Covariant Calculus for Effective String Theories

TL;DR

This work develops a covariant calculus for effective string theories in arbitrary dimensions, addressing limitations of the Polchinski–Strominger (PS) framework by formulating two equivalent covariant formalisms that realize conformal symmetry as a residual gauge invariance. By fixing a universal transformation law and employing either a non-intrinsic induced metric or an intrinsic Weyl-covariant structure, the authors provide a systematic method to construct conformally invariant actions to all orders in $1/R$ while carefully treating quantum measures and field redefinitions. They show that the PS integrand cannot be covariantised within this scheme, whereas Drummond-type corrections can be organized into a small, three-parameter space at order $R^{-6}$, yielding a constrained effective action distinct from the PS ansatz. The framework clarifies how reparametrisation, Weyl symmetry, and denominator regularity shape the allowed effective actions, with potential implications for comparisons to lattice simulations and phenomenology in non-critical string-like systems.

Abstract

A covariant calculus for the construction of effective string theories is developed. Effective string theory, describing quantum string-like excitations in arbitrary dimension, has in the past been constructed using the principles of conformal field theory, but not in a systematic way. Using the freedom of choice of field definition, a particular field definition is made in a systematic way to allow an explicit construction of effective string theories with manifest exact conformal symmetry. The impossibility of a manifestly invariant description of the Polchinski-Strominger Lagrangian is demonstrated and its meaning is explained.