Abstract
We study splitting and joining interactions of giant gravitons with angular momenta N1/2 ≪ J ≪ N in the type IIB string theory on AdS5 × S5 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} = 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.
Highlights
On the gravity side, being extended objects, it is rather challenging to go beyond kinematics and study their dynamical interaction process except for so-called heavy-heavy-light three point interactions
We study splitting and joining interactions of giant gravitons with angular momenta N 1/2 J N in the type IIB string theory on AdS5 × S5 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
Summary
The tiny graviton matrix model was proposed by Sheikh-Jabbari as a candidate for the discrete lightcone quantisation (DLCQ) of the type IIB string theory on the maximally supersymmetric ten-dimensional plane-wave background [21]. With these replacements (2.11)–(2.14) we obtain the bosonic part of the lightcone Hamiltonian of the IIB plane-wave matrix model [21],5. The full supersymmetric IIB plane-wave matrix model with PSU(2|2) × PSU(2|2) × U(1) symmetry is given by the following lightcone Hamiltonian [21]:. In order for the plane-wave approximation to be valid, the radius of each giant graviton rl should be much smaller than RS (anti)instanton solutions of the IIB plane-wave matrix model. As will be elaborated further, the (anti-)instantons describe splitting or joining interactions of concentric giants. Similar (anti-)instantons have been discussed in the BMN matrix model [13, 15] and our analysis will be analogous to theirs
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