scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

scholarly journals Higher spin Chern–Simons theory and the super Boussinesq hierarchy

2018 ◽  
Vol 33 (14n15) ◽  
pp. 1850085
Author(s):  
Michael Gutperle ◽  
Yi Li
Keyword(s):  
Time Evolution ◽  
Gauge Transformation ◽  
Poisson Structure ◽  
Higher Spin Gravity ◽  
Hamiltonian Structure ◽  
Evolution Equations ◽  
Simons Theory ◽  
Higher Spin ◽  
Chern Simons ◽  
Chern Simons Theory

In this paper, we construct a map between a solution of supersymmetric Chern–Simons higher spin gravity based on the superalgebra [Formula: see text] with Lifshitz scaling and the [Formula: see text] super Boussinesq hierarchy. We show that under this map the time evolution equations of both theories coincide. In addition, we identify the Poisson structure of the Chern–Simons theory induced by gauge transformation with the second Hamiltonian structure of the super Boussinesq hierarchy.

scholarly journals Chern-Simons: Fano and Calabi-Yau

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Amihay Hanany ◽  
Yang-Hui He
Keyword(s):  
Algebraic Geometry ◽  
Complete Classification ◽  
Simons Theory ◽  
Del Pezzo Surfaces ◽  
Fano Threefolds ◽  
Del Pezzo ◽  
Chern Simons ◽  
Chern Simons Theory

We present the complete classification of smooth toric Fano threefolds, known to the algebraic geometry literature, and perform some preliminary analyses in the context of brane tilings and Chern-Simons theory on M2-branes probing Calabi-Yau fourfold singularities. We emphasise that these 18 spaces should be as intensely studied as their well-known counterparts: the del Pezzo surfaces.

scholarly journals A classification of semilocal vortices in a Chern–Simons theory

2016 ◽  
Vol 33 (2) ◽  
pp. 575-595
Author(s):  
Jann-Long Chern ◽  
Zhi-You Chen ◽  
Sze-Guang Yang
Keyword(s):  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals A higher-spin Chern-Simons theory of anyons

2014 ◽  
Vol 11 (7) ◽  
pp. 977-980 ◽  
Author(s):  
N. Boulanger ◽  
P. Sundell ◽  
M. Valenzuela
Keyword(s):  
Simons Theory ◽  
Higher Spin ◽  
Chern Simons ◽  
Chern Simons Theory

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 Chern-Simons matter theories and higher spin gravity

2017 ◽  
Vol 2017 (7) ◽  
Author(s):  
Ergin Sezgin ◽  
Evgeny D. Skvortsov ◽  
Yaodong Zhu
Keyword(s):  
Higher Spin Gravity ◽  
Higher Spin ◽  
Chern Simons

scholarly journals Integrability and spectral form factor in Chern–Simons formulation

2020 ◽  
Vol 35 (24) ◽  
pp. 2050143
Author(s):  
Chen-Te Ma ◽  
Hongfei Shu
Keyword(s):  
Form Factor ◽  
Random Matrix ◽  
Integrable Model ◽  
Toda Chain ◽  
Simons Theory ◽  
Spectral Form ◽  
Higher Spin ◽  
Chain Theory ◽  
Matrix Spectrum ◽  
Chern Simons

We study the integrability from the spectral form factor in the Chern–Simons formulation. The effective action in the higher spin sector was not derived so far. Therefore, we begin from the SL(3) Chern–Simons higher spin theory. Then the dimensional reduction in this Chern–Simons theory gives the SL(3) reparametrization invariant Schwarzian theory, which is the boundary theory of an interacting theory between the spin-2 and spin-3 fields at the infrared or massless limit. We show that the Lorentzian SL(3) Schwarzian theory is dual to the integrable model, SL(3) open Toda chain theory. Finally, we demonstrate the application of open Toda chain theory from the SL(2) case. The numerical result shows that the spectral form factor loses the dip-ramp-plateau behavior, consistent with integrability. The spectrum is not a Gaussian random matrix spectrum. We also give an exact solution of the spectral form factor for the SL(3) theory. This solution provides a similar form to the SL(2) case for [Formula: see text]. Hence the SL(3) theory should also do not have a Gaussian random matrix spectrum.

scholarly journals Supersymmetric localization on dS: sum over topologies

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Rudranil Basu ◽  
Augniva Ray
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Higher Spin Gravity ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Higher Spin ◽  
3D Gravity ◽  
Chern Simons ◽  
Perturbative Result

AbstractWe find the exact quantum gravity partition function on the static patch of 3d de Sitter spacetime. We have worked in the Chern Simons formulation of 3d gravity. To obtain a non-perturbative result, we supersymmetrized the Chern Simons action and used the technique of supersymmetric localization. We have obtained an exact non-perturbative result for the spin-2 gravity case. We comment on the divergences present in the theory. We also comment on higher spin gravity theories and analyse the nature of divergences present in such theories.

scholarly journals Averaging over moduli in deformed WZW models

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Junkai Dong ◽  
Thomas Hartman ◽  
Yikun Jiang
Keyword(s):  
Moduli Space ◽  
Central Charge ◽  
Principal Result ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Chern Simons ◽  
Conserved Currents ◽  
Matter Fields ◽  
Chern Simons Theory

Abstract WZW models live on a moduli space parameterized by current-current deformations. The moduli space defines an ensemble of conformal field theories, which generically have N abelian conserved currents and central charge c > N. We calculate the average partition function and show that it can be interpreted as a sum over 3-manifolds. This suggests that the ensemble-averaged theory has a holographic dual, generalizing recent results on Narain CFTs. The bulk theory, at the perturbative level, is identified as U(1)2N Chern-Simons theory coupled to additional matter fields. From a mathematical perspective, our principal result is a Siegel-Weil formula for the characters of an affine Lie algebra.

Sign in / Sign up

Export Citation Format

Share Document