The holography of duality in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

The space of ${\cal N}=4$ supersymmetric Yang-Mills theories exhibits an intricate structure global one-form symmetries and $SL(2,\mathbb{Z})$ duality orbits. In this paper we study from the point view holographic dual Type IIB string theory. Generalizing work by Witten, map different based on gauge algebras $su(N)$, $so(N)$, $sp(N)$ to a choice boundary conditions bulk fields. We show how their anomalies, as well properties theories, arise in picture. Along way prove that number disjoint orbits for $su(N)$ is given square divisors $N$.