Field Definitions, Spectrum and Universality in Effective String Theories

TL;DR

This paper compares the spectra of effective string theories by Polchinski-Strominger and Nambu-Goto, showing their similarities at third order, and discusses the role of field redefinitions and measure transformations in these theories.

Contribution

It provides a detailed analysis of the spectrum and field redefinitions in effective string theories, establishing their equivalence and consistency across dimensions.

Findings

Third-order terms in spectrum match between theories.

Polchinski-Strominger theory is consistent in any dimension.

Field redefinitions affect measure and theory equivalence.

Abstract

It is shown, by explicit calculation, that the third-order terms in inverse string length in the spectrum of the effective string theories of Polchinski and Strominger are also the same as in Nambu-Goto theory, in addition to the universal Luescher terms. While the Nambu-Goto theory is inconsistent outside the critical dimension, the Polchinski-Strominger theory is by construction consistent for any space-time dimension. In the analysis of the spectrum, care is taken not to use any field redefinition, as it is felt that this has the potential to obscure important points. Nevertheless, as field redefinition is an important tool and the definition of the field should be made precise, a careful analysis of the choice of field definition leading to the terms in the action is also presented. Further, it is shown how a choice of field definition can be made in a systematic way at higher orders. To this end the transformation of measure involved is calculated, in the context of effective string theory, and thereby a quantum evaluation made of equivalence of theories related by a field redefinition. It is found that there are interesting possibilities resulting from a redefinition of fluctuation field.