Localized quench in 1+1 conformal field theory

Maria Tikhanovskaya,V.A Andrianov,M.D Fitkevich,A.A Andrianov,V.A Matveev,V.A Rubakov,V.T Kim

doi:10.1051/epjconf/201612505026

Maria Tikhanovskaya, V.A Andrianov + Show 5 more

Open Access

https://doi.org/10.1051/epjconf/201612505026

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Abstract

We study the boundary dual of AdS3 spacetime with a point particle. Particles in AdS3 generate topological defects, which allows to formulate the geodesic image method for boundary correlators. We propose the generalization of the geodesic recipe to arbitrary time intervals in case of the bulk spacetime deformed by a point particle.

Highlights

The AdS/CFT - correspondence [1] is the correspondence between (d + 1) dimensional gravity of the AdS spacetime and d - dimensional quantum field theory on the boundary of the space
We propose the generalization of the geodesic recipe to arbitrary time intervals in case of the bulk spacetime deformed by a point particle
Timelike geodesics in asymptotically AdS spacetimes cannot reach the boundary, the timelike region is unavailable to the prescription, unless there is an analytical continuation from the original Euclidean form

Summary

Introduction

The AdS/CFT - correspondence [1] is the correspondence between (d + 1) dimensional gravity of the AdS spacetime and d - dimensional quantum field theory on the boundary of the space. The geodesic approximation directly relates correlation functions of the boundary QFT to geometry of the bulk spacetime. The geodesic prescription is valid only either for Euclidean spacetimes, or for spacelike-separated points in the Lorentzian case. Timelike geodesics in asymptotically AdS spacetimes cannot reach the boundary, the timelike region is unavailable to the prescription, unless there is an analytical continuation from the original Euclidean form. In [3] a non-trivial Euclidean continuation was constructed for the Vaidya spacetime Another method that was used in [3, 4] is making use of discontinuous timelike geodesics which go through Poincare horizon. In our work the prescription for calculation two point correlation function in geodesic approximation for the case when the particle deforms the AdS3 spacetime is presented. We generalize the prescription to timelike-separated points by utilizing a set of auxiliary geodesics

AdS3 spacetime with particles

AdS3 spacetime with static particle

AdS3 spacetime with moving particle

Holographic image method and correlation function

Conclusion