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The Donaldson-Witten function for gauge groups of rank larger than one

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arxiv hep-th/9802185 v2 pith:4NHWUZE6 submitted 1998-02-26 hep-th

Marcos Marino , Gregory Moore This is my paper · ORCID
classification hep-th
keywords gaugemathcaltheorycorrelationcorrelatorsexpressionsfieldfunctions
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We study correlation functions in topologically twisted $\mathcal{N}=2, d=4$ supersymmetric Yang-Mills theory for gauge groups of rank larger than one on compact four-manifolds $X$. We find that the topological invariance of the generator of correlation functions of BRST invariant observables is not spoiled by noncompactness of field space. We show how to express the correlators on simply connected manifolds of $b_{2,+}(X)>0$ in terms of Seiberg-Witten invariants and the classical cohomology ring of $X$. For manifolds $X$ of simple type and gauge group SU(N) we give explicit expressions of the correlators as a sum over $\mathcal{N}=1$ vacua. We describe two applications of our expressions, one to superconformal field theory and one to large $N$ expansions of SU(N) $\mathcal{N}=2, d=4$ supersymmetric Yang-Mills theory.

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Cited by 3 Pith papers

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  1. Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories

    hep-th 2024-11 conditional novelty 8.0 of 10

    For any 4d N=2 theory, topologically twisted partition functions depend on the diffeomorphism type, 't Hooft fluxes, and a generalized spin-c structure.

  2. Instantons from Blow-up

    hep-th 2019-08 conditional novelty 7.0 of 10

    The instanton partition function of many 4d N=2 and 5d N=1 gauge theories is fully determined by the perturbative part via generalized Nakajima-Yoshioka blowup equations.

  3. Defects, nested instantons and comet shaped quivers

    hep-th 2019-07 unverdicted novelty 7.0 of 10

    Proposes comet-shaped quiver gauge theories for surface defects with nested instantons in 4D gauge theories on T^2 × T*C_{g,k} and gives conjectural explicit formulae for the virtual equivariant elliptic genus of bund...

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