchy of Hamiltonian partial differential equations. In the particular case of quantum cohomology the tau-function of a solution to the hierarchy generates the…

We present a method of removing all infinite sums from the various forms of the mirror TBA equations and the energy formula of the AdS/CFT spectral problem. This new formulation of the TBA system is quasi-local because Y-functions that are…

We provide a framework for generic 4D conformal bootstrap computations. It is based on the unification of two independent approaches, the covariant (embedding) formalism and the non-covariant (conformal frame) formalism. We construct their…

We consider a discrete classical integrable model on the 3-dimensional cubic lattice. The solutions of this model can be used to parameterize the Boltzmann weights of the different 3-dimensional spin models. We have found the general…

We consider certain examples of applications of the general methods, based on geometry and integrability of matrix models, described in hep-th/0601212. In particular, the nonlinear differential equations, satisfied by quasiclassical…

Integrable defects in two-dimensional integrable models are purely transmitting thus topological. By fusing them to integrable boundaries new integrable boundary conditions can be generated, and, from the comparison of the two solved…

Many two-dimensional conformal field theories have an alternative integrable scattering description, which reproduces their spectrum of conformal weights. Taking as an example the case of the Lee-Yang nonunitary CFT and the 3-state Potts…

A universal differential equation is a nontrivial differential equation the solutions of which approximate to arbitrary accuracy any continuous function on any interval of the real line. On the other hand, there has been much interest in…

We construct (2+1)-dimensional lattice systems, which we call fusion surface models. These models have finite non-invertible symmetries described by general fusion 2-categories. Our method can be applied to build microscopic models with,…

We develop a new method for obtaining branching rules for affine Kac-Moody Lie algebras at negative integer levels. This method uses fusion rules for vertex operator algebras of affine type. We prove that an infinite family of ordinary…

We derive general bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. In any CFT containing a scalar primary phi of dimension d we show that crossing symmetry of <phi…

Topological defect lines (TDLs) in two-dimensional conformal field theories (CFTs) are standard examples of generalized symmetries in quantum field theory. Integrable lattice incarnations of these TDLs, such as those provided by…

Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…

We study the algebras underlying solvable lattice models of the type fusion interaction round the face (IRF). We propose that the algebras are universal, depending only on the number of blocks, which is the degree of polynomial equation…

We propose the notion of integrable boundary in the context of discrete integrable systems on quad-graphs. The equation characterizing the boundary must satisfy a compatibility equation with the one characterizing the bulk that we called…