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Smeared D0 charge and the Gubser-Mitra conjecture

Simon F. Ross, Toby Wiseman

TL;DR

This paper extends the Gubser-Mitra conjecture to black p-branes carrying smeared D0-brane charge by leveraging an M-theory boost to relate smeared D0 configurations to charge-free ones. It shows that the threshold (dynamical) instability and the Euclidean negative mode are independent of the smeared D0 parameter $\beta$ and that the corresponding thermodynamic instability boundaries, when D0 is allowed to vary, align with GM's prediction. The authors verify these results across several examples, including D2-D0, D4-D0, and F1-D0 bound states, and further argue that the same independence extends to general brane bound states via twisted reductions. Collectively, the work provides strong evidence that GM stability holds in smeared D0 settings and clarifies the appropriate thermodynamic ensembles for these systems.

Abstract

We relate a Dp or NS-brane with D0-brane charge smeared over its worldvolume to the system with no D0-charge. This allows us to generalise Reall's partial proof of the Gubser-Mitra conjecture. We show explicitly for specific examples that the dynamical instability coincides with thermodynamic instability in the ensemble where the D0-brane charge can vary. We also comment on consistency checks of the conjecture for more complicated systems, using the example of the D4 with F1 and D0 charges smeared on its worldvolume.

Smeared D0 charge and the Gubser-Mitra conjecture

TL;DR

This paper extends the Gubser-Mitra conjecture to black p-branes carrying smeared D0-brane charge by leveraging an M-theory boost to relate smeared D0 configurations to charge-free ones. It shows that the threshold (dynamical) instability and the Euclidean negative mode are independent of the smeared D0 parameter and that the corresponding thermodynamic instability boundaries, when D0 is allowed to vary, align with GM's prediction. The authors verify these results across several examples, including D2-D0, D4-D0, and F1-D0 bound states, and further argue that the same independence extends to general brane bound states via twisted reductions. Collectively, the work provides strong evidence that GM stability holds in smeared D0 settings and clarifies the appropriate thermodynamic ensembles for these systems.

Abstract

We relate a Dp or NS-brane with D0-brane charge smeared over its worldvolume to the system with no D0-charge. This allows us to generalise Reall's partial proof of the Gubser-Mitra conjecture. We show explicitly for specific examples that the dynamical instability coincides with thermodynamic instability in the ensemble where the D0-brane charge can vary. We also comment on consistency checks of the conjecture for more complicated systems, using the example of the D4 with F1 and D0 charges smeared on its worldvolume.

Paper Structure

This paper contains 6 sections, 42 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Connecting thermodynamic and dynamical instability
  3. Adding D0-brane charge
  4. Examples
  5. Adding D0 charge to general brane bound states
  6. Conclusions

Figures (1)

  • Figure 1: The boundary of stability for the D4-smeared D0 system, as a function of $\sqrt{Q_4 V_4/M}$ and $\sqrt{Q_0/M}$. The system is stable to the right of the line. The circle indicates the BPS bound.