Abstract
We propose a set of novel expansions of Nekrasov’s instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on {mathrm{mathbb{C}}}_{q,{t}^{-1}}^2times {mathbb{S}}^1 , we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces {mathrm{mathbb{C}}}_qtimes {mathbb{S}}^1 , {mathrm{mathbb{C}}}_{t^{-1}}times {mathbb{S}}^1 and their intersection along {mathbb{S}}^1 . These new expansions are natural from the BPS/CFT viewpoint, as they can be matched with Wq,t correlators involving an arbitrary number of screening charges of two kinds. Our constructions generalize and interpolate existing results in the literature.
Highlights
Strings [18,19,20,21]
We propose a set of novel expansions of Nekrasov’s instanton partition functions
Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on C2q,t−1 × S1, we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces Cq × S1, Ct−1 × S1 and their intersection along S1
Summary
To give a brief summary of our results, we start by recalling one of the most frequently used representation of the instanton partition function of 5d N = 1 U(N ) pure Yang-Mills theory on C2q,t−1 × S1, written as a sum over arbitrary Young diagrams Y = {YA|A = 1, . Frequently used, is as a sum over the instanton number k = |Y |, namely. A less obvious expansion, which is our starting point, organizes the instanton partition function as a sum over the number of rows of the Young diagrams. If we denote by Y[d, d] the set of Young diagrams Y having maximal squares of size {dA ×dA|A = 1, . We denote by Y[r, c] the set of Young diagrams having their maximal rectangles of shape {rA × cA|A = 1 . The sake of clarity we will be mostly interested in pure Yang-Mills theory, but our analysis can be generalized to include matter and quiver theories
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