Probes in AdS 3 Quantum Gravity
Alejandra Castro
Abstract The Chern–Simons formulation of three-dimensional gravity is a powerful framework to explore non-perturbative aspects of quantum gravity; it allows
us to describe properties of gravitational theories without resorting to a metric
description. For higher spin gravity this is particularly important, where a geometric
formulation can be cumbersome. Here we will review how this formalism has
provided unique insights regarding the local properties of higher spin gravity in
AdS 3 . We will discuss various definitions of black holes in AdS 3 gravity, and how
to probe them using the observables that naturally arise in Chern–Simons theory.
Keywords AdS/CFT · Black holes · Higher spin gravity
1 Introduction
Higher spin theories are gravitational theories that challenge our geometrical
intuition. A higher spin theory is characterized by being somewhat crowed by
symmetries: the theory introduces massless higher spin fields whose gauge symmetries and interactions spoil the standard notions of causality and curvature that
we hold sacred otherwise. Very natural concepts in general relativity, such as black
holes, become rather puzzling in higher spin gravity. This makes higher spin gravity
an excellent arena to explore the repercussions of having violent modifications of
general relativity. The aim of this review is to explore potential definitions of black
holes in gravitational theories that lack such a geometrical description.
An important appeal of higher spin gravity is that it allows us to introduce nonlinear and non-geometrical features classically. These are features we expect to
arise in quantum gravity, but are generically difficult to quantify. Within higher spin
gravity there is a rather powerful example: in three dimensions the massless higher
A. Castro ()
Institute for Theoretical Physics, University of Amsterdam, Amsterdam, The Netherlands
e-mail: a.castro@uva.nl
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_36
389
Alejandra Castro
Abstract The Chern–Simons formulation of three-dimensional gravity is a powerful framework to explore non-perturbative aspects of quantum gravity; it allows
us to describe properties of gravitational theories without resorting to a metric
description. For higher spin gravity this is particularly important, where a geometric
formulation can be cumbersome. Here we will review how this formalism has
provided unique insights regarding the local properties of higher spin gravity in
AdS 3 . We will discuss various definitions of black holes in AdS 3 gravity, and how
to probe them using the observables that naturally arise in Chern–Simons theory.
Keywords AdS/CFT · Black holes · Higher spin gravity
1 Introduction
Higher spin theories are gravitational theories that challenge our geometrical
intuition. A higher spin theory is characterized by being somewhat crowed by
symmetries: the theory introduces massless higher spin fields whose gauge symmetries and interactions spoil the standard notions of causality and curvature that
we hold sacred otherwise. Very natural concepts in general relativity, such as black
holes, become rather puzzling in higher spin gravity. This makes higher spin gravity
an excellent arena to explore the repercussions of having violent modifications of
general relativity. The aim of this review is to explore potential definitions of black
holes in gravitational theories that lack such a geometrical description.
An important appeal of higher spin gravity is that it allows us to introduce nonlinear and non-geometrical features classically. These are features we expect to
arise in quantum gravity, but are generically difficult to quantify. Within higher spin
gravity there is a rather powerful example: in three dimensions the massless higher
A. Castro ()
Institute for Theoretical Physics, University of Amsterdam, Amsterdam, The Netherlands
e-mail: a.castro@uva.nl
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_36
389