The ABCDEFG of Little Strings

Nathan Haouzi, Can Kozçaz

Published 2017-11-29Version 1

Starting from type IIB string theory on an $ADE$ singularity, the (2,0) little string arises when one takes the string coupling $g_s$ to 0. In this setup, we give a unified description of the codimension-two defects of the little string, for any simple Lie algebra ${\mathfrak{g}}$. Geometrically, these are D5 branes wrapping 2-cycles of the singularity. Equivalently, the defects are specified by a certain set of weights of $^L {\mathfrak{g}}$, the Langlands dual of ${\mathfrak{g}}$. As a first application, we show that the partition function of the ${\mathfrak{g}}$-type quiver gauge theory on the defect is equal to the 3-point conformal block of the ${\mathfrak{g}}$-type $q$-deformed Toda theory in the Coulomb gas formalism. As a second application, we make contact with Bala--Carter theory to show that in the CFT limit, the Coulomb branch of the defects flows to a nilpotent orbit of ${\mathfrak{g}}$, and that all nilpotent orbits of ${\mathfrak{g}}$ arise in this way.