Fractal Theory Space: Spacetime of Noninteger Dimensionality

Details Fractal Theory Space: Spacetime of Noninteger Dimensionality Fractal Theory Space: Spacetime of Noninteger Dimensionality

2002-10-08

arxiv.org/abs/hep-th/0210076v2

Phys.Rev.D67:085004,2003

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, 6 figures; Paper has been amplified with a more detailed discussion of a number of technical issues

Scientific paper

10.1103/PhysRevD.67.085004

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.

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