Donaldson invariants for nonsimply connected manifolds

Abstract

We study Coulomb branch (``u-plane'') integrals for $\mathcal{N}=2$ supersymmetric $SU(2),SO(3)$ Yang-Mills theory on 4-manifolds $X$ of $b_1(X)>0,b_2^{+}(X)=1$. Using wall-crossing arguments we derive expressions for the Donaldson invariants for manifolds with $b_1(X)>0,b_2^{+}(X)>0$. Explicit expressions for $X=\IC P^1 \times F_g$, where $F_g$ is a Riemann surface of genus $g$ are obtained using Kronecker's double series identity. The result might be useful in future studies of quantum cohomology.

22 pages, harvmac b-mode, equation (5.17) corrected, two equations added

References in corpus (3)

• Integrable Hierarchies and Contact Terms in u-plane Integrals of Topologically Twisted Supersymmetric Gauge Theories
• Jacobi forms and the structure of Donaldson invariants for 4-manifolds with b_+=1
• Massey and Fukaya products on elliptic curves

Cited by in corpus (17)

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• Duality and Mock Modularity
• Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories
• Duality from Topological Symmetry
• Cutting and gluing with running couplings in $\mathcal{N}=2$ QCD
• Matrix Models and Gravitational Corrections
• Duality in Topological Quantum Field Theories
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• The $u$-plane integral, mock modularity and enumerative geometry
• Mocking the u-plane integral
• Donaldson-Witten theory, surface operators and mock modular forms
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• Higgs Bundles and Four Manifolds