Quantum qLanglands Correspondence
Abstract
We formulate a twoparameter generalization of the geometric Langlands correspondence, which we prove for all simplylaced Lie algebras. It identifies the qconformal blocks of the quantum affine algebra and the deformed Walgebra associated to two Langlands dual Lie algebras. Our proof relies on recent results in quantum Ktheory of the Nakajima quiver varieties. The physical origin of the correspondence is the 6d little string theory. The quantum Langlands correspondence emerges in the limit in which the 6d string theory becomes the 6d conformal field theory with (2,0) supersymmetry.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.03146
 Bibcode:
 2017arXiv170103146A
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 116 pages, 4 figures. Minor changes. Version accepted for publication in Trudy Moskovskogo Matematicheskogo Obshchestva. (Transactions of the Moscow Mathematical Society.)