M-strings, Elliptic Genera and N=4 String Amplitudes

Abstract

We study mass-deformed N=2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)-brane webs in type II string theory using Nekrasov's instanton calculus, secondly, the (refined) topological string using the topological vertex formalism and thirdly, M theory via the elliptic genus of certain M-strings configurations. We argue for a large class of theories that these approaches yield the same gauge theory partition function which we study in detail. To make their modular properties more tangible, we consider a fourth approach by connecting the partition function to the equivariant elliptic genus of R^4 through a (singular) theta-transform. This form appears naturally as a specific class of one-loop scattering amplitudes in type II string theory on T^2, which we calculate explicitly.

65 pages, a section on calculation of partition function using Nekrasov's instanton calculus is added

References in corpus (17)

• The Refined Topological Vertex
• Notes on the K3 Surface and the Mathieu group M_24
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• On D=5 super Yang-Mills theory and (2,0) theory
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• Instanton calculus in R-R background and the topological string
• A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions
• Direct Production of Lightest Regge Resonances
• Mathieu Moonshine in the elliptic genus of K3
• Flux interactions on D-branes and instantons
• BKM Lie superalgebras from counting twisted CHL dyons
• Non-perturbative effective interactions from fluxes
• N=4 Topological Amplitudes and String Effective Action
• Generalized Kac-Moody Algebras from CHL dyons
• Harmonicity in N=4 supersymmetry and its quantum anomaly
• Borcherds Algebras and N=4 Topological Amplitudes
• Instanton Calculus With R-R Background And Topological Strings

Cited by in corpus (42)

• 6d Conformal Matter
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• On orbifolds of M-Strings
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
• tt* Geometry in 3 and 4 Dimensions
• E + E $\to$ H
• On Exceptional Instanton Strings
• Instanton-Monopole Correspondence from M-Branes on ${\mathbb{S}}^1$ and Little String Theory
• Elliptic genera of ALE and ALF manifolds from gauged linear sigma models
• M String, Monopole String and Modular Forms
• Triality in Little String Theories
• An elliptic Virasoro symmetry in 6d
• Dual Little Strings from F-Theory and Flop Transitions
• Modular anomaly equations in N=2* theories and their large-N limit
• Self-Duality and Self-Similarity of Little String Orbifolds
• Topological vertex formalism with O5-plane
• Dual Little Strings and their Partition Functions
• On the Elliptic Genus of Three E-strings and Heterotic Strings
• 3d Mirror Symmetry from S-duality
• From Little String Free Energies Towards Modular Graph Functions
• Beyond Triality: Dual Quiver Gauge Theories and Little String Theories
• More on topological vertex formalism for 5-brane webs with O5-plane
• New Supersymmetric Localizations from Topological Gravity
• Five-Dimensional Gauge Theories from Shifted Web Diagrams
• 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
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory
• Elliptic modular double and 4d partition functions
• Probing the Moduli Dependence of Refined Topological Amplitudes
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• The Enhancement of Supersymmetry in M-strings
• Symmetric Orbifold Theories from Little String Residues
• $DE$-type little strings from glued brane webs
• Mock Modular Index of M2-M5 Brane System
• A string realisation of $\Omega$-deformed Abelian $\mathcal{N}=2^{\ast }$ theory
• Affine characters at negative level and elliptic genera of non-critical strings
• Elliptic Genus, Anomaly Cancellation and Heterotic M-theory
• Compactified Webs and Domain Wall Partition Functions
• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras