Metric-like formalism for matter fields coupled to 3D higher spin gravity

DOI10.1088/0264-9381/31/1/015003zbMATH Open1287.83038arXiv1304.7941OpenAlexW2149420600MaRDI QIDQ5405315

Author name not available (Why is that?)

Publication date: 2 April 2014

Published in: (Search for Journal in Brave)

Abstract: Action integral for a matter system composed of 0- and 2-forms,

C

and

B_{m u u}

, topologically coupled to 3D spin-3 gravity is considered first in the frame-like formalism. The field

C

satisfies an eq of motion,

. With a suitable gauge fixing of a new local symmetry and diffeomorphism, only one component of

B_{m u u}

, say

B_{p h i r}

, remains non-vanishing and satisfies an equation similar to that for

C

with

A_{m u}

and

interchanged. The spin connection is eliminated by solving the eq of motion for the total action, and in the resulting metric-like formalism,

(B C)^{2}

interaction terms are induced because of the torsion. The world-volume components of the matter field,

C^{0}

,

C^{m u}

and

C^{(m u u)}

, are introduced by contracting the local-frame index of

C

with those of the inverse vielbeins,

E_{a}^{m u}

and

E_{a}^{(m u u)}

, which were defined by the present authors in ArXiv:1209.0894 [hep-th]. The metric-like fields, as well as the new connections and the generalized curvature tensors, introduced in the above mentioned paper, are explicitly expressed in terms of the metric

g_{m u u}

and the spin-3 field

p h i_{m u u l a m b d a}

by means of the

p h i

-expansion. The action integral for the pure spin-3 gravity in the metric-like formalism up to

c a l O (p h i^{2})

, obtained before in the literature, is re-derived. Then the matter action is re-expressed in terms of

g_{m u u}

,

p h i_{m u u h o}

and the covariant derivatives for spin-3 geometry. Spin-3 gauge transformation is extended to the matter fields.

Full work available at URL: https://arxiv.org/abs/1304.7941

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