Related papers: Fusion rules for the continuum sectors of the Vira…
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…
We revisit the study of singular points in N=2 SQCD with classical gauge groups. Using a technique proposed recently by Gaiotto, Seiberg and Tachikawa we find that the low-energy physics at the maximally singular point involves two…
We identify the algebra of matrix elements of big projective modules in category O with the regular functions on the big Bruhat cell of G. Analogous extensions of the regular representations of the affine Lie and Virasoro algebras yield…
We use ideas of generalized self-duality conditions to construct real scalar field theories in (1 + 1)-dimensions with exact self dual sectors. The approach is based on a pre-potential U that defines the topological charge and the potential…
Using the recently developed notion of a fractional Virasoro algebra, we explore the implied operator product expansions in nonlocal conformal field theories and their geometric meaning. We probe the interplay between classical nonlocality…
The boundary conditions on multiply connected extra dimensions play major rolls in gauge-Higgs unification theory. Different boundary conditions, having been given in ad hoc manner so far, lead to different theories. To solve this…
SU(2)xU(1) electroweak gauge model without Higgs sector is extended by a new vector field C interacting with leptons and quarks of both chiralities. This interaction is treated under a dynamical assumption in a self-consistent…
The phase structure of the finite SU(2)xSU(2) theory with N=2 supersymmetry, broken to N=1 by mass terms for the adjoint-valued chiral multiplets, is determined exactly by compactifying the theory on a circle of finite radius. The exact…
We continue the study of null-vector equations in relation with partition functions of (systems of) Schramm-Loewner Evolutions (SLEs) by considering the question of fusion. Starting from $n$ commuting SLEs seeded at distinct points, the…
The generalization of squeezing is realized in terms of the Virasoro algebra. The higher-order squeezing can be introduced through the higher-order time-dependent potential, in which the standard squeezing operator is generalized to…
In the first part of my talk I will explain a solution to the extension of Lie's problem on classification of "local continuous transformation groups of a finite-dimensional manifold" to the case of supermanifolds. (More precisely, the…
We construct boundary states in a particular c=1 conformal field theory, the SU(2)_1/G orbifold with G a binary finite subgroup of SU(2). These states preserve the conformal symmetry, at least, but break rational symmetries of the SU(2)_1/G…
We develop a calculus of variations for functionals on certain spaces of conformal maps. Such a space \Omega\ is composed of all maps that are conformal on domains containing a fix compact annular set of the Riemann sphere, and that are…
We define a 3-point Virasoro algebra, and construct a representation of it on a previously defined Fock space for the 3-point affine algebra $\mathfrak{sl}(2, \mathcal R) \oplus\left( \Omega_{\mathcal R}/d{\mathcal R}\right)$.
We study a bosonic string with one end free and the other confined to a D-brane. Only the odd oscillator modes are allowed, which leads to a Virasoro algebra of even Virasoro modes only. The theory is quantized in a gauge where world-sheet…
We investigate the properties of hadronic matter and nuclei be means of a generalized $SU(3)\times SU(3)$ $\sigma$ model with broken scale invariance. In mean-field approximation, vector and scalar interactions yield a saturating nuclear…
The supersymmetric grand unified theory where the SU(5) gauge symmetry is broken by the Hosotani mechanism predicts the existence of adjoint chiral superfields whose masses are at the supersymmetry breaking scale. The Higgs sector is…
The initial classification of fusion rules have shown that rational conformal field theory is very limited. In this paper we study the fusion rules of extend ed current algebras. Explicit formulas are given for the S matrix and the fusion…
This is the continuation of our study of the Levin-Wen model based on an arbitrary unitary fusion category $\mathcal{C}$ on the infinite plane. The ground state of the Levin-Wen model hosts anyonic excitations whose fusion and braiding…
Ground state of weakly bound dimers and trimers with a radius extending well into the classically forbidden region is explored, with the goal to test the predicted universality of quantum halo states. The focus of the study are molecules…