Ordinary-derivative formulation of conformal low-spin fields

R. R. Metsaev

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Ordinary-derivative formulation of conformal low-spin fields

R. R. Metsaev

High Energy Physics - Theory · Submitted 30 Jul 2007

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The authors' main claim Ordinary-derivative Lagrangian of interacting Weyl gravity in 4d is obtained.

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Conformal fields in flat space-time of even dimension greater than or equal to four are studied. Second-derivative formulation for spin 0,1,2 conformal bosonic fields and first-derivative formulation for spin 1/2,3/2 conformal fermionic fields are developed. For the spin 1,3/2,2 conformal fields, we obtain gauge invariant Lagrangians and the corresponding gauge transformations. Gauge symmetries are realized by involving Stueckelberg fields and auxiliary fields. Realization of global conformal boost symmetries is obtained. Modified Lorentz and de Donder gauge conditions are introduced. Ordinary-derivative Lagrangian of interacting Weyl gravity in 4d is obtained. In our approach, the field content of Weyl gravity, in addition to conformal graviton field, includes one auxiliary rank-2 symmetric tensor field and one Stueckelberg vector field. With respect to the auxiliary tensor field, the Lagrangian contains, in addition to other terms, the Pauli-Fierz mass term. Using the ordinary-derivative Lagrangian of Weyl gravity, we discuss interrelation of Einstein AdS gravity and Weyl gravity via breaking conformal gauge symmetries. Also, we demonstrate use of the light-cone gauge for counting on-shell degrees of freedom in higher-derivative conformal field theories.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Conformal fields in flat space-time of even dimension greater than or equal to four are studied.	background 0.76	0.62	0.03	asserted 0.91
s1	Second-derivative formulation for spin 0,1,2 conformal bosonic fields and first-derivative formulation for spin 1/2,3/2 conformal fermionic fields are developed.	contribution 0.83	0.93	0.15	asserted 1.00
s2	For the spin 1,3/2,2 conformal fields, we obtain gauge invariant Lagrangians and the corresponding gauge transformations.	result 0.53	0.94	0.12	asserted 1.00
s3	Gauge symmetries are realized by involving Stueckelberg fields and auxiliary fields.	method 0.80	0.86	0.06	asserted 1.00
s4	Realization of global conformal boost symmetries is obtained.	result 0.72	0.91	0.09	asserted 1.00
s5	Modified Lorentz and de Donder gauge conditions are introduced.	method 0.67	0.89	0.04	asserted 1.00
s6	Ordinary-derivative Lagrangian of interacting Weyl gravity in 4d is obtained.	result 0.54	0.95	0.27	asserted 1.00
s7	In our approach, the field content of Weyl gravity, in addition to conformal graviton field, includes one auxiliary rank-2 symmetric tensor field and one Stueckelberg vector field.	result 0.81	0.88	0.13	asserted 1.00
s8	With respect to the auxiliary tensor field, the Lagrangian contains, in addition to other terms, the Pauli-Fierz mass term.	result 0.93	0.88	0.08	asserted 1.00
s9	Using the ordinary-derivative Lagrangian of Weyl gravity, we discuss interrelation of Einstein AdS gravity and Weyl gravity via breaking conformal gauge symmetries.	contribution 0.60	0.93	0.19	asserted 0.98
s10	Also, we demonstrate use of the light-cone gauge for counting on-shell degrees of freedom in higher-derivative conformal field theories.	contribution 0.79	0.90	0.07	asserted 1.00

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Original abstract

Conformal fields in flat space-time of even dimension greater than or equal to four are studied. Second-derivative formulation for spin 0,1,2 conformal bosonic fields and first-derivative formulation for spin 1/2,3/2 conformal fermionic fields are developed. For the spin 1,3/2,2 conformal fields, we obtain gauge invariant Lagrangians and the corresponding gauge transformations. Gauge symmetries are realized by involving Stueckelberg fields and auxiliary fields. Realization of global conformal boost symmetries is obtained. Modified Lorentz and de Donder gauge conditions are introduced. Ordinary-derivative Lagrangian of interacting Weyl gravity in 4d is obtained. In our approach, the field content of Weyl gravity, in addition to conformal graviton field, includes one auxiliary rank-2 symmetric tensor field and one Stueckelberg vector field. With respect to the auxiliary tensor field, the Lagrangian contains, in addition to other terms, the Pauli-Fierz mass term. Using the ordinary-derivative Lagrangian of Weyl gravity, we discuss interrelation of Einstein AdS gravity and Weyl gravity via breaking conformal gauge symmetries. Also, we demonstrate use of the light-cone gauge for counting on-shell degrees of freedom in higher-derivative conformal field theories.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Partially Massless Fields During Inflation
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Einstein Gravity from Conformal Gravity
hep-th 2011-05 conditional novelty 7.0 of 10

A Neumann boundary condition on four-dimensional conformal gravity selects the Einstein solutions at tree level, so its action reproduces the semiclassical de Sitter and Euclidean anti-de Sitter wavefunctions, and in ...
Partially-massless higher-spin algebras and their finite-dimensional truncations
hep-th 2015-08 conditional novelty 6.0 of 10

Partially-massless higher-spin algebras truncate to finite-dimensional algebras identified with the symmetry algebras of one-row Young-diagram representations of so(d+2) when the continuous parameter equals d/2 plus a...
Partition function of free conformal higher spin theory
hep-th 2014-06 conditional novelty 6.0 of 10

The canonical partition function of free conformal higher-spin theory is computed in closed form for all even dimensions, and the summed Casimir energy vanishes under the regularization that also cancels the conformal...
On partition function and Weyl anomaly of conformal higher spin fields
hep-th 2013-09 accept novelty 5.0 of 10

The 4D conformal higher-spin partition function factorizes into partially-massless determinants, yielding spin-s Weyl anomaly coefficients whose bosonic a_s matches an independent AdS/CFT result and whose regularized ...

Show 1 more citing papers

Partial Masslessness and Conformal Gravity
hep-th 2012-08 accept novelty 5.0 of 10

Partially massless spin-2 fields propagate only in Einstein backgrounds and cannot be extended to a fully interacting theory via conformal gravity, which generates only the standard cubic Noether vertices.

How the literature uses it

38 arXiv papers cite this in 88 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 60 sentences without a confident label

Builds on it 5 papers

In the present paper, we generalize results in Ref [ref] to the case of arbitrary spin bosonic conformal fields.

Ordinary-derivative formulation of conformal totally symmetric arbitrary spin bosonic fields · Introduction · 1.00
In other words, in this paper we extend approach in Refs. [ref] to the cases of the long, partial-short and special conformal fields.

Long, partial-short, and special conformal fields · Introduction · 1.00
The present paper is a sequel to our papers [ref] , where the ordinary-derivative formulation of conformal fields was developed.

Conformal totally symmetric arbitrary spin fermionic fields · Introduction · 0.94

Uses its method or tool 5 papers

i) To obtain light-cone gauge formalism for the fields, we use Lagrangian gauge invariant formulation of AdS fields developed in Refs. [ref] and gauge invariant Lagrangian ordinary-derivative formulation of conformal fields in flat space developed in Refs. [ref] .

Light-cone gauge approach to arbitrary spin fields, currents, and shadows · Introduction · 0.99
In this paper, we applied the ordinary-derivative approach, developed in Ref. [ref] , to the study of conformal self-dual fields in flat space of even dimension.

Conformal self-dual fields · Standard approach to self-dual fields · 0.98
In this paper we discuss $6d$ conformal gravity using the framework of ordinary-derivative approach developed in Ref. [ref] .

6d conformal gravity · Introduction · 0.94

Compares with it 6 papers

[For $(A)dS_4$, we note the interesting coincidence of the mass square for shift symmetric $k=0$ abelian massive vector field in Ref. [ref] and mass square of the abelian massive vector field entering unitary subsector of $4d$ conformal gravity in Sec.6 in Ref. [ref] .]

Conformal Yang-Mills field in (A)dS space · Introduction · 0.84
For the case of symmetric HS fields, it would be interesting to compare the result with the nonlinear action proposed by Segal [ref] and with the free second-order action proposed by Metsaev [ref] .

Bosonic conformal higher--spin fields of any symmetry · Weyl module · 0.98
Dependence on derivatives of $R^a$ appears e.g., in ordinary-derivative approach to conformal fields [ref] .]

Gauge invariant two-point vertices of shadow fields, AdS/CFT, and conformal fields · Global conformal symmetries · 0.93

Cites it as background 8 papers

For conformal field in flat space, Lagrangian man02-26112011-11xx was obtained in Refs. [ref] .

Light-cone gauge approach to arbitrary spin fields, currents, and shadows · Introduction · 0.89
[ Ordinary-derivative actions for conformal fields are discussed in Refs. [ref] - [ref] .]

CFT adapted approach to massless fermionic fields, AdS/CFT, and fermionic conformal fields · Conformal fermionic fields · 0.99
Ordinary-derivative Lagrangian for fields man-14122016-08 may be found in Ref. [ref] .

General light-cone gauge approach to conformal fields and applications to scalar and vector fields · Introduction · 0.91

What it cites · 16 sentences without a confident label

Uses the method or tool of 2 papers

[ To realize those additional gauge symmetries we adopt the approach of Refs. [ref] which turns out to be the most useful for our purposes.]; iii) realization of global conformal symmetries should be local.

On Massive High Spin Particles in (A)dS · Introduction · 0.99
[ To realize those additional gauge symmetries we adopt the approach of Refs. [ref] which turns out to be the most useful for our purposes.]; iii) realization of global conformal symmetries should be local.

Gauge invariant formulation of massive totally symmetric fermionic fields in (A)dS space · Introduction · 0.99

Cites as background 18 papers

It is the shadow fields that are used to discuss conformally invariant equations of motion and Lagrangian formulations (see e.g. [ref] , [ref] , [ref]

Conformal Higher Spin Theory · Introduction · 0.87
It is the shadow fields that are used to discuss conformally invariant equations of motion and Lagrangian formulations (see e.g. [ref] , [ref] , [ref]

Conformally Covariant Differential Operators: Properties and Applications · Introduction · 0.87
[ In the framework higher-derivative formulation, uniqueness of interacting spin 2 conformal field theory was discussed in [ref] .]

A derivation of Weyl gravity · Ordinary-derivative formulation of spin 3/2 conformal fermionic Dirac field · 0.92

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