Related papers: Integrable Boundaries, Conformal Boundary Conditio…
Gauged WZNW models are integrable conformal field theories. We integrate the classical \slu{} theory with periodic boundary conditions, which describes closed strings moving in a curved target-space geometry. We calculate its Poisson…
For QFTs in AdS the boundary correlation functions remain conformal even if the bulk theory has a scale. This allows one to constrain RG flows with numerical conformal bootstrap methods. We apply this idea to flows between two-dimensional…
A simplicial complex of dimension $d-1$ is said to be balanced if its graph is $d$-colorable. Juhnke-Kubitzke and Murai proved an analogue of the generalized lower bound theorem for balanced simplicial polytopes. We establish a…
An informal introduction to our recent work on the principal chiral model with boundary. We found that both classically integrable boundary conditions and quantum boundary S-matrices were classified by the symmetric spaces G/H. The…
Inspired by recent results on the effect of integrable boundary conditions on the bulk behavior of an integrable system, and in particular on the behavior of an existing defect we systematically formulate the Lax pairs in the simultaneous…
We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object. Conditions are given for the existence or nonexistence of coherent associative structures for such fusion rules,…
We propose a novel approach to study conformal field theories (CFTs) in general dimensions. In the conformal bootstrap program, one usually searches for consistent CFT data that satisfy crossing symmetry. In the new approach, we reverse the…
The possible boundary conditions consistent with the integrability of the classical sine-Gordon equation are studied. A boundary value problem on the half-line $x\leq 0$ with local boundary condition at the origin is considered. The most…
We introduce new methods to describe admissible states of the six-vertex and the eight-vertex lattice models of statistical mechanics. For the six-vertex model, we view the admissible states as differential forms on a grid graph. This…
We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion…
The standard paradigm of topological phases posits that two phases with identical symmetries are separated by a bulk phase transition, while symmetry breaking provides a path in parameter space that allows adiabatic connection between the…
We analyze 2+1 dimensional Yang-Mills theory regularized on a lattice with twisted boundary conditions in the spatial directions. In previous work it was shown that the observables in the non-zero electric flux sectors obey the so-called…
We find boundaries of Borel-Serre compactifications of locally symmetric spaces, for which any filling is incompressible. We prove this result by showing that these boundaries have small singular models and using these models to obstruct…
In this article we summarize our efforts in simulating Yang-Mills theories coupled to matter fields transforming under the fundamental and adjoint representations of the gauge group. In the context of composite Higgs scenarios, gauge…
It is shown that a simple Lie group $G$ ($ \neq {\rm SL}_2$) can be locally characterised by an integrability condition on an $\operatorname{Aut}(\mathfrak{g})$ structure on the tangent bundle, where $\operatorname{Aut}(\mathfrak{g})$ is…
Among (conformal) quantum field theories, the rational conformal field theories are singled out by the fact that their correlators can be constructed from a modular tensor category C with a distinguished object, a symmetric special…
Exploring a mapping among $n$-state spin and vertex models on the square lattice we argue that a given integrable spin model with edge weights satisfying the rapidity difference property can be formulated in the framework of an equivalent…
We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the…
Given any asymptotically flat 3-manifold $(M,g)$ with smooth, non-empty, compact boundary $\Sigma$, the conformal conjecture states that for every $\delta>0$, there exists a metric $g' = u^4 g$, with $u$ a harmonic function, such that the…
The AdS/CFT correspondence relates the expectation value of Wilson loops in N=4 SYM to the area of minimal surfaces in AdS_5 In this paper we consider minimal area surfaces in generic Euclidean AdS_{n+1} using the Pohlmeyer reduction in a…