Superconformal index of low-rank gauge theories via the Bethe Ansatz

A bstract We study the Bethe Ansatz formula for superconformal index, in case of 4d $$ \mathcal{N} N = 4 super-Yang-Mills with gauge group SU( N ). observe that not all solutions to Equations (BAEs) contribute and thus formulate “reduced BAEs” such only their contribute. then propose, sharpening a conjecture Arabi Ardehali et al. [1], there is one-to-one correspondence between branches reduced BAEs vacua 1 * theory. test proposal SU(2) SU(3). In SU(3), we confirm continuous family solutions, whose contribution index non-vanishing.