M String, Monopole String and Modular Forms

Abstract

We study relations between M-strings (one-dimensional intersections of M2-branes and M5-branes) in six dimensions and m-strings (magnetically charged monopole strings) in five dimensions. For specific configurations, we propose that the counting functions of BPS bound-states of M-strings capture the elliptic genus of the moduli space of m-strings. We check this proposal for the known cases, the Taub-NUT and Atiyah-Hitchin spaces for which we find complete agreement. Furthermore, we analyze the modular properties of the M-string free energies, which do not transform covariantly under SL(2,Z). However, for a given number of M-strings, we find that there exists a unique combination of unrefined genus-zero free energies that transforms as a Jacobi form under a congruence subgroup of SL(2,Z). These combinations correspond to summing over different numbers of M5-branes and make sense only if the distances between them are all equal. We explain that this is a necessary condition for the m-string moduli space to be factorizable into relative and center-of-mass parts.

80 pages, 4 embedded figures, 5 long tables; v2. typos fixed; v3. published version with title change

References in corpus (8)

• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• On D=5 super Yang-Mills theory and (2,0) theory
• Strings of Minimal 6d SCFTs
• Mathieu Moonshine in the elliptic genus of K3
• Elliptic genera of ALE and ALF manifolds from gauged linear sigma models
• From strings in 6d to strings in 5d
• Elliptic genera of monopole strings

Cited by in corpus (26)

• F-Theory, Spinning Black Holes and Multi-string Branches
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Anomaly of strings of 6d $\mathcal{N}=(1,0)$ theories
• Revisiting the classifications of 6d SCFTs and LSTs
• Instanton-Monopole Correspondence from M-Branes on ${\mathbb{S}}^1$ and Little String Theory
• An elliptic Virasoro symmetry in 6d
• Self-Duality and Self-Similarity of Little String Orbifolds
• From Little String Free Energies Towards Modular Graph Functions
• D-type fiber-base duality
• From strings in 6d to strings in 5d
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• Bound States of Little Strings and Symmetric Orbifold CFTs
• Five-Brane Webs and Highest Weight Representations
• Dihedral Symmetries of Gauge Theories from Dual Calabi-Yau Threefolds
• $\mathcal{N}=2^{\star }$ from Topological Amplitudes in String Theory
• Probing the Moduli Dependence of Refined Topological Amplitudes
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Symmetric Orbifold Theories from Little String Residues
• The Enhancement of Supersymmetry in M-strings
• Mock Modular Index of M2-M5 Brane System
• Symmetries in A-Type Little String Theories, Part I
• Elliptic Genus, Anomaly Cancellation and Heterotic M-theory
• Compactified Webs and Domain Wall Partition Functions
• Domain walls and M2-branes partition functions: M-theory and ABJM Theory
• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras