Effective String Theory Simplified

TL;DR

The authors present a gauge-invariant effective string theory in $D$ dimensions by embedding into the Polyakov formalism and introducing a composite Liouville field to cancel Weyl anomalies, enabling a systematic operator classification organized by inverse string length. They show that at next-to-leading order (NLO) all observables are universal, while at NNLO universality can fail due to curvature-squared terms, though certain static-string configurations retain universality. The framework leverages a Weyl-covariant derivative and the $\mathcal{I}_{11}$-dressing rule to constrain the operator basis, and it analyzes OPEs to demonstrate that the $T$–$X$ OPE remains unrenormalized to $O(\beta)$ and the $T$–$T$ OPE yields the correct central charge $c=26$. The results clarify the relationship to the older Polchinski-Strominger approach, provide a consistent path for comparing gauges, and yield concrete predictions for long-string dynamics and potential observable universality across different string configurations.

Abstract

In this set of notes we simplify the formulation of the Poincare'-invariant effective string theory in D dimensions by adding an intrinsic metric and embedding its dynamics into the Polyakov formalism. We use this formalism to construct operators order by order in the inverse physical length of the string, in a fully gauge-invariant framework. We use this construction to discuss universality and nonuniversality of observables up to and including next-to-next-to-leading order in the long string expansion.