A Two-Loop Test of M(atrix) Theory

TL;DR

This paper computes the two-loop correction to the effective potential between two D0-branes in M(atrix) theory, confirming the stability of the leading order result and providing evidence for the theory's consistency at higher orders.

Contribution

It presents the first two-loop calculation of the effective potential in M(atrix) theory, showing no renormalization of the leading velocity-dependent term at this order.

Findings

Two-loop corrections do not alter the $v^4/r^7$ potential.

The effective potential remains stable at two loops.

Supports the validity of M(atrix) theory predictions.

Abstract

We consider the scattering of two Dirichlet zero-branes in M(atrix) theory. Using the formulation of M(atrix) theory in terms of ten-dimensional super Yang-Mills theory dimensionally reduced to $(0+1)$-dimensions, we obtain the effective (velocity dependent) potential describing these particles. At one-loop we obtain the well known result for the leading order of the effective potential $V_{eff}\sim v^4/r^7$, where $v$ and $r$ are the relative velocity and distance between the two zero-branes respectively. A calculation of the effective potential at two-loops shows that no renormalizations of the $v^4$-term of the effective potential occur at this order.