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arXiv · 2407.11164

Seiberg-Witten curves of $\widehat{D}$-type Little Strings

Baptiste Filoche·Stefan Hohenegger·Taro Kimura
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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 $\widehat{A}$-type Little String Theories (LSTs) are very well studied, much less is known about the $\widehat{D}$-type, where for example the Seiberg-Witten curve (SWC) is only known in the case of the $\widehat{D}_4$ theory. In this work, we provide a general construction of this curve for arbitrary $\widehat{D}_{M}$ 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 $\widehat{D}_M$ 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 $SO(2M)$.

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Baptiste Filoche, Stefan Hohenegger, Taro Kimura. 2024-07-15. Seiberg-Witten curves of $\widehat{D}$-type Little Strings. https://arxiv.org/abs/2407.11164

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