D0-D4 brane tachyon condensation to a BPS state and its excitation spectrum in noncommutative super Yang-Mills theory

TL;DR

This paper studies the decay of unstable D0-D4 brane systems into BPS states within noncommutative super Yang-Mills theory, revealing new insights into tachyon condensation, excitation spectra, and phase transitions influenced by B-field backgrounds.

Contribution

It provides a detailed analysis of tachyon condensation, computes the tachyon potential, and links excitation spectra to T-duality, proposing a phase transition at self-dual B-field configurations.

Findings

Tachyon potential reproduces the complete mass defect.

Excitation spectrum matches fluxon solutions via T-duality.

Number of states varies significantly at self-dual B-field.

Abstract

We investigate the D0-D4-brane system for different B-field backgrounds including the small instanton singularity in noncommutative SYM theory. We discuss the excitation spectrum of the unstable state as well as for the BPS D0-D4 bound state. We compute the tachyon potential which reproduces the complete mass defect. The relevant degrees of freedom are the massless (4,4) strings. Both results are in contrast with existing string field theory calculations. The excitation spectrum of the small instanton is found to be equal to the excitation spectrum of the fluxon solution on R^2_theta x R which we trace back to T-duality. For the effective theory of the (0,0) string excitations we obtain a BFSS matrix model. The number of states in the instanton background changes significantly when the B-field becomes self-dual. This leads us to the proposal of the existence of a phase transition or cross over at self-dual B-field.