Massive Hermitian Gravity

TL;DR

This paper develops a massive Hermitian gravity theory using a complex Higgs multiplet, ensuring ghost-free behavior at linear order and providing insights into mass generation for graviton and antisymmetric tensor fields.

Contribution

It generalizes Einstein-Strauss Hermitian gravity with a complex Higgs multiplet, achieving equal mass for graviton and antisymmetric tensor, and analyzes ghost-free conditions.

Findings

Both graviton and antisymmetric tensor acquire the same mass.

The theory is ghost free around Minkowski background at linear order.

Strong coupling scales are determined, with potential nonlinear ghosts decoupling.

Abstract

Einstein-Strauss Hermitian gravity was recently formulated as a gauge theory where the tangent group is taken to be the pseudo-unitary group instead of the orthogonal group. A Higgs mechanism for massive gravity was also formulated. We generalize this construction to obtain massive Hermitian gravity with the use of a complex Higgs multiplet. We show that both the graviton and antisymmetric tensor acquire the same mass. At the linearized level, the theory is ghost free around Minkowski background and describes a massive graviton with five degrees of freedom and an antisymmetric field with three degrees of of freedom. We determine the strong coupling scales for these degrees of freedom and argue that the potential nonlinear ghosts, if they exist, have to decouple from the gravitational degrees of freedom in strong coupling regime.