The Long Range Gravitational Potential Energy Between Strings

TL;DR

This paper calculates the one-loop gravitational potential energy between long parallel strings, revealing a non-zero long-range interaction that arises quantum mechanically, unlike the classical case where it vanishes.

Contribution

It provides the first explicit calculation of the quantum gravitational potential between strings, including the effects of bulk scalar fields, and discusses implications for higher p-branes and cosmology.

Findings

Quantum correction induces a long-range potential between strings.

Potential depends on tensions, separation, and Newton's constant.

Results extend to p-branes and have cosmological implications.

Abstract

We calculate the gravitational potential energy between infinitely long parallel strings with tensions \tau_1 and \tau_2. Classically, it vanishes, but at one loop, we find that the long range gravitational potential energy per unit length is U/L = 24G_N^2\tau_1\tau_2/(5 \pi a^2) + ..., where a is the separation between the strings, G_N is Newton's constant, and we set \hbar = c =1. The ellipses represent terms suppressed by more powers of G_N \tau_i. Typically, massless bulk fields give rise at one loop to a long range potential between p-branes in space-times of dimension p+2+1. The contribution to this potential from bulk scalars is computed for arbitrary p (strings correspond to p=1) and in the case of three-branes its possible relevance for cosmological quintessence is commented on.