D-particle Dynamics and Bound States

TL;DR

This work analyzes the low-energy dynamics of two D-particles in type IIA string theory by dimensionally reducing ten-dimensional $N=1$ SU(2) SYM to 0+1 dimensions and applying the Born–Oppenheimer approximation. It demonstrates the existence of non-BPS bound states with energies lifted by an amount scaling as $λ^{1/3}$ above the BPS mass $M_{\rm BPS}=2/λ$, interpretable as a linear potential from strings stretched between the D-particles. The spectrum is studied via a detailed separation into fast nondegenerate directions and slow radial motion on a conical vacuum moduli space, with a radial Schrödinger problem yielding the characteristic $E_{\rm tot}=λ^{1/3}\epsilon$ scaling and metastability. A string-theoretic interpretation links these bound states to configurations of open strings and suggests possible connections to eleven-dimensional supergravity/M-theory through a KK radius $R\sim λ^{2/3}$. The results provide insight into non-BPS excitations, their degeneracies, and potential implications for black hole entropy corrections in the D-particle regime.

Abstract

We study the low energy effective theory describing the dynamics of D-particles. This corresponds to the quantum mechanical system obtained by dimensional reduction of $9+1$ dimensional supersymmetric Yang-Mills theory to $0+1$ dimensions and can be interpreted as the non relativistic limit of the Born-Infeld action. We study the system of two like-charged D-particles and find evidence for the existence of non-BPS states whose mass grows like $λ^{1/3}$ over the BPS mass. We give a string interpretation of this phenomenon in terms of a linear potential generated by strings stretching from the two D-particles. Some comments on the possible relations to black hole entropy and eleven dimensional supergravity are also given.