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

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 Land R-handed sectors, and the two types of Higgs fields should be generated.