PP-wave Green-Schwarz superstring, polygon divergent structure and conformal field theory

TL;DR

This paper evaluates the effective action of the pp-wave Green-Schwarz superstring, demonstrating its conformal invariance despite complex divergence structures, by analyzing harmonic and group coordinate formulations.

Contribution

It introduces group coordinates preserving conformal symmetry and analyzes divergence structures, showing the superstring remains a conformal field theory.

Findings

Bosonic and fermionic effective actions cancel, confirming conformality.

Logarithmic divergences from n-gons in group coordinates are manageable.

Superstring theory remains conformal despite complex divergence structures.

Abstract

In the semi-light cone gauge $g_{ab}=e^{2\phi}\delta_{ab}$, $\bar{\gamma}^+\theta=0$, we evaluate the $\phi$-dependent effective action for the pp-wave Green-Schwarz (GS) superstring in both harmonic and group coordinates. When we compute the fermionic $\phi$-dependent effective action in harmonic coordinates, we find a new triangular one-loop Feynman diagram. We show that the bosonic $\phi$-dependent effective action cancels with the fermionic one, indicating that the pp-wave GS superstring is a conformal field theory. We introduce the group coordinates preserving $SO(4)\times SO(4)$ and conformal symmetry. Group coordinates are interesting because vertex operators take simple forms in them. The new feature in group coordinates is that there are logarithmic divergences from n-gons, so that the divergent structure is more complicated than in harmonic coordinates. After summing over all contributions from n-gons, we show that in group coordinates, the GS superstring on pp-wave RR background is still a conformal field theory.