Quantum effects for extrinsic geometry of strings via the generalized Weierstrass representation

TL;DR

This paper investigates quantum effects on string extrinsic geometry using the generalized Weierstrass representation, calculating correlators and discussing singularities within a perturbative framework.

Contribution

It introduces a novel application of the generalized Weierstrass representation to quantum string geometry and computes correlators exactly at one-loop for extrinsic Polyakov action.

Findings

Exact one-loop correlators for primary fields are obtained.

Infrared singularity's geometrical interpretation is provided.

Perturbative treatment of Nambu-Goto and curvature actions is demonstrated.

Abstract

The generalized Weierstrass representation for surfaces in $\Bbb{R}^{3}$ is used to study quantum effects for strings governed by Polyakov-Nambu-Goto action. Correlators of primary fields are calculated exactly in one-loop approximation for the pure extrinsic Polyakov action. Geometrical meaning of infrared singularity is discussed. The Nambu-Goto and spontaneous curvature actions are treated perturbatively.