# Extended Hořava Gravity with Physical Ground-State Wavefunction

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## Abstract

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## 1. Introduction

- (i)
- The theory is power-counting renormalizable, in the sense that the candidate theory should be renormalizable in the UV regime;
- (ii)
- The theory has a healthy IR behavior, namely, the theory should be free of ghosts and does not have strong coupling;
- (iii)
- The theory can be well quantized in the sense that the theory has a stable vacuum state (physical ground state). Generally speaking, in accordance with the symmetry of the theory, the number of allowed terms in the action is large. As we will see in Section 5, to ensure the theory has a stable vacuum, the allowed terms in the actions should be carefully selected such that the probability density is finite and normalized. In other words, to have a physical ground state, the theory should have a finite (and normalized) probability density. To ensure there is a finite probability density, one has to select suitable terms in the action such that the Euclidean action of the theory is positive definite. We should emphasize that this selection is not unique. What we will adopt in the present paper is one of the choices.

## 2. Anisotropic Theory of Gravity

## 3. Power-Counting Renormalizable

## 4. IR Behavior

## 5. Quantization of the Theory

#### 5.1. Brief Review of Stochastic Quantization

#### 5.2. Quantization of BPS Model

#### 5.3. Stochastic Quantization of Our Model

## 6. Conclusions and Discussions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**MDPI and ACS Style**

Shu, F.-W.; Zhang, T.
Extended Hořava Gravity with Physical Ground-State Wavefunction. *Symmetry* **2021**, *13*, 100.
https://doi.org/10.3390/sym13010100

**AMA Style**

Shu F-W, Zhang T.
Extended Hořava Gravity with Physical Ground-State Wavefunction. *Symmetry*. 2021; 13(1):100.
https://doi.org/10.3390/sym13010100

**Chicago/Turabian Style**

Shu, Fu-Wen, and Tao Zhang.
2021. "Extended Hořava Gravity with Physical Ground-State Wavefunction" *Symmetry* 13, no. 1: 100.
https://doi.org/10.3390/sym13010100