Lorentz completion of effective string (and p-brane) action

TL;DR

The paper introduces a systematic method to construct Lorentz-invariant effective actions for confining strings and p-branes, revealing that leading deviations from the Nambu-Goto action relate to scalar curvature squared.

Contribution

A new general method is developed to systematically generate higher-order Lorentz-invariant terms in the effective action of strings and p-branes, based on a three-step prescription.

Findings

The leading bulk deviation from Nambu-Goto action is proportional to scalar curvature squared.

The method ensures Lorentz invariance of the constructed terms.

Provides a systematic way to include higher-order corrections in effective string and p-brane actions.

Abstract

The formation of a confining string (or a p-brane) in a Poincare' invariant theory breaks spontaneously this symmetry which is thereby realized non-linearly in the effective action of these extended objects. As a consequence the form of the action is strongly constrained. A new general method is described to obtain in a systematic way higher order Lorentz invariant contributions to this action. We find a simple recipe to promote a term invariant under the stability subgroup to an expression invariant under the whole Lorentz group. It is based on the following three steps: in the saturation of worldsheet (or worldvolume) indices replace the Minkowski metric with the inverse of the induced metric; in the saturation of indices of the transverse coordinates describing the position of the extended object replace the Euclidean metric with a certain new metric; finally replace the field derivatives of order higher than two with a certain covariant derivative. Lorentz invariance of the expression modified this way immediately follows. We find in particular that the leading bulk deviation of the Nambu Goto action in any space-time dimensions is proportional to the square of scalar curvature.