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Much Ado About Nothing

Vijay Balasubramanian, Klaus Larjo, Joan Simon

TL;DR

Balasubramanian, Larjo, and Simón analyze the semiclassical decay of AdS5 orbifolds with a circle (a false vacuum) via a bubble of nothing, with the bounce given by Euclidean AdS-Schwarzschild. They identify the false vacuum from multiple perspectives—the topological black hole, a near-horizon Milne D3-brane setup, and Euclidean continuation—and show two inequivalent flat limits corresponding to a KK vacuum and Milne space, tied to the decay mechanism in the presence of a negative cosmological constant. By computing boundary-stress-tensor masses and Euclidean actions, they demonstrate that the small Euclidean AdS-Schwarzschild hole provides the appropriate instanton, while energy conservation requires an energy bath to compensate the instantaneous mass difference; localization on $S^5$ is expected to play a crucial role in the ten-dimensional theory. The work also discusses a field-theory dual description as a novel analytic continuation of thermal ${\cal N}=4$ SYM on ${S^3\times S^1}$ and situates the decay within a broader class of AdS fluxbrane quotients, linking nonperturbative gravity instabilities to barrier-penetration dynamics in the dual gauge theory.

Abstract

We describe the semiclassical decay of a class of orbifolds of AdS space via a bubble of nothing. The bounce is the small Euclidean AdS-Schwarzschild solution. The negative cosmological constant introduces subtle features in the conservation of energy during the decay. A near-horizon limit of D3-branes in the Milne orbifold spacetime gives rise to our false vacuum. Conversely, a focusing limit in the latter produces flat space compactified on a circle. The dual field theory description involves a novel analytic continuation of the thermal partition function of Yang-Mills theory on a three-sphere times a circle.

Much Ado About Nothing

TL;DR

Balasubramanian, Larjo, and Simón analyze the semiclassical decay of AdS5 orbifolds with a circle (a false vacuum) via a bubble of nothing, with the bounce given by Euclidean AdS-Schwarzschild. They identify the false vacuum from multiple perspectives—the topological black hole, a near-horizon Milne D3-brane setup, and Euclidean continuation—and show two inequivalent flat limits corresponding to a KK vacuum and Milne space, tied to the decay mechanism in the presence of a negative cosmological constant. By computing boundary-stress-tensor masses and Euclidean actions, they demonstrate that the small Euclidean AdS-Schwarzschild hole provides the appropriate instanton, while energy conservation requires an energy bath to compensate the instantaneous mass difference; localization on is expected to play a crucial role in the ten-dimensional theory. The work also discusses a field-theory dual description as a novel analytic continuation of thermal SYM on and situates the decay within a broader class of AdS fluxbrane quotients, linking nonperturbative gravity instabilities to barrier-penetration dynamics in the dual gauge theory.

Abstract

We describe the semiclassical decay of a class of orbifolds of AdS space via a bubble of nothing. The bounce is the small Euclidean AdS-Schwarzschild solution. The negative cosmological constant introduces subtle features in the conservation of energy during the decay. A near-horizon limit of D3-branes in the Milne orbifold spacetime gives rise to our false vacuum. Conversely, a focusing limit in the latter produces flat space compactified on a circle. The dual field theory description involves a novel analytic continuation of the thermal partition function of Yang-Mills theory on a three-sphere times a circle.

Paper Structure

This paper contains 22 sections, 65 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. The false vacuum
  3. The topological black hole as an orbifold
  4. Branes on the Milne spacetime
  5. Euclidean continuation
  6. Focusing limits
  7. Kruskal coordinates
  8. Schwarzschild coordinates
  9. Mass
  10. Semiclassical instability
  11. Decay of the topological black hole
  12. Localization:
  13. Energy conservation
  14. Euclidean actions of the relevant spaces
  15. Flat space limit:
  16. ...and 7 more sections

Figures (3)

  • Figure 1: The topological black hole. The surfaces $S_{f,p}$ are future and past singularities where timelike geodesics end. Infinity is connected and is topologically $S^3 \times S^1 \times R$ where $R$ represents time. $H_f$ is a future horizon -- light rays from the region interior to $H_f$ cannot reach infinity. (For details on the causal structure, see banadossimongeorgina).
  • Figure 2: Action of the Euclidean Schwarzschild black hole as a function of $x = r_h/R_{{\rm AdS}}$ where the periodicity of Euclidean time is set by in terms of $r_h$ by (\ref{['eq:period']}). The small black holes have $x < 1/\sqrt{2}$ while the large black holes have $x>1/\sqrt{2}$. We have set $3\pi^2 R_{{\rm AdS}}^3 / 16G =1$.
  • Figure 3: Action difference between the Euclidean Schwarzschild black holes and the false vacuum as a function of $x = r_h/R_{{\rm AdS}}$. The bounce solutions, corresponding to the small black holes, arise for $x < 1/\sqrt{2}$. We have set $3\pi^2 R_{{\rm AdS}}^3 / 16G =1$.