Elliptic genera of ALE and ALF manifolds from gauged linear sigma models

Abstract

We compute the equivariant elliptic genera of several classes of ALE and ALF manifolds using localization in gauged linear sigma models. In the sigma model computation the equivariant action corresponds to chemical potentials for U(1) currents and the elliptic genera exhibit interesting pole structure as a function of the chemical potentials. We use this to decompose the answers into polar terms that exhibit wall crossing and universal terms. We compare our results to previous results on the large radius limit of the Taub-NUT elliptic genus and also discuss applications of our results to counting of BPS world-sheet spectrum of monopole strings in the 5d N=2 super Yang-Mills theory and self-dual strings in the 6d N=(2,0) theories.

arXiv comment1+60 pages

References in corpus (44)

• Phases of $N=2$ Theories In Two Dimensions
• Two-Dimensional Black Hole and Singularities of CY Manifolds
• Elliptic genera of 2d N=2 gauge theories
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole
• Exact Results in D=2 Supersymmetric Gauge Theories
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Duality of the Fermionic 2d Black Hole and N=2 Liouville Theory as Mirror Symmetry
• New Connections Between 4D and 5D Black Holes
• NS5-Branes, T-Duality and Worldsheet Instantons
• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• M5-branes from gauge theories on the 5-sphere
• 2d Index and Surface operators
• Sphere Partition Functions and the Zamolodchikov Metric
• On instantons as Kaluza-Klein modes of M5-branes
• Exact Kahler Potential from Gauge Theory and Mirror Symmetry
• Comments on the Spectrum of CHL Dyons
• Supersymmetric Index from Black Hole Entropy
• The non-compact elliptic genus: mock or modular
• Geometry of N=1 Dualities in Four Dimensions
• Worldsheet Instanton Corrections to the Kaluza-Klein Monopole
• SL(2,R)/U(1) Supercoset and Elliptic Genera of Non-compact Calabi-Yau Manifolds
• Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries
• Singular Monopoles and Supersymmetric Gauge Theories in Three Dimensions
• Dyons and S-Duality in N=4 Supersymmetric Gauge Theory
• Orbifolds and Solitons
• Electromagnetic Duality and $SU(3)$ Monopoles
• Gravitational Instantons of Type D_k
• A Twisted Non-compact Elliptic Genus
• M-strings, Elliptic Genera and N=4 String Amplitudes
• Worldsheet Descriptions of Wrapped NS Five-Branes
• ALE manifolds and Conformal Field Theory
• Non-holomorphic Modular Forms and SL(2,R)/U(1) Superconformal Field Theory
• Counting all dyons in N =4 string theory
• A holomorphic anomaly in the elliptic genus
• Brane bending and monopole moduli
• Localization and real Jacobi forms
• Self-dual Strings and 2D SYM
• Genus Two Surface and Quarter BPS Dyons: The Contour Prescription
• Exact Partition Functions on RP2 and Orientifolds
• Moonshine in Fivebrane Spacetimes
• Elliptic genera and real Jacobi forms
• T-duality Transformation of Gauged Linear Sigma Model with F-term
• Elliptic genera of monopole strings

Cited by in corpus (26)

• Universal Features of BPS Strings in Six-dimensional SCFTs
• Instanton-Monopole Correspondence from M-Branes on ${\mathbb{S}}^1$ and Little String Theory
• M String, Monopole String and Modular Forms
• From 3d duality to 2d duality
• Supersymmetric localization in two dimensions
• A 2d (0,2) appetizer
• Wall-crossing made smooth
• Single-centered black hole microstate degeneracies from instantons in supergravity
• Duality and Mock Modularity
• Witten Index for Noncompact Dynamics
• APS $\eta$-invariant, path integrals, and mock modularity
• Semi-doubled Gauged Linear Sigma Model for Five-branes of Codimension Two
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• New supersymmetric index of heterotic compactifications with torsion
• Heterotic Hyper-Kahler Flux Backgrounds
• An Elliptic Triptych
• Three-Charge Black Holes and Quarter BPS States in Little String Theory
• Mock modularity from black hole scattering states
• Squashed toric sigma models and mock modular forms
• The Enhancement of Supersymmetry in M-strings
• Dynamics of Two-Dimensional $\mathcal{N}=(2,2)$ Supersymmetric Theories with Semichiral Superfields I
• Three Avatars of Mock Modularity
• Quarter-BPS states in orbifold sigma models with ADE singularities
• Localization of Gauged Linear Sigma Model for KK5-branes
• N=(4,4) Vector Multiplets on Curved Two-Manifolds
• Localized Kaluza-Klein 6-brane