CHAPTER 2
LIGHTCONE WORLD SHEET FORMALISI.
In this chapter we give an overview of the construction we call the Lightcone World
Sheet. The formalism was originally invented by Bardakci and Thorn [5] and was
presented as a concrete mechanism to see the world sheet behavior of large N, matrix
quantum field theory. In that paper the authors establish the first Lightcone World Sheet
from a scalar matrix quantum field theory with an interaction term of gTro3/V N and
indicate how the the approach might be extended to more general field theories. This
extension is carried out in a number of later papers by Thorn and collaborators. The
formalism is the fundamental backdrop to the work presented in this thesis, since the
world sheet picture allows for new interpretations and methodology for investigating the
field theory, among others the Monte Carlo techniques of chapter 4. The Lightcone World
Sheet describes a wide collection of field theories in terms of a path integral over fields
that live in a two dimensional space referred to as the world sheet. The mechanics of the
procedure is described in this chapter.
2.1 Introduction to the Lightcone World Sheet Formalism
Consider the simplest case of a Lightcone World Sheet, namely the one presented by
Bardakci and Thorn in their paper from 2002 [5], describing a scalar matrix field theory
with cubic interaction. In order to shed light on the main concepts of the mechanism it
is in order to sketch in some detail the steps presented therein, since as a field theory it
is the simplest possible case, and because the matrix scalar field theory will be applied
later when we look at Monte Carlo studies. Consider therefore the dynamics of the planar
diagrams of a large Nc matrix quantum field theory with action given by