Unstable solitons on noncommutative tori and D-branes

TL;DR

This paper constructs exact solutions in super Yang-Mills theory on noncommutative tori that model unstable D-brane systems, matching string spectra and energies, thus advancing understanding of D-brane dynamics in noncommutative geometry.

Contribution

It introduces a new class of solutions on noncommutative tori that generalize previous solitons and accurately reproduce string spectra and energies for D-brane systems.

Findings

Spectrum of fluctuations matches string spectrum in decoupling limit.

Correctly reproduces energies and binding energies of D-brane systems.

Provides examples of solitons representing intermediate-dimensional branes.

Abstract

We describe a class of exact solutions of super Yang-Mills theory on even-dimensional noncommutative tori. These solutions generalize the solitons on a noncommutative plane introduced in hep-th/0009142 that are conjectured to describe unstable D2p-D0 systems. We show that the spectrum of quadratic fluctuations around our solutions correctly reproduces the string spectrum of the D2p-D0 system in the Seiberg-Witten decoupling limit. In particular the fluctuations correctly reproduce the 0-0 string winding modes. For p=1 and p=2 we match the differences between the soliton energy and the energy of an appropriate SYM BPS state with the binding energies of D2-D0 and D4-D0 systems. We also give an example of a soliton that we conjecture describes branes of intermediate dimension on a torus such as a D2-D4 system on a four-torus.