scholarly journals 3D gravity, Chern–Simons and higher spins: A mini introduction

2015 ◽  
Vol 30 (32) ◽  
pp. 1530023 ◽  
Author(s):  
K. Surya Kiran ◽  
Chethan Krishnan ◽  
Avinash Raju
Keyword(s):  
Flat Space ◽  
Simons Theory ◽  
Abelian Gauge ◽  
Higher Spin ◽  
Dimensional Gravity ◽  
3D Gravity ◽  
Higher Spins ◽  
Chern Simons ◽  
Hilbert Action ◽  
Chern Simons Theory

We give a review on (a) elements of (2+1)-dimensional gravity, (b) some aspects of its relation to Chern–Simons theory, (c) its generalization to couple higher spins, and (d) cosmic singularity resolution as an application in the context of flat space higher spin theory. A knowledge of the Einstein–Hilbert action, classical non-Abelian gauge theory and some (negotiable amount of) maturity are the only pre-requisites.

scholarly journals Poincaré series, 3d gravity and averages of rational CFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Viraj Meruliya ◽  
Sunil Mukhi ◽  
Palash Singh
Keyword(s):  
Poincaré Series ◽  
Simons Theory ◽  
Partition Functions ◽  
Moody Algebra ◽  
Modular Invariant ◽  
Poincare Series ◽  
Single Genus ◽  
3D Gravity ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We investigate the Poincaré series approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)k WZW models provide unitary examples for which the Poincaré series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT’s sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and all relevant values of k. We then study other WZW models, notably SU(N)1 and SU(3)k, and find that each class presents rather different features. Finally we consider multiple genus-1 boundaries, where we find a class of seed functions for the Poincaré sum that reproduces both disconnected and connected contributions — the latter corresponding to analogues of 3-manifold “wormholes” — such that the expected average is correctly reproduced.

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 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 REPRESENTATIONS OF COMPOSITE BRAIDS AND INVARIANTS FOR MUTANT KNOTS AND LINKS IN CHERN-SIMONS FIELD THEORIES

1995 ◽  
Vol 10 (22) ◽  
pp. 1635-1658 ◽  
Author(s):  
P. RAMADEVI ◽  
T.R. GOVINDARAJAN ◽  
R.K. KAUL
Keyword(s):  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Abelian Gauge ◽  
Gauge Groups ◽  
Knot Invariants ◽  
Conformal Field ◽  
Chern Simons ◽  
Knots And Links ◽  
Chern Simons Theory

We show that any of the new knot invariants obtained from Chern-Simons theory based on an arbitrary non-Abelian gauge group do not distinguish isotopically inequivalent mutant knots and links. In an attempt to distinguish these knots and links, we study Murakami (symmetrized version) r-strand composite braids. Salient features of the theory of such composite braids are presented. Representations of generators for these braids are obtained by exploiting properties of Hilbert spaces associated with the correlators of Wess-Zumino conformal field theories. The r-composite invariants for the knots are given by the sum of elementary Chern-Simons invariants associated with the irreducible representations in the product of r representations (allowed by the fusion rules of the corresponding Wess-Zumino conformal field theory) placed on r individual strands of the composite braid. On the other hand, composite invariants for links are given by a weighted sum of elementary multicolored Chern-Simons invariants. Some mutant links can be distinguished through the composite invariants, but mutant knots do not share this property. The results, though developed in detail within the framework of SU(2) Chern-Simons theory are valid for any other non-Abelian gauge groups.

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 Erratum to: “A higher-spin Chern–Simons theory of anyons”

2016 ◽  
Vol 13 (3) ◽  
pp. 416-416
Author(s):  
N. Boulanger ◽  
P. Sundell ◽  
M. Valenzuela
Keyword(s):  
Simons Theory ◽  
Higher Spin ◽  
Chern Simons ◽  
Chern Simons Theory
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