Fractal Theory Space: Spacetime of Noninteger Dimensionality
Abstract
We construct matter field theories in ``theory space'' that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and Yang-Mills gauge fields. In the continuum limit these models describe physics in a noninteger spatial dimension which appears above a RG invariant ``compactification scale,'' M. The energy distribution of KK modes above M is controlled by an exponent in a scaling relation of the vacuum energy (Coleman-Weinberg potential), and corresponds to the dimensionality. For truncated-s-simplex lattices with coordination number s the spacetime dimensionality is 1+(3+2ln(s)/ln(s+2)). The computations in theory space involve subtleties, owing to the 1+3 kinetic terms, yet the resulting dimensionalites are equivalent to thermal spin systems. Physical implications are discussed.
Cite
@article{arxiv.hep-th/0210076,
title = {Fractal Theory Space: Spacetime of Noninteger Dimensionality},
author = {Christopher T. Hill},
journal= {arXiv preprint arXiv:hep-th/0210076},
year = {2008}
}
Comments
28 pages, 6 figures; Paper has been amplified with a more detailed discussion of a number of technical issues