Symmetries in A-type little string theories. Part I. Reduced free energy and paramodular groups

Abstract

We analyse the symmetries of a class of A-type little string theories that are engineered by N parallel M5-branes with M2-branes stretched between them. This paper deals with the so-called reduced free energy, which only receives contributions from the subset of the BPS states that carry the same charges under all the Cartan generators of the underlying gauge algebra. We argue (and check explicitly in a number of examples) that the former is invariant under the paramodular group ΣN ⊂ Sp(4, ℚ), which gets extended to a subgroup of Sp(4, ℝ) in the Nekrasov-Shatashvili-limit. This extension agrees with the observation made in [18] that these BPS states form a symmetric orbifold CFT. Furthermore, we argue that ΣN (along with other symmetries) places strong constraints on the BPS counting function that governs the intersection between the M5- and M2-branes.