Abstract
We continue our study of symmetries of a class of little string theories of A-type, which are engineered by N parallel M5-branes probing a flat transverse space. Extending the analysis of the companion paper [1], we discuss the part of the free energy that is sensitive to the details of the 𝔞N−1 gauge structure, by computing explicit series expansions for the cases N = 2, 3, 4. Based on these examples, we find a class of functions that we conjecture to resum whole sectors in the instanton expansion of the free energy and which combine in a natural manner its modular properties as well as the gauge symmetry. These functions have previously been introduced in the literature as the generating functions of multi-divisor sums and in the case N = 2 can also be cast into the form of a generalised Eisenstein series. We use these resummed contributions to the free energy to perform a number of non-trivial consistency checks for our results.
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Bastian, B., Hohenegger, S. Symmetries in A-type little string theories. Part II. Eisenstein series and generating functions of multiple divisor sums. J. High Energ. Phys. 2020, 16 (2020). https://doi.org/10.1007/JHEP03(2020)016
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DOI: https://doi.org/10.1007/JHEP03(2020)016