798 citations · 3.1k across the 77 of their papers we have counts for
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Quantum Langlands dualities of boundary conditions, D-modules, and conformal blocks
Edward Frenkel, Davide Gaiotto
We review and extend the vertex algebra framework linking gauge theory constructions and a quantum deformation of the Geometric Langlands Program. The relevant vertex algebras are…
Quantum q-Langlands Correspondence
Mina Aganagic, Edward Frenkel, Andrei Okounkov
We formulate a two-parameter generalization of the geometric Langlands correspondence, which we prove for all simply-laced Lie algebras. It identifies the q-conformal blocks of the…
Instantons beyond topological theory II
E. Frenkel, A. Losev, N. Nekrasov
The present paper is the second part of our project in which we describe quantum field theories with instantons in a novel way by using the "infinite radius limit" (rather than the…
Notes on instantons in topological field theory and beyond
E. Frenkel, A. Losev, N. Nekrasov
This is a brief summary of our studies of quantum field theories in a special limit in which the instantons are present, the anti-instantons are absent, and the perturbative correc…
Instantons beyond topological theory I
E. Frenkel, A. Losev, N. Nekrasov
Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corr…
Lectures on the Langlands Program and Conformal Field Theory
Edward Frenkel
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introdu…
Mirror symmetry in two steps: A-I-B
Edward Frenkel, Andrei Losev
We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric varie…
Thermodynamic Bethe Ansatz and Dilogarithm Identities I
Edward Frenkel, Andras Szenes
We consider the (A_n,A_1) Y-system arising in the Thermodynamic Bethe Ansatz. We prove the periodicity of solutions of this Y-system conjectured by Al.B. Zamolodchikov, and the dil…
Free field realizations in representation theory and conformal field theory
Edward Frenkel
Invited lecture at the International Congress of Mathematicians, Zuerich, August 3-11, 1994 (extended version), reviews free field realizations of affine Kac-Moody and W-algebras a…
W_{1+\infty} and W(gl_N) with central charge N
E. Frenkel, V. Kac, A. Radul +1
We study representations of the central extension of the Lie algebra of differential operators on the circle, the W-infinity algebra. We obtain complete and specialized character f…
Gaudin Model, Bethe Ansatz and Critical Level
Boris Feigin, Edward Frenkel, Nikolai Reshetikhin
We propose a new method of diagonalization of hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on Wakimoto modules over affine algebra…
Kac-Moody Groups and Integrability of Soliton Equations
Boris Feigin, Edward Frenkel
A new approach to integrability of affine Toda field theories and closely related to them KdV hierarchies is proposed. The flows of a hierarchy are explicitly identified with infin…
Integrals of Motion and Quantum Groups
Boris Feigin, Edward Frenkel
A homological construction of integrals of motion of the classical and quantum Toda field theories is given. Using this construction, we identify the integrals of motion with cohom…
Crystal bases, dilogarithm identities and torsion in algebraic K-groups
Edward Frenkel, Andras Szenes
We give a new interpretation and proof of the dilogarithm identities, associated to the affine Kac-Moody algebra sl(2)^, using the path description of the corresponding crystal bas…
Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities
Boris Feigin, Edward Frenkel
We prove that the dimensions of coinvariants of certain nilpotent subalgebras of the Virasoro algebra do not change under deformation in the case of irreducible representations of…
Dilogarithm identities, q-difference equations and the Virasoro algebra
Edward Frenkel, Andras Szenes
We give a new proof of the dilogarithm identities, associated to the (2,2n+1) minimal models of the Virasoro algebra.