Related papers: Fusion rules and boundary conditions in the c=0 tr…
The classification of rational conformal field theories is reconsidered from the standpoint of boundary conditions. Solving Cardy's equation expressing the consistency condition on a cylinder is equivalent to finding integer valued…
We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…
The Zariski closure of the boundary of the set of matrices of nonnegative rank at most 3 is reducible. We give a minimal generating set for the ideal of each irreducible component. In fact, this generating set is a Grobner basis with…
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…
An infinite set of operator-valued relations that hold for reducible representations of the sl(2)_k algebra is derived. These relations are analogous to those recently obtained by Zamolodchikov which involve logarithmic fields associated to…
Two different approaches to calculate the fusion rules of the c_{p,1} series of logarithmic conformal field theories are discussed. Both are based on the modular transformation properties of a basis of chiral vacuum torus amplitudes, which…
This paper resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, by discussing the foundations for a conceptual model of a dilute miscible solute undergoing…
We consider the four dimensional abelian topological BF theory with a planar boundary introduced following the Symanzik's method. We find the most general boundary conditions compatible with the fields equations broken by the boundary. The…
This is a set of notes which reviews and addresses issues in the SL(2,R) conformal field theory, while working primarily in a basis of vertex operators of definite weight under the affine algebra. Following a review of the H3 coset model…
We continue our study of Hilbert space representations of the Reflection Equation Algebra, again focusing on the algebra constructed from the $R$-matrix associated to the $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We develop a form…
We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…
Criterion for a companion matrix to have a certain number of flat portions on the boundary of its numerical range is given. The criterion is specialized to the cases of 3-by-3 and 4-by-4 matrices. In the latter case, it is proved that a…
We study the $c=-2$ model of logarithmic conformal field theory in the presence of a boundary using symplectic fermions. We find boundary states with consistent modular properties. A peculiar feature of this model is that the vacuum…
This is a continuation of arXiv:0908.4053, where, among other things, we classified irreducible representations of the triplet vertex algebra W_{2,3}. In this part we extend the classification to W_{2,p}, for all odd p>3. We also determine…
We systematically study the boundaries of one-dimensional, 2-color cellular automata depending on 4 cells, begun from simple initial conditions. We determine the exact growth rates of the boundaries that appear to be reducible. Morphic…
Finite versions of W-algebras are introduced by considering (symplectic) reductions of finite dimensional simple Lie algebras. In particular a finite analogue of $W^{(2)}_3$ is introduced and studied in detail. Its unitary and non-unitary,…
We discuss boundary conditions for conformal field theories that preserve the boundary Poincare invariance. As in the bulk field theories, a question arises whether boundary scale invariance leads to boundary conformal invariance. With…
We construct unitary, stable, and interacting conformal boundary conditions for a free massless scalar in four dimensions by coupling it to edge modes living on a boundary. The boundary theories we consider are bosonic and fermionic QED$_3$…
We initiate the mathematical study of the boundary Carrollian conformal algebra (BCCA), an infinite-dimensional Lie algebra recently discovered in the context of Carrollian physics. The BCCA is an intriguing object from both physical and…
In two-dimensional conformal field theory, we analyze conformally invariant boundary conditions which break part of the bulk symmetries. When the subalgebra that is preserved by the boundary conditions is the fixed algebra under the action…