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Holographic Particle Detection

Vijay Balasubramanian, Simon F. Ross

TL;DR

This paper investigates how holography encodes localized bulk objects, specifically point particles and black hole formation, in AdS3/CFT. It demonstrates that CFT two-point functions, evaluated as propagators in a WKB/geodesic approximation, develop kinks whose positions and discontinuities reveal the bulk particle locations, motions, and even matter distribution inside event horizons. By boosting stationary particles and analyzing collisions, the authors show that two kinks can merge into one at black hole formation, providing a boundary signature of horizon physics and a unitary interior description. The work highlights the power and limits of non-local gauge-theory observables in reconstructing bulk geometry and suggests how these ideas might extend to higher dimensions and more complex bulk configurations.

Abstract

In anti-de Sitter (AdS) space, classical supergravity solutions are represented "holographically" by conformal field theory (CFT) states in which operators have expectation values. These 1-point functions are directly related to the asymptotic behaviour of bulk fields. In some cases, distinct supergravity solutions have identical asymptotic behaviour; so dual expectation values are insufficient to distinguish them. We argue that non-local objects in the gauge theory can resolve the ambiguity, and explicitly show that collections of point particles in AdS_3 can be detected by studying kinks in dual CFT Green functions. Three dimensional black holes can be formed by collision of such particles. We show how black hole formation can be detected in the holographic dual, and calculate CFT quantities that are sensitive to the distribution of matter inside the event horizon.

Holographic Particle Detection

TL;DR

This paper investigates how holography encodes localized bulk objects, specifically point particles and black hole formation, in AdS3/CFT. It demonstrates that CFT two-point functions, evaluated as propagators in a WKB/geodesic approximation, develop kinks whose positions and discontinuities reveal the bulk particle locations, motions, and even matter distribution inside event horizons. By boosting stationary particles and analyzing collisions, the authors show that two kinks can merge into one at black hole formation, providing a boundary signature of horizon physics and a unitary interior description. The work highlights the power and limits of non-local gauge-theory observables in reconstructing bulk geometry and suggests how these ideas might extend to higher dimensions and more complex bulk configurations.

Abstract

In anti-de Sitter (AdS) space, classical supergravity solutions are represented "holographically" by conformal field theory (CFT) states in which operators have expectation values. These 1-point functions are directly related to the asymptotic behaviour of bulk fields. In some cases, distinct supergravity solutions have identical asymptotic behaviour; so dual expectation values are insufficient to distinguish them. We argue that non-local objects in the gauge theory can resolve the ambiguity, and explicitly show that collections of point particles in AdS_3 can be detected by studying kinks in dual CFT Green functions. Three dimensional black holes can be formed by collision of such particles. We show how black hole formation can be detected in the holographic dual, and calculate CFT quantities that are sensitive to the distribution of matter inside the event horizon.

Paper Structure

This paper contains 18 sections, 55 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Classical probes and dual expectation values
  3. Scale-radius duality: the power of symmetry
  4. Resolving bulk objects with propagators
  5. Stationary particles in ${\rm AdS}_{3}$
  6. ${\rm AdS}_{3}$ geodesics and dual propagators
  7. Stationary particles
  8. Moral of the story:
  9. Moving particles in ${\rm AdS}_{3}$
  10. Locating the particle:
  11. Relation to higher dimensions:
  12. Colliding particles
  13. Locating the particles prior to collision:
  14. The flat space limit:
  15. Collision below the black hole threshold:
  16. ...and 3 more sections

Figures (7)

  • Figure 1: Coordinate systems for a stationary point particle in ${\rm AdS}_{3}$. The region $\pi + \gamma \leq \phi \leq \pi -\gamma$ and $-\gamma \leq \phi \gamma$ are removed in C1 and C2 respectively. The edges of the excised regions are identified.
  • Figure 2: Coordinate systems for a moving point particle in ${\rm AdS}_{3}$. The edges of the excised regions are identified.
  • Figure 3: Colliding particles in ${\rm AdS}_{3}$. The edges of the excised regions are identified.
  • Figure 4: (a) Particle collision below threshold, (b) Evolution after collision below threshold, (c) Horizon formation above threshold, (d) Collision above threshold, (e) Evolution above threshold
  • Figure 5: COM, BTZ and Matschull's BTZ$_{\rm M}$ slices of a black hole spacetime formed by collision of lightlike particles. The slices are drawn at different times for pictorial clarity. This is not really a Penrose diagram -- the mappings between the coordinate systems do not preserve circular symmetry, and so we have simply displayed fixed angle slices in each.
  • ...and 2 more figures