Self-Intersection Numbers and Random Surfaces on the Lattice

Details Self-Intersection Numbers and Random Surfaces on the Lattice Self-Intersection Numbers and Random Surfaces on the Lattice

1995-05-05

arxiv.org/abs/hep-th/9505028v1

Nucl.Phys. B452 (1995) 526-544

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, LaTex

Scientific paper

10.1016/0550-3213(95)00387-8

String theory in 4 dimensions has the unique feature that a topological term, the oriented self-intersection number, can be added to the usual action. It has been suggested that the corresponding theory of random surfaces wold be free from the problem encountered in the scaling of the string tension. Unfortunately, in the usual dynamical triangulation it is not clear how to write such a term. We show that for random surfaces on a hypercubic lattice however, the analogue of the oriented self-intersection number $I[\s]$ can be defined and computed in a straightforward way. Furthermore, $I[\s]$ has a genuine topological meaning in the sense that it is invariant under the discrete analogue of continuous deformations. The resulting random surface model is no longer free and may lead to a non trivial continuum limit.

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