Lattice approach to string theory

Abstract

We construct a lattice version of dual string theory, which we hope will be useful in systematically analyzing the properties of that theory. Mass renormalization is discussed, and the familiar tachyon problem is seen to arise so long as counterterms are restricted to be local. The dual-loop expansion is discussed and the origin of the critical dimension elucidated. In the interacting theory, the critical dimension is required for Lorentz invariance, but it is also the only dimension for which the coupling-constant renormalization is finite. The choice of bare coupling constant, ${g}_{0}=1$, is seen to be particularly attractive. If we make this choice, the string interaction coupling constant is calculable in terms of the fundamental rest tension ${T}_{0}$. The instabilities associated with tachyons are discussed, and we propose a method for discovering whether the interactions stabilize the theory. Application of our ideas to the baryon three-string problem is also mentioned.