scholarly journals Exploring three-dimensional higher-spin supergravity based on sl(N|N − 1) Chern-Simons theories

2012 ◽  
Vol 2012 (11) ◽  
Author(s):  
Hai Siong Tan
Keyword(s):  
Three Dimensional ◽  
Higher Spin ◽  
Chern Simons

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 Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Zhijin Li
Keyword(s):  
Higher Spin Symmetry ◽  
Three Dimensional ◽  
Spin Symmetry ◽  
Complete Classification ◽  
Point Function ◽  
Opposite Parity ◽  
Hooft Coupling ◽  
Higher Spin ◽  
Single Trace ◽  
Chern Simons

Abstract Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the planar four-point functions at arbitrary ’t Hooft coupling λ in the CFTs with slightly broken higher spin symmetry. We use a bootstrap approach based on the approximate higher spin Ward identity. We show that the bootstrap equation is separated into two parts with opposite parity charges, and it leads to a recursion relation for the λ expansions of the correlation functions. The λ expansions terminate at order λ2 and the solutions are exact in λ. Our work generalizes the approach proposed by Maldacena and Zhiboedov to four-point correlators, and it amounts to an on-shell study for the 3D Chern-Simons vector models and their holographic duals in AdS4. Besides, we show that the same results can also be obtained rather simply from bosonization duality of 3D Chern-Simons vector models. The odd term at order O(λ) in the spinning four-point function relates to the free boson correlator through a Legendre transformation. This provides new evidence on the 3D bosonization duality at the spinning four-point function level. We expect this work can be generalized to a complete classification of general four-point functions of single trace currents.

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 The 3d $$ \mathcal{N} $$ = 6 bootstrap: from higher spins to strings to membranes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Damon J. Binder ◽  
Shai M. Chester ◽  
Max Jerdee ◽  
Silviu S. Pufu
Keyword(s):  
Block Decomposition ◽  
Point Function ◽  
Present Evidence ◽  
Bootstrap Techniques ◽  
Wide Range ◽  
Higher Spin ◽  
Tensor Multiplet ◽  
Higher Spins ◽  
M Theory ◽  
Chern Simons

Abstract We study the space of 3d $$ \mathcal{N} $$ N = 6 SCFTs by combining numerical bootstrap techniques with exact results derived using supersymmetric localization. First we derive the superconformal block decomposition of the four-point function of the stress tensor multiplet superconformal primary. We then use supersymmetric localization results for the $$ \mathcal{N} $$ N = 6 U(N)k × U(N + M)−k Chern-Simons-matter theories to determine two protected OPE coefficients for many values of N, M, k. These two exact inputs are combined with the numerical bootstrap to compute precise rigorous islands for a wide range of N, k at M = 0, so that we can non-perturbatively interpolate between SCFTs with M-theory duals at small k and string theory duals at large k. We also present evidence that the localization results for the U(1)2M × U (1 + M)−2M theory, which has a vector-like large-M limit dual to higher spin theory, saturates the bootstrap bounds for certain protected CFT data. The extremal functional allows us to then conjecturally reconstruct low-lying CFT data for this theory.

scholarly journals Fermi gas approach to general rank theories and quantum curves

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Naotaka Kubo
Keyword(s):  
Matrix Models ◽  
Critical Role ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Partition Functions ◽  
Density Matrices ◽  
General Rank ◽  
Chern Simons ◽  
The Ideal

Abstract It is known that matrix models computing the partition functions of three-dimensional $$ \mathcal{N} $$ N = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.

scholarly journals Wilson loop algebras and quantum K-theory for Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Line ◽  
Quantum Cohomology ◽  
Three Dimensional ◽  
Loop Algebra ◽  
Loop Algebras ◽  
Verlinde Algebra ◽  
K Theory ◽  
Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Three-dimensional Maxwellian extended Newtonian gravity and flat limit

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Patrick Concha ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez ◽  
Gustavo Rubio
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Expansion Method ◽  
Gravity Models ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
Relativistic Limit ◽  
Expansion Procedure ◽  
Three Space ◽  
Chern Simons

Abstract In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.

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.

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