Abstract
We compute the instanton partition functions of SCFTs in class . We obtain this result via orbifolding Dp/D(p-4) brane systems and calculating the partition function of the supersymmetric gauge theory on the worldvolume of K D(p-4) branes. Starting with D5/D1 setups probing a orbifold singularity we obtain the K instanton partition functions of 6d theories on in the presence of orbifold defects on T2 via computing the 2d superconformal index of the worldvolume theory on K D1 branes wrapping the T2. We then reduce our results to the 5d and to the 4d instanton partition functions. For k = 1 we check that we reproduce the known elliptic, trigonometric and rational Nekrasov partition functions. Finally, we show that the instanton partition functions of quivers in class can be obtained from the class mother theory partition functions with gauge factors via imposing the ‘orbifold condition’ with and , on the Coulomb moduli and the mass parameters.
Highlights
In recent years much progress has been made towards the non-perturbative study of four dimensional (4d) gauge theories with extended supersymmetry
N = 2∗) and its 5d and 6d uplifts: mass deformed 5d N = 2 MSYM on S1 and 6d (2, 0) theory on T 2. This is obtained via the computation of the superconformal index (SCI) of the (4, 4) 2d gauge theory living on the worldvolume of the K D1 branes with quiver depicted in Figure 4, which we set up using a supercharge that survives the orbifold projection that will come
Since the D-instantons serve as sources for those currents and the associated instanton number Kni! T [U (Kni) is related to the partition {Kni} following our discussion in Section 4.1 we may weight each contribution with fugacities q6d,ni for each current and assemble the quantity
Summary
In recent years much progress has been made towards the non-perturbative study of four dimensional (4d) gauge theories with extended supersymmetry. Many protected quantities, such as partition functions [7] and correlation functions of BPS operators in class S SCFTs may be computed as observables of a 2d theory which lives on C [8, 9]. N = 2∗) and its 5d and 6d (trigonometric and elliptic) uplifts: mass deformed 5d N = 2 MSYM on S1 and 6d (2, 0) theory on T 2 This is obtained via the computation of the SCI of the (4, 4) 2d gauge theory living on the worldvolume of the K D1 branes with quiver depicted, which we set up using a supercharge that survives the orbifold projection that will come next. Technical details are presented in the appendix to not interrupt the flow of the main text
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