$$ \mathcal{N} $$ = 4 SYM, Argyres-Douglas theories, and an exact graded vector space isomorphism

A bstract In this first of two papers, we explain in detail the simplest example a broader set relations between apparently very different theories. Our relates $$ \mathfrak{su}(2) su 2 \mathcal{N} N = 4 super Yang-Mills (SYM) to theory call “(3, 2)”. This latter is an exactly marginal diagonal SU(2) gauging three D 3 (SU(2)) Argyres-Douglas (AD) We begin by observing that Schur indices these theories are related algebraic transformation surprisingly reminiscent index transformations describing spontaneous symmetry breaking on Higgs branch. However, breaks half supersymmetry SYM as well its full 2 F flavor symmetry. Moreover, it does so interesting way when viewed through lens corresponding 2D vertex operator algebras (VOAs): affine currents small super-Virasoro algebra at c ? 9 get mapped \mathcal{A}(6) A 6 stress tensor and some conformal descendants, while extra side higher-dimensional fermionic their descendants side. prove facets exact graded vector space isomorphism (GVSI) VOAs. GVSI respects U(1) r charge parent 4D briefly sketch how more general \mathfrak{su}(N) infinite class AD via generalizations our example. conclude showing that, theories, VOA saturates new inequality number strong generators.