Multi-Body Interactions of D-Particles in Supergravity and Matrix Theory

TL;DR

This paper analyzes three-body interactions of D-particles using supergravity and Matrix theory, showing precise agreement and supporting the Matrix-theory conjecture as a nonperturbative M-theory definition.

Contribution

It provides a detailed derivation of three-body interactions in supergravity and computes corresponding two-loop contributions in Matrix theory, confirming their agreement.

Findings

Supergravity yields a complete classical three-body interaction expression.

Matrix theory two-loop calculations match supergravity predictions.

Results support the Matrix-theory conjecture as a nonperturbative M-theory framework.

Abstract

We present detailed analyses of the 3-body interactions of D-particles from both sides of 11 dimensional supergravity and Matrix theory. In supergravity, we derive a complete expression for the classical bosonic effective action for D-particles including 2-and 3-body interaction terms. In Matrix theory, we compute 1-particle irreducible contributions to the eikonal phase shift in the two-loop approximation. The results precisely agree with the predictions from supergravity and thus provide a strong support to the discrete light-cone interpretation of the Matrix-theory conjecture as a possible nonperturbative definition of M-theory.