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Quasinormal modes for nonextreme Dp-branes and thermalizations of super-Yang-Mills theories

Kengo Maeda, Makoto Natsuume, Takashi Okamura

Abstract

The nonextreme Dp-brane solutions in type II supergravity(in the near-horizon limit) are expected to be dual to (p+1)-dimensional noncompact supersymmetric Yang-Mills theories at finite temperature. We study the translationally invariant perturbations along the branes in those backgrounds and calculate quasinormal frequencies numerically. These frequencies should determine the thermalization time scales in the dual Yang-Mills theories.

Quasinormal modes for nonextreme Dp-branes and thermalizations of super-Yang-Mills theories

Abstract

The nonextreme Dp-brane solutions in type II supergravity(in the near-horizon limit) are expected to be dual to (p+1)-dimensional noncompact supersymmetric Yang-Mills theories at finite temperature. We study the translationally invariant perturbations along the branes in those backgrounds and calculate quasinormal frequencies numerically. These frequencies should determine the thermalization time scales in the dual Yang-Mills theories.

Paper Structure

This paper contains 13 sections, 48 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Gauge/gravity dualities for D$p$-branes
  3. Bulk geometry
  4. Validity of supergravity descriptions
  5. Numerical approaches for QN frequencies
  6. Basic equations
  7. A numerical method to obtain QN frequencies
  8. Discussion of results
  9. $p=1$ and $p=4$
  10. $p=2$
  11. Sensibility on the boundary condition
  12. Summary
  13. Review of Quasinormal Modes

Figures (2)

  • Figure 1: QN frequencies for D$1$($\times$), D$2$($\circ$), D$3$($\triangle$) and D$4$-branes($+$). Each straight line is determined by the least-square fitting.
  • Figure 2: The dependence of the lowest QN frequency on the location of the boundary condition $x_b$. The left figure (right figure) is the real (imaginary) part of the QN frequency.