Action functionals for strings in four dimensions

TL;DR

This paper classifies all possible surface action functionals in four-dimensional space that depend on derivatives and are invariant under rigid motions.

Contribution

It provides a complete description of all first- and second-derivative dependent, rigid motion invariant action functionals for surfaces in four dimensions.

Findings

Complete classification of invariant action functionals

Identification of all functionals depending on derivatives

Framework for analyzing surface actions in 4D

Abstract

All possible action functionals on the space of surfaces in ${\bf R}^4$ that depend only on first and second derivatives of the functions, entering the equation of the surface, and satisfy the condition of invariance with respect to rigid motions are described.