Giant graviton interactions and M2-branes ending on multiple M5-branes

Abstract

Abstract We study splitting and joining interactions of giant gravitons with angular momenta N 1/2 ≪ J ≪ N in the type IIB string theory on AdS 5 × S 5 by describing them as instantons in the tiny graviton matrix model introduced by Sheikh-Jabbari. At large J the instanton equation can be mapped to the four-dimensional Laplace equation and the Coulomb potential for m point charges in an n-sheeted Riemann space corresponds to the m-to-n interaction process of giant gravitons. These instantons provide the holographic dual of correlators of all semi-heavy operators and the instanton amplitudes exactly agree with the pp-wave limit of Schur polynomial correlators in $$ \mathcal{N} $$ N = 4 SYM computed by Corley, Jevicki and Ramgoolam. By making a slight change of variables the same instanton equation is mathematically transformed into the Basu-Harvey equation which describes the system of M2-branes ending on M5-branes. As it turns out, the solutions to the sourceless Laplace equation on an n-sheeted Riemann space correspond to n M5-branes connected by M2-branes and we find general solutions representing M2-branes ending on multiple M5-branes. Among other solutions, the n = 3 case describes an M2-branes junction ending on three M5-branes. The effective theory on the moduli space of our solutions might shed light on the low energy effective theory of multiple M5-branes.