Gravitational behavior of an effective topological field theory in a gravitational instanton background

Abstract

Effective topological field theories describe the properties of Dirac fermions in the low-energy regime. In this work, we introduce a new emergent gravity model by considering Dirac fermions invariant under local de Sitter transformations in four-dimensional open manifolds. In the context of Cartan geometry, fermions couple to spacetime through a $Spin(5)$ Cartan connection that can be decomposed in spin connection and tetrads. In presence of a gravitational instanton background, we show that the corresponding effective topological field theory becomes a dynamical gravitational theory with a positive cosmological constant and Barbero-Immirzi parameter. At classical level and in absence of matter, this theory is compatible with general relativity.

7 pages, published version

References in corpus (3)

• Quantum gravity in terms of topological observables
• Generalizing the Kodama State II: Properties and Physical Interpretation
• Gauge Gravity: a forward-looking introduction

Cited by in corpus (5)

• Exact helicoidal and catenoidal solutions in Einstein-Maxwell theory
• On the Emergent Dynamics of Fermions in Curved Spacetime
• From topological to topologically massive gravity through the gauge principle
• NUT Solutions in Einstein-Maxwell-scalar-Gauss-Bonnet Gravity
• Emergent Dynamics of Spacetime and Matter from a Topological Phase