Related papers: Fusion Rules in N=1 Superconformal Minimal Models
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…
The W-infinity minimal models are conformal field theories which can describe the edge excitations of the hierarchical plateaus in the quantum Hall effect. In this paper, these models are described in very explicit terms by using a bosonic…
The holomorphic Coulomb gas formalism is a set of rules for computing minimal model observables using free field techniques. We attempt to derive and clarify these rules using standard techniques of QFT. We begin with a careful examination…
We propose bulk 3D N=4 rank-0 superconformal field theories, which are related to 2D N=1 supersymmetric minimal models, SM(2, ...) and SM(3, ...), via recently discovered non-unitary bulk-boundary correspondence. The correspondence relates…
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…
The Verlinde formula computes the dimension of conformal blocks associated to simple Lie algebras and stable pointed curves. If a simply-laced simple Lie algebra admits a nontrivial diagram automorphism, then this automorphism acts on the…
We develop analytical and numerical methods for the matrix thermofield in the large $N$ limit. Through the double collective representation on the Schwinger-Keldysh contour, it provides thermodynamical properties and finite temperature…
We study the dynamics of N=1 supersymmetric systems consisting of the strongly-coupled superconformal theory T_N, SU(N) gauge groups, and fundamental chiral multiplets. We demonstrate that such systems exhibit familiar phenomena such as…
The $(p_+,p_-)$ singlet algebra is a vertex operator algebra that is strongly generated by a Virasoro field of central charge $1-6(p_+-p_-)^2/p_+p_-$ and a single Virasoro primary field of conformal weight $(2p_+-1)(2p_--1)$. Here, the…
Weakly interacting quantum fluids allow for a natural kinetic theory description which takes into account the fermionic or bosonic nature of the interacting particles. In the simplest cases, one arrives at the Boltzmann-Nordheim equations…
We study a class of models in which $N$ flavors of massless fermions on the half line are coupled by an arbitrary orthogonal matrix to $N$ rotors living on the boundary. Integrating out the rotors, we find the exact partition function and…
Based on our earlier work on free field realizations of conformal blocks for conformal field theories with $SL(2)$ current algebra and with fractional level and spins, we discuss in some detail the fusion rules which arise. By a careful…
In two recent papers, an isometric conformal transformation has been introduced that eliminates potential interaction terms from the Schr\"odinger equation for central potential problems. The method has been demonstrated for both the…
The Coulomb branch indices of Argyres-Douglas theories on $L(k,1)\times S^{1}$ are recently identified with matrix elements of modular transforms of certain $2d$ vertex operator algebras in a particular limit. A one parameter generalization…
We present some new exact results for general four-dimensional superconformal field theories. We derive differential equations governing the coupling constant dependence of chiral primary correlators. For N=2 theories we show that the…
By generalizing a fermionic construction, a natural relation is found between SL(2) degenerate conformal field theories and some N=2 discrete superconformal series. These non-unitary models contain, as a subclass, N=2 minimal models. The…
We develop a Coulomb gas formalism for boundary conformal field theory having a $W$ symmetry and illustrate its operation using the three state Potts model. We find that there are free-field representations for six $W$ conserving boundary…
We reformulate the matrix models of minimal superstrings as loop gas models on random surfaces. In the continuum limit, this leads to the identification of minimal superstrings with certain bosonic string theories, to all orders in the…
Let V be a simple vertex operator algebra satisfying the following conditions: (i) The homogeneous subspaces of V of weights less than 0 are 0, the homogeneous subspace of V of weight 0 is spanned by the vacuum and V' is isomorphic to V as…
Links between certain stochastic evolutions of conformal maps and conformal field theory have been studied in the realm of SLE and by utilizing singular vectors in highest-weight modules of the Virasoro algebra. It was recently found that…