Superconformal index of low-rank gauge theories via the Bethe Ansatz
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Date
2021
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Abstract
We study the Bethe Ansatz formula for the superconformal index, in the case of 4d
N = 4 super-Yang-Mills with gauge group SU(N). We observe that not all solutions to
the Bethe Ansatz Equations (BAEs) contribute to the index, and thus formulate “reduced
BAEs” such that all and only their solutions contribute. We then propose, sharpening a
conjecture of Arabi Ardehali et al. [1], that there is a one-to-one correspondence between
solutions to the reduced BAEs and vacua of the 4d N = 1∗theory on S1. We test the
proposal in the case of SU(2) and SU(3). In the case of SU(3), we confirm that there is
a continuous family of solutions, whose contribution to the index is non-vanishing.