Matter coupling in Minimal Massive 3D Gravity and spinor-matter interactions in exterior algebra formalism

Abstract

In this work, by employing the exterior algebra formalism, we study the matter coupling in Minimal Massive 3D Gravity (MMG) by first considering that the matter Lagrangian is connection-independent and then considering that the matter coupling is connection-dependent. The matter coupling in MMG has been previously investigated in the work Arvanitakis {\it et al} (2014 {\it Class. Quantum Grav.} {\bf 31} 235012) in tensorial notation where the matter Lagrangian is considered to be connection-independent. In the first part of the present paper, we revisit the connection-independent matter coupling by using the language of differential forms. We derive the MMG field equation and construct the related source 2-form. We also obtain the consistency relation within this formalism. Next, we examine the case where the matter Lagrangian is connection-dependent. In particular, we concentrate on the spinor-matter coupling and obtain the MMG field equation by explicitly constructing the source term. We also get the consistency relation that the source term should satisfy in order that spinor-matter coupled MMG equation be consistent.

arXiv commentUpdated version, Title and Abstract changed, accepted for publication

References in corpus (28)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• Holographic Gravitational Anomalies
• Minimal Massive 3D Gravity
• On the Generalized Minimal Massive Gravity
• Matter coupling in 3D "Minimal Massive Gravity"
• Dirac fields in f(R)-gravity with torsion
• Exotic Massive 3D Gravity
• Extended massive gravity in three dimensions
• Spontaneously Broken 3d Hietarinta/Maxwell Chern-Simons Theory and Minimal Massive Gravity
• On 3D Minimal Massive Gravity
• Minimal Massive 3D Gravity Unitarity Redux
• On Solutions of Minimal Massive 3D Gravity
• On Exact Solutions and the Consistency of 3D Minimal Massive Gravity
• Exotic massive 3D gravities from truncation
• An alternative derivation of the Minimal massive 3D gravity
• On the Energy-Momentum Density of Gravitational Plane Waves
• Kundt solutions of Minimal Massive 3D Gravity
• Homogeneous Solutions of Minimal Massive 3D Gravity
• New Improved Massive Gravity and Three Dimensional Spacetimes of Constant Curvature and Constant Torsion
• "Self-dual" solutions of topologically massive gravity coupled with the Maxwell-Chern-Simons theory
• Metric formulation of the simple theory of 3d massive gravity
• Hamiltonian formalism of Minimal Massive Gravity
• Weyl Covariant Theories of Gravity in Riemann-Cartan-Weyl Space-times II. Minimal Massive Gravity
• Dirac field in topologically massive gravity
• Holographically Viable Extensions of Topologically Massive and Minimal Massive Gravity?
• Warped $Ad{S}_3$ black hole in minimal massive gravity with first order formalism
• Circularly symmetric solutions of Minimal Massive Gravity at its merger point

Cited by in corpus (1)

• A note on the pp-wave solution of Minimal Massive 3D Gravity coupled with Maxwell-Chern-Simons theory