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

TL;DR

This paper explores the interactions of giant gravitons in type IIB string theory and their relation to M2-branes ending on multiple M5-branes, using instanton solutions in matrix models and connections to the Basu-Harvey equation.

Contribution

It introduces a novel instanton-based approach to describe giant graviton interactions and links these to M-brane configurations via mathematical transformations.

Findings

Instanton solutions map to Coulomb potentials in Riemann spaces.

Exact agreement with known correlators in ${\ m N}=4$ SYM.

Solutions describe M2-branes ending on multiple M5-branes.

Abstract

We study splitting and joining interactions of giant gravitons with angular momenta $N^{1/2}\ll J\ll N$ in the type IIB string theory on $AdS_5 \times S^5$ 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 ${\cal N}=4$ 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 M$2$-branes ending on M$5$-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.