4d Gauge Theory and Gravity Generated from 3d Ones at High Energy

TL;DR

This paper explores how 4d gauge theories and gravity can emerge from 3d theories at high energy through fermion condensation, offering a novel approach to generating the standard model from lower-dimensional theories.

Contribution

It proposes a mechanism for generating 4d gauge theories and gravity from 3d theories using fermion condensation, addressing issues like the doubling problem and lattice discretization.

Findings

4d Einstein gravity can be generated from multiple 3d copies.

4d gauge interactions are correctly produced from 3d theories, even with asymmetry.

The model suggests a promising way to derive the standard model from lower-dimensional theories.

Abstract

Dynamical generation of 4d gauge theories and gravity at low energy from the 3d ones at high energy is studied, based on the fermion condensation mechanism recently proposed by Arkani-Hamed, Cohen and Georgi. For gravity, 4d Einstein gravity is generated from the multiple copy of the 3d ones, by referring to the two form gravity. Since the 3d Einstein action without matter coupling is topological, ultraviolet divergences are less singular in our model. In the gauge model, matter fermions are introduced on the discrete lattice following Wilson. Then, the 4d gauge interactions are correctly generated from the 3d theories even in the left-right asymmetric theories of the standard model. In order for this to occur, the Higgs fields as well as the gauge fields of the extra dimension should be generated by the fermion condensates. Therefore, the generation of the 4d standard model from the multiple copy of the 3d ones is quite promising. To solve the doubling problem in the weak interaction sector, two kinds of discrete lattices have to be introduced separately for L- and R-handed sectors, and the two types of Higgs fields should be generated.