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A. Castro
spin sector can be consistently described using Chern–Simons theory. Depending on
the gauge group we assign to the theory, we will have a different spectrum of higher
spin fields. For example, these include pure AdS 3 gravity [1, 2], gravity coupled
to Abelian gauge fields, and a tower of massless spin-s fields coupled to a gravity,
among many other examples. This can be viewed as truncations of the interacting
Prokushkin–Vasiliev higher spin theory [3, 4] which includes in addition massive
scalar fields.
In the context of AdS 3 /CFT 2 , the Chern–Simons sector captures the chiral
algebra of the dual two-dimensional CFTs which have an extended symmetry
algebras of W-type [5–8]. And here is where the AdS/CFT correspondence has
provided a useful framework to organize our understanding of higher spin gravity:
it is rather clear how to define, e.g. correlation functions, currents, and sources
on both sides of the correspondence. What this description lacks is the addition
of light primary fields that are generic in CFTs. Nevertheless, the Chern–Simons
sector will suffice to probe how deviations from general relativity can affect our
understanding of gravity, and in particular the mechanics behind black holes. For
reviews on holographic aspects of AdS 3 /CFT 2 involving higher spin fields, we refer
the reader to [9, 10] and references within.
As we mentioned before, our main goal here is to be capable of describing
black holes in higher spin gravity. In the absence of a metric, which is crucial
for giving a notion of causality, it is rather non-trivial to think of a definition
of black hole at a non-linear and non-local level. Is it the horizon its defining
property? Is it the high mass density that gives rise to a curvature singularity? Is
it the thermodynamic nature the defining feature? Or the fact that it is the fastest
scrambler? Or something else, such as the ring-down pattern? All of these are, in
my opinion, valid starting points. The remarkable property of general relativity is
that these facts are generically implied by each other. But as we modify violently
the interactions, it is not clear if we should expect that these different properties are
still so intimately tied: perhaps one could find important deviations from the usual
lore in a two-derivative theory of gravity.
In the following I will present one general strategy our community has taken to
define a black hole in higher spin gravity. This strategy was initially put forward in
the original proposal of [11] and further refined in later work, as we will elaborate
in the following sections. I leave it as a challenge to the reader to further explore
and question this starting point: any deviations from the lore of GR would be very
interesting! And as we will see, some of these deviations are already present given
the modest starting point we take.
This talk covers only three topics in this field: Euclidean black holes (Sect. 3),
extremal black holes (Sect. 4), and Wilson lines in higher spin gravity (Sect. 5).
There are also many other topics in higher spin gravity that I will not explore. I
will provide references as appropriate, but unfortunately the field is rather large so
many interesting corners will be left out here.
A. Castro
spin sector can be consistently described using Chern–Simons theory. Depending on
the gauge group we assign to the theory, we will have a different spectrum of higher
spin fields. For example, these include pure AdS 3 gravity [1, 2], gravity coupled
to Abelian gauge fields, and a tower of massless spin-s fields coupled to a gravity,
among many other examples. This can be viewed as truncations of the interacting
Prokushkin–Vasiliev higher spin theory [3, 4] which includes in addition massive
scalar fields.
In the context of AdS 3 /CFT 2 , the Chern–Simons sector captures the chiral
algebra of the dual two-dimensional CFTs which have an extended symmetry
algebras of W-type [5–8]. And here is where the AdS/CFT correspondence has
provided a useful framework to organize our understanding of higher spin gravity:
it is rather clear how to define, e.g. correlation functions, currents, and sources
on both sides of the correspondence. What this description lacks is the addition
of light primary fields that are generic in CFTs. Nevertheless, the Chern–Simons
sector will suffice to probe how deviations from general relativity can affect our
understanding of gravity, and in particular the mechanics behind black holes. For
reviews on holographic aspects of AdS 3 /CFT 2 involving higher spin fields, we refer
the reader to [9, 10] and references within.
As we mentioned before, our main goal here is to be capable of describing
black holes in higher spin gravity. In the absence of a metric, which is crucial
for giving a notion of causality, it is rather non-trivial to think of a definition
of black hole at a non-linear and non-local level. Is it the horizon its defining
property? Is it the high mass density that gives rise to a curvature singularity? Is
it the thermodynamic nature the defining feature? Or the fact that it is the fastest
scrambler? Or something else, such as the ring-down pattern? All of these are, in
my opinion, valid starting points. The remarkable property of general relativity is
that these facts are generically implied by each other. But as we modify violently
the interactions, it is not clear if we should expect that these different properties are
still so intimately tied: perhaps one could find important deviations from the usual
lore in a two-derivative theory of gravity.
In the following I will present one general strategy our community has taken to
define a black hole in higher spin gravity. This strategy was initially put forward in
the original proposal of [11] and further refined in later work, as we will elaborate
in the following sections. I leave it as a challenge to the reader to further explore
and question this starting point: any deviations from the lore of GR would be very
interesting! And as we will see, some of these deviations are already present given
the modest starting point we take.
This talk covers only three topics in this field: Euclidean black holes (Sect. 3),
extremal black holes (Sect. 4), and Wilson lines in higher spin gravity (Sect. 5).
There are also many other topics in higher spin gravity that I will not explore. I
will provide references as appropriate, but unfortunately the field is rather large so
many interesting corners will be left out here.