Giant gravitons and the emergence of geometric limits in $\beta$-deformations of ${\cal N}=4$ SYM

Understand

We study a one parameter family of supersymmetric marginal deformations of ${\cal N}=4$ SYM with $U(1)^3$ symmetry, known as $\beta$-deformations, to understand their dual $AdS\times X$ geometry, where $X$ is a large classical geometry in the $g_{YM}^2N\to \infty$ limit.

• We argue that we can determine whether or not $X$ is geometric by studying the spectrum of open strings between giant gravitons states, as represented by operators in the field theory, as we take $N\to\infty$ in certain double scaling limits.
• We study the conditions under which these open strings can give rise to a large number of states with energy far below the string scale.
• The number-theoretic properties of $\beta$ are very important.