New conformal higher spin gravities in 3d

Grigoriev, Maxim; Lovrekovic, Iva; Skvortsov, Evgeny

doi:10.1007/jhep01(2020)059

Cited by 46 publications

(56 citation statements)

References 67 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Models for generalised conformal higher-spin gauge fields [16][17][18][19][20][21][22][23][24][25] in arbitrary conformally flat backgrounds were first constructed in [15]. Below we summarise their main properties.…”

Section: Generalised Conformal Gauge Fieldsmentioning

confidence: 99%

“…However, such a formulation has been developed only recently [15], and it also works for generalised CHS models. The latter describe conformal spin-s fields of depth t > 1, which have been studied for more than thirty years [16][17][18][19][20][21][22][23][24][25]. Dynamics of the conformal graviton (s = 2) can be consistently defined on an arbitrary Bach-flat background, since the corresponding gauge-invariant model is obtained by linearising the Weyl gravity action about its stationary point, and the equation of motion for conformal gravity is that the Bach tensor vanishes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalised conformal higher-spin fields in curved backgrounds

Kuzenko

Ponds

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

The problem of constructing gauge-invariant actions for conformal higher-spin fields in curved backgrounds is known to be notoriously difficult. In this paper we present gauge-invariant models for conformal maximal depth fields with spin s = 5/2 and s = 3 in four-dimensional Bach-flat backgrounds. We find that certain lower-spin fields must be introduced to ensure gauge invariance when s > 2, which is analogous to a conjecture made earlier in the literature for conformal higher-spin fields of minimal depth.

show abstract

Section: Generalised Conformal Gauge Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalised conformal higher-spin fields in curved backgrounds

Kuzenko

Ponds

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…This is an algebraic equation for the Ricci tensor in terms of torsion 21 . The Ricci scalar is obtained by contracting with G νσ ,…”

Section: Vacuum Equation For the Ricci Tensormentioning

confidence: 99%

“…At a more technical level, the present model can be viewed as a reformulation (rather than a 2 It may also be interesting to compare it with chiral higher spin gravity [15,16], where an action can be written in light-cone gauge. An action formulation is also possible for conformal higher spin gravity [17,18], notably in 3 dimensions [19][20][21].3 A somewhat related proposal was put forward in [22] where the matrices are interpreted as covariant derivatives, which formally leads to the Einstein equations. However this is not quite borne out here.…”

mentioning

confidence: 99%

Higher-spin gravity and torsion on quantized space-time in matrix models

Steinacker

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

A geometric formalism is developed which allows to describe the non-linear regime of higher-spin gravity emerging on a cosmological quantum space-time in the IKKT matrix model. The vacuum solutions are Ricci-flat up to an effective vacuum energy-momentum tensor quadratic in the torsion, which arises from a Weitzenböck-type higher spin connection. Torsion is expected to be significant only at cosmic scales and around very massive objects, and could behave like dark matter. A non-linear equation for the torsion tensor is found, which encodes the Yang-Mills equations of the matrix model. The metric and torsion transform covariantly under a higher-spin generalization of volume-preserving diffeomorphisms, which arises from the gauge invariance of the matrix model. known as UV/IR mixing [2][3][4]. They cancel only in the maximally supersymmetric IKKT matrix model [5], which should thus have the best chance to describe physics, leading to an unexpected link with string theory. However, it is not obvious how to obtain gravity from Yang-Mills-type matrix models such as the IKKT model. There are intriguing hints such as non-local gauge transformations and Ricci-flat propagating metric fluctuations [6][7][8], but the presence of an anti-symmetric tensor θ µν in space-time leads to a dangerous breaking of Lorentz invariance. This problem can be overcome by considering a higher-spin generalization, where θ µν is replaced by a twisted bundle of such tensors over space-time. This is realized in a simple solution of the IKKT model with a mass term interpreted as cosmological FLRW space-time M, based on the doubleton representations of so(4, 2) [9, 10], cf. [11]. It leads to a higher spin gauge theory which is invariant under a higher spin generalization of volume-preserving diffeomorphisms, ghost-free at the linearized level, and includes spin 2 gravitons. A linearized Schwarzschild-like solution was also found [12]. The theory has intriguing structural similarities with Vasilievs higherspin gravity [13,14], but also crucial differences 2 : it is defined through an action, both IR and UV scale parameters are present, and there are 5 propagating metric modes which could be interpreted as "would-be massive" gravitons. In the present paper, we study that higher-spin theory at the non-linear level. This is not straightforward because the model is of Yang-Mills type, there is no Einstein-Hilbert action, and everything is based on Poisson brackets (or commutators). The gauge symmetry corresponds to generalized diffeomorphisms rather than local Lorentz transformations 3 , hence it is not some reformulation of GR in the spirit of MacDowell-Mansouri [23]. A more appropriate approach can be found in a paper by Langmann and Szabo (LS) [24], who pointed out that a dimensional reduction of a gauge theory in 8-dimensional phase space with suitable constraints can be interpreted in terms of 4-dimensional teleparallel gravity through torsion. Although their setup does not provide a complete theory, a similar strategy provides a geometric unders...

show abstract

“…In the original calculation of the gravitational parity anomaly [36], just the variations of the structure (27) were considered, exactly for this reason.…”

mentioning

confidence: 99%

Remark on the synergy between the heat kernel techniques and the parity anomaly

Kurkov

Leone

2019

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

In this paper, we demonstrate that not only the heat kernel techniques are useful for computation of the parity anomaly, but also the parity anomaly turns out to be a powerful mean in studying the heat kernel. We show that the gravitational parity anomaly on 4D manifolds with boundaries can be calculated using the general structure of the heat kernel coefficient a 5 for mixed boundary conditions, keeping all the weights of various geometric invariants as unknown numbers. The symmetry properties of the η-invariant allow to fix all the relevant unknowns. As a byproduct of this calculation we get an efficient and independent crosscheck (and confirmation) of the correction of the general structure of a 5 for mixed boundary conditions, previously suggested in Ref.

show abstract

New conformal higher spin gravities in 3d

Cited by 46 publications

References 67 publications

Generalised conformal higher-spin fields in curved backgrounds

Generalised conformal higher-spin fields in curved backgrounds

Higher-spin gravity and torsion on quantized space-time in matrix models

Remark on the synergy between the heat kernel techniques and the parity anomaly

Contact Info

Product

Resources

About