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Real-time gauge/gravity duality and ingoing boundary conditions

Balt C. van Rees

Abstract

In arXiv:0805.0150 [hep-th] and arXiv:0812.2909 [hep-th] a general prescription was presented for the computation of real-time correlation functions using the gauge/gravity duality. I apply this prescription to the specific case of retarded thermal correlation functions and derive the usual ingoing boundary conditions at the horizon for bulk fields. The derivation allows me to clarify various issues, in particular the generalization to higher-point functions and the relevance of including the regions beyond the horizon.

Real-time gauge/gravity duality and ingoing boundary conditions

Abstract

In arXiv:0805.0150 [hep-th] and arXiv:0812.2909 [hep-th] a general prescription was presented for the computation of real-time correlation functions using the gauge/gravity duality. I apply this prescription to the specific case of retarded thermal correlation functions and derive the usual ingoing boundary conditions at the horizon for bulk fields. The derivation allows me to clarify various issues, in particular the generalization to higher-point functions and the relevance of including the regions beyond the horizon.

Paper Structure

This paper contains 8 sections, 15 equations, 2 figures.

Table of Contents

  1. Introduction
  2. A complete dictionary
  3. Ingoing boundary conditions
  4. On-shell action and correlation functions
  5. Higher-point correlation functions
  6. Conclusion
  7. Discussion
  8. Acknowledgments

Figures (2)

  • Figure 1: A real-time thermal contour in the complex time plane. The circles should be identified. The two Lorentzian segments are labelled 1 and 2 on which we have sources $J_1$ and $J_2$, respectively.
  • Figure 2: The Euclidean segment of the contour is filled in with a disk; the two Lorentzian segments with two copies of a part of an eternal black hole.