scholarly journals Integrable systems and the boundary dynamics of higher spin gravity on AdS3

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Emilio Ojeda ◽  
Alfredo Pérez
Keyword(s):  
Boundary Conditions ◽  
Gauge Group ◽  
Higher Spin Gravity ◽  
Three Dimensional ◽  
Hamiltonian Reduction ◽  
Asymptotic Region ◽  
Integrable Hierarchy ◽  
Integrable Structure ◽  
Highest Weight ◽  
Higher Spin

Abstract We introduce a new set of boundary conditions for three-dimensional higher spin gravity with gauge group SL(3, ℝ) × SL(3, ℝ), where its dynamics at the boundary is described by the members of the modified Boussinesq integrable hierarchy. In the asymptotic region the gauge fields are written in the diagonal gauge, where the excitations go along the generators of the Cartan subalgebra of sl(3, ℝ) ⊕ sl(3, ℝ). We show that the entire integrable structure of the modified Boussinesq hierarchy, i.e., the phase space, the Poisson brackets and the infinite number of commuting conserved charges, are obtained from the asymptotic structure of the higher spin theory. Furthermore, its known relation with the Boussinesq hierarchy is inherited from our analysis once the asymptotic conditions are re-expressed in the highest weight gauge. Hence, the Miura map is recovered from a purely geometric construction in the bulk. Black holes that fit within our boundary conditions, the Hamiltonian reduction at the boundary, and the generalization to higher spin gravity with gauge group SL(N, ℝ) × SL(N, ℝ) are also discussed.

scholarly journals Chaos in three-dimensional higher spin gravity

2019 ◽  
Vol 2019 (7) ◽  
Author(s):  
Prithvi Narayan ◽  
Junggi Yoon
Keyword(s):  
Higher Spin Gravity ◽  
Three Dimensional ◽  
Higher Spin

scholarly journals Gravitational dual of averaged free CFT’s over the Narain lattice

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Alfredo Pérez ◽  
Ricardo Troncoso
Keyword(s):  
Partition Function ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Simons Theory ◽  
Energy Tensor ◽  
The Family ◽  
Stress Energy ◽  
Higher Spin ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract It has been recently argued that the averaging of free CFT’s over the Narain lattice can be holographically described through a Chern-Simons theory for U (1)D×U (1)D with a precise prescription to sum over three-dimensional handlebodies. We show that a gravitational dual of these averaged CFT’s would be provided by Einstein gravity on AdS3 with U (1)D−1× U (1)D−1 gauge fields, endowed with a precise set of boundary conditions closely related to the “soft hairy” ones. Gravitational excitations then go along diagonal SL (2, ℝ) generators, so that the asymptotic symmetries are spanned by U (1)D× U (1)D currents. The stress-energy tensor can then be geometrically seen as composite of these currents through a twisted Sugawara construction. Our boundary conditions are such that for the reduced phase space, there is a one-to-one map between the configurations in the gravitational and the purely abelian theories. The partition function in the bulk could then also be performed either from a non-abelian Chern-Simons theory for two copies of SL (2, ℝ) × U (1)D−1 generators, or formally through a path integral along the family of allowed configurations for the metric. The new boundary conditions naturally accommodate BTZ black holes, and the microscopic number of states then appears to be manifestly positive and suitably accounted for from the partition function in the bulk. The inclusion of higher spin currents through an extended twisted Sugawara construction in the context of higher spin gravity is also briefly addressed.

scholarly journals Semi-classical unitarity in three-dimensional higher spin gravity for non-principal embeddings

2013 ◽  
Vol 30 (10) ◽  
pp. 104004 ◽  
Author(s):  
H Afshar ◽  
M Gary ◽  
D Grumiller ◽  
R Rashkov ◽  
M Riegler
Keyword(s):  
Higher Spin Gravity ◽  
Three Dimensional ◽  
Higher Spin

scholarly journals Limits of JT gravity

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Daniel Grumiller ◽  
Jelle Hartong ◽  
Stefan Prohazka ◽  
Jakob Salzer
Keyword(s):  
Boundary Conditions ◽  
Light Cone ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Hamiltonian Reduction ◽  
Dilaton Gravity ◽  
Group Manifold ◽  
Particle Action

Abstract We construct various limits of JT gravity, including Newton-Cartan and Carrollian versions of dilaton gravity in two dimensions as well as a theory on the three-dimensional light cone. In the BF formulation our boundary conditions relate boundary connection with boundary scalar, yielding as boundary action the particle action on a group manifold or some Hamiltonian reduction thereof. After recovering in our formulation the Schwarzian for JT, we show that AdS-Carroll gravity yields a twisted warped boundary action. We comment on numerous applications and generalizations.

scholarly journals Black holes in three dimensional higher spin gravity: a review

2013 ◽  
Vol 46 (21) ◽  
pp. 214001 ◽  
Author(s):  
Martin Ammon ◽  
Michael Gutperle ◽  
Per Kraus ◽  
Eric Perlmutter
Keyword(s):  
Black Holes ◽  
Higher Spin Gravity ◽  
Three Dimensional ◽  
Higher Spin

scholarly journals On resolutions of cosmological singularities in higher-spin gravity

2019 ◽  
Vol 28 (15) ◽  
pp. 1950168
Author(s):  
Benjamin Burrington ◽  
Leopoldo A. Pando Zayas ◽  
Nicholas Rombes
Keyword(s):  
Gauge Group ◽  
Three Dimensional ◽  
Big Bang ◽  
Simons Theory ◽  
Gauge Potential ◽  
Cosmological Singularity ◽  
Gauge Transformations ◽  
Higher Spin ◽  
Chern Simons ◽  
Chern Simons Theory

We study the resolution of certain cosmological singularity in the context of higher-spin three-dimensional gravity. We consider gravity coupled to a spin-3 field realized as Chern–Simons theory with gauge group [Formula: see text]. In this context, we elaborate and extend a singularity resolution scheme proposed by Krishnan and Roy. We discuss the resolution of a big bang singularity in the case of gravity coupled to a spin-4 field realized as Chern–Simons theory with gauge group [Formula: see text]. In all these cases, we show the existence of gauge transformations that do not change the holonomy of the Chern–Simons gauge potential and lead to metrics without the initial singularity. We argue that such transformations always exist in the context of gravity coupled to a spin-[Formula: see text] field when described by Chern–Simons with gauge group [Formula: see text].

scholarly journals Asymptotically flat spacetimes in three-dimensional higher spin gravity

2013 ◽  
Vol 2013 (9) ◽  
Author(s):  
Hernán A. González ◽  
Javier Matulich ◽  
Miguel Pino ◽  
Ricardo Troncoso
Keyword(s):  
Higher Spin Gravity ◽  
Three Dimensional ◽  
Asymptotically Flat ◽  
Higher Spin ◽  
Flat Spacetimes

scholarly journals Near horizon dynamics of three dimensional black holes

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Daniel Grumiller ◽  
Wout Merbis
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Einstein Gravity ◽  
Hamiltonian Reduction ◽  
Total Derivative ◽  
Zero Modes ◽  
Derivative Term ◽  
Total Derivative Term

We perform the Hamiltonian reduction of three dimensional Einstein gravity with negative cosmological constant under constraints imposed by near horizon boundary conditions. The theory reduces to a Floreanini–Jackiw type scalar field theory on the horizon, where the scalar zero modes capture the global black hole charges. The near horizon Hamiltonian is a total derivative term, which explains the softness of all oscillator modes of the scalar field. We find also a (Korteweg–de Vries) hierarchy of modified boundary conditions that we use to lift the degeneracy of the soft hair excitations on the horizon.

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