Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories

Abstract

The low energy effective couplings of a four-dimensional $\mathcal{N}=2$ supersymmetric gauge theory to topological invariants of the background gravitational field are described by two functions $A$ and $B$. These two functions play an important role in the study of topologically twisted four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and in the computation of central charges of $\mathcal{N}=2$ superconformal theories. In this paper, we compute $A$ and $B$ from the partition function in the $\Omega$-background for $\mathrm{SU}(2)$ gauge theories. Our results not only confirm the predicted expressions of the effective gravitational couplings, but also give the previously undetermined overall multiplicative factors. We also analyze $A$ and $B$ for the $\mathrm{SU}(N)$ super-Yang-Mills theory, and confirm all the previous predictions.

40 pages. v2: minor corrections and additional references; v3: numerous minor improvements

References in corpus (3)

• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
• Donaldson-Witten theory and indefinite theta functions
• Seiberg-Witten geometry of four-dimensional N=2 SO-USp quiver gauge theories, I

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