M‐strings, elliptic genera and N = 4 string amplitudes

2013/10/31 by Stefan Hohenegger, S. Hohenegger, A. Iqbal +1 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Equivariant map #Gauge theory #Homotopy and Cohomology in Algebraic Topology #Instanton #Non-critical string theory #Noncommutative and Quantum Gravity Theories #Partition function (quantum field theory) #String duality #String field theory #String theory #Topological string theory #hep-th #math-ph #math.MP

paper · pdf · doi:10.1002/prop.201300035

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

openalex publication_date 2014/02/12 · arxiv created 2014/03/11 · arxiv updated 2015/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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 ℂ 2 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.

Citations

• N = 2 type II-heterotic duality and higher-derivative F-terms
• Algebras, BPS states, and strings
• Moduli dependence of string loop corrections to gauge coupling constants
• BKM Lie superalgebras from dyon spectra in Z N CHL orbifolds for composite N
• Automorphic forms onO s +2,2(R) and infinite products
• Phases of N = 2 theories in two dimensions
• Two Dimensional Gauge Theories Revisited
• Non-Abelian tensor towers and (2,0) superconformal theories
• Worldsheet realization of the refined topological string
• The moment map and equivariant cohomology
• Harmonicity in N=4 supersymmetry and its quantum anomaly
• BPS states in the duality web of the Omega deformation

Cited by

• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras
• Self-duality and self-similarity of little string orbifolds