Related papers: Two-point Functions in Affine Current Algebra and …
We study the quantum theory of a simple general relativistic quantum model of two coupled harmonic oscillators and compute the two-point function following a proposal first introduced in the context of loop quantum gravity.
A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Applying the generators of the closed subalgebra generated by…
In this thesis steps are taken in the direction of formulating non-critical strings in the framework of the $G/G$ approach. A major part of the thesis is concerned with conformal field theory based on affine $SL(2)$ current algebra, in…
We classify integrable irreducible highest weight representations of non-twisted affine Lie superalgebras. We give a free field construction in the level~1 case. The analysis of this construction shows, in particular, that in the simplest…
In this short note, we provide OPEs for several affine W-algebras associated with Lie algebras of rank two and give some direct applications.
A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this…
We study the category of graded finite-dimensional representations of the polynomial current algebra associated to a simple Lie algebra. We prove that the category has enough injectives and compute the graded character of the injective…
The microscopic theories of quantum gravity related to integrable lattice models can be constructed as special deformations of pure gravity. Each such deformation is defined by a second order differential operator acting on the coupling…
Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several…
An AF-algebra is assigned to each cusp form f of weight two; we study properties of this operator algebra, when f is a Hecke eigenform.
We introduce the affine Vogan diagrams of complex simple Lie algebras. These are generalizations of Vogan diagrams, and we study the involutions represented by them. We apply these diagrams to study the symmetric pairs, in particular the…
We calculate four-point correlation functions of two weight-2 and two weight-3 1/2-BPS operators in \mathcal{N}=4 SYM in the large N limit in supergravity approximation. By the AdS/CFT conjecture, these operators are dual to AdS…
We present a systematic derivation for a general formula for the n-point coupling constant valid for affine Toda theories related to any simple Lie algebra {\bf g}. All n-point couplings with $n \geq 4$ are completely determined in terms of…
We consider string junctions with endpoints on a set of branes of IIB string theory defining an ADE-type gauge Lie algebra. We show how to characterize uniquely equivalence classes of junctions related by string/brane crossing through…
It is pointed out that affine Lie algebras appear to be the natural mathematical structure underlying the notion of integrability for two-dimensional systems. Their role in the construction and classification of 2D integrable systems is…
Affine quantum gravity involves (i) affine commutation relations to ensure metric positivity, (ii) a regularized projection operator procedure to accomodate first- and second-class quantum constraints, and (iii) a hard-core interpretation…
The purpose of this paper is to introduce the new concept of weighted floating functions associated with log concave or $s$-concave functions. This leads to new notions of weighted functional affine surface areas. Their relation to more…
We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…
We consider three-point couplings in simple Lie algebras -- singlets in triple tensor products of their integrable highest weight representations. A coupling can be expressed as a linear combination of products of finitely many elementary…
Each irreducible representation of the affine group of a finite field has a unique maximal inductive algebra, and it is self adjoint.