# Higgs–Chern–Simons Gravity Models in d = 2n + 1 Dimensions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{a}and the scalar field $\psi \equiv {\varphi}^{D}$. Additionally, we define the covariant derivative ${D}_{\mu}\mathsf{\Phi}$ of the Higgs scalar

^{a}is a vector field (with ${\varphi}^{\mu}={e}_{\mu}^{a}{\varphi}^{a}$ in a coordinate frame), which, however, has rather unusual dynamics, as will be seen below. As such, ϕ

^{a}is not a gauge (masless or massive) field; it has rather a geometric content.

## 2. HCSG Models in $2n+1$ Dimensions, $n=1,2,3$

#### 2.1. General Expressions

^{a}.

#### 2.2. The General CSG Lagrangians and the Connection with the Einstein–Lovelock Hierarchy

## 3. The Solutions

#### 3.1. The $d=3$ Case

#### 3.2. The $d=5$ Case

#### 3.2.1. An Exact Solution

#### 3.2.2. No Backreacting Solutions on a Fixed Black Hole Background

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Radu, E.; Tchrakian, D.H.
Higgs–Chern–Simons Gravity Models in *d* = 2*n* + 1 Dimensions. *Symmetry* **2020**, *12*, 2064.
https://doi.org/10.3390/sym12122064

**AMA Style**

Radu E, Tchrakian DH.
Higgs–Chern–Simons Gravity Models in *d* = 2*n* + 1 Dimensions. *Symmetry*. 2020; 12(12):2064.
https://doi.org/10.3390/sym12122064

**Chicago/Turabian Style**

Radu, Eugen, and D. H. Tchrakian.
2020. "Higgs–Chern–Simons Gravity Models in *d* = 2*n* + 1 Dimensions" *Symmetry* 12, no. 12: 2064.
https://doi.org/10.3390/sym12122064