Seiberg-Witten curves of \( \hat{D} \)-type Little Strings

Abstract

Little Strings are a type of non-gravitational quantum theories that contain extended degrees of freedom, but behave like ordinary Quantum Field Theories at low energies. A particular class of such theories in six dimensions is engineered as the world-volume theory of an M5-brane on a circle that probes a transverse orbifold geometry. Its low energy limit is a supersymmetric gauge theory that is described by a quiver in the shape of the Dynkin diagram of the affine extension of an ADE-group. While the so-called \( \hat{A} \)-type Little String Theories (LSTs) are very well studied, much less is known about the \( \hat{D} \)-type, where for example the Seiberg-Witten curve (SWC) is only known in the case of the \( {\hat{D}}_4 \) theory. In this work, we provide a general construction of this curve for arbitrary \( {\hat{D}}_M \) that respects all symmetries and dualities of the LST and is compatible with lower-dimensional results in the literature. For M = 4 our construction reproduces the same curve as previously obtained by other methods. The form in which we cast the SWC for generic \( {\hat{D}}_M \) allows to study the behaviour of the LST under modular transformations and provides insights into a dual formulation as a circular quiver gauge theory with nodes of Sp(M − 4) and SO(2M).