Noncommutative Quantization in 2D Conformal Field Theory

TL;DR

This paper explores noncommutative quantization of a 2D free bosonic string, showing that certain key features are preserved while others are deformed, with implications for conformal invariance.

Contribution

It introduces a noncommutative harmonic oscillator framework for quantizing 2D strings and analyzes the resulting effects on partition functions and correlation functions.

Findings

Partition function remains undeformed after rescaling and radius adjustment.

Four point function is deformed but preserves sl(2,C) invariance.

First Ward identity of the deformed theory is derived.

Abstract

The simplest possible noncommutative harmonic oscillator in two dimensions is used to quantize the free closed bosonic string in two flat dimensions. The partition function is not deformed by the introduction of noncommutativity, if we rescale the time and change the compactification radius appropriately. The four point function is deformed, preserving, nevertheless, the sl(2,C) invariance. Finally the first Ward identity of the deformed theory is derived.