Superconformal invariance and the geography of four-manifolds

Abstract

The correlation functions of supersymmetric gauge theories on a four-manifold X can sometimes be expressed in terms of topological invariants of X. We show how the existence of superconformal fixed points in the gauge theory can provide nontrivial information about four-manifold topology. In particular, in the example of gauge group SU(2) with one doublet hypermultiplet, we derive a theorem relating classical topological invariants such as the Euler character and signature to sum rules for Seiberg-Witten invariants.

59 pages, harvmac b mode, four figures, some clarifications and references added

References in corpus (6)

• The BPS Spectra and Superconformal Points in Massive N=2 Supersymmetric QCD
• Donaldson invariants for nonsimply connected manifolds
• N=4 Supersymmetric Yang-Mills Theory on a Kaehler Surface
• Mass Perturbations in Twisted N=4 Supersymmetric Gauge Theories
• The Geometry of Supersymmetric Gauge Theories in Four Dimensions
• Four-manifold geography and superconformal symmetry

Cited by in corpus (24)

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• A counterexample to the a-'theorem'
• Trisecting non-Lagrangian theories
• PU(2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees
• Conformal topological Yang-Mills theory and de Sitter holography
• Donaldson-Witten theory and indefinite theta functions
• Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories
• Will we ever classify simply-connected smooth 4-manifolds?
• PU(2) monopoles and a conjecture of Marino, Moore, and Peradze
• Duality in Topological Quantum Field Theories
• Rational surfaces and symplectic 4-manifolds with one basic class
• The SO(3) monopole cobordism and superconformal simple type
• The Partition Function Of Argyres-Douglas Theory On A Four-Manifold
• Superconformal simple type and Witten's conjecture
• Extremal Bundles on Calabi-Yau Threefolds
• Euler number of Instanton Moduli space and Seiberg-Witten invariants
• Remarks on twisted theories with matter
• Effective Gravitational Couplings of Higher-Rank Supersymmetric Gauge Theories
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• Donaldson = Seiberg-Witten from Mochizuki's formula and instanton counting
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• Duality in the Context of Topological Quantum Field Theory
• Virtual Morse-Bott index, moduli spaces of pairs, and applications to topology of smooth four-manifolds