The effective theory of strings

TL;DR

This paper demonstrates that the Nambu-Goto string and its higher-dimensional variants can be quantized as effective theories in any target space dimension by expanding around classical configurations using advanced quantum field theory tools.

Contribution

It introduces a method to quantize the Nambu-Goto string in any dimension, considering arbitrary classical backgrounds and maintaining diffeomorphism invariance, using perturbative algebraic QFT techniques.

Findings

Quantization of Nambu-Goto string in any dimension.

Framework for arbitrary classical background configurations.

Preservation of diffeomorphism invariance during quantization.

Abstract

We show that the Nambu-Goto string, and its higher dimensional generalizations, can be quantized, in the sense of an effective theory, in any dimension of the target space. The crucial point is to consider expansions around classical string configurations. We are using tools from perturbative algebraic quantum field theory, quantum field theory on curved spacetimes, and the Batalin-Vilkovisky formalism. Our model has some similarities with the L\"uscher-Weisz string, but we allow for arbitrary classical background string configurations and keep the diffeomorphism invariance.