From Little String Free Energies Towards Modular Graph Functions

Abstract

We study the structure of the non-perturbative free energy of a one-parameter class of little string theories (LSTs) of A-type in the so-called unrefined limit. These theories are engineered by $N$ M5-branes probing a transverse flat space. By analysing a number of examples, we observe a pattern which suggests to write the free energy in a fashion that resembles a decomposition into higher-point functions which can be presented in a graphical way reminiscent of sums of (effective) Feynman diagrams: to leading order in the instanton parameter of the LST, the $N$ external states are given either by the fundamental building blocks of the theory with $N=1$, or the function that governs the counting of BPS states of a single M5-brane coupling to one M2-brane on either side. These states are connected via an effective coupling function which encodes the details of the gauge algebra of the LST and which in its simplest (non-trivial) form is captured by the scalar Greens function on the torus. More complicated incarnations of this function show certain similarities with so-called modular graph functions, which have appeared in the study of Feynman amplitudes in string- and field theory. Finally, similar structures continue to exist at higher instanton orders, which, however, also contain contributions that can be understood as the action of (Hecke) operators on the leading instanton result.

30 pages, minor corrections

References in corpus (16)

• The Refined Topological Vertex
• Higher genus modular graph functions, string invariants, and their exact asymptotics
• Mathieu Moonshine in the elliptic genus of K3
• From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
• Revisiting the classifications of 6d SCFTs and LSTs
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings
• Triality in Little String Theories
• All-order alpha'-expansion of one-loop open-string integrals
• Elliptic multiple zeta values, modular graph functions and genus 1 superstring scattering amplitudes
• Beyond Triality: Dual Quiver Gauge Theories and Little String Theories
• Bound States of Little Strings and Symmetric Orbifold CFTs
• M5 branes and Theta Functions
• Dihedral Symmetries of Gauge Theories from Dual Calabi-Yau Threefolds
• The ABCDEFG of Little Strings
• Symmetries in A-Type Little String Theories, Part I

Cited by in corpus (9)

• Generating series of all modular graph forms from iterated Eisenstein integrals
• The SAGEX Review on Scattering Amplitudes, Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their $\mathcal{N}=4$ supersymmetric Yang-Mills duals
• Poincaré series for modular graph forms at depth two. II. Iterated integrals of cusp forms
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• Basis Decompositions and a Mathematica Package for Modular Graph Forms
• To the cusp and back: Resurgent analysis for modular graph functions
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Symmetric Orbifold Theories from Little String Residues
• Symmetries in A-Type Little String Theories, Part I