Twistor variational principle for null strings

TL;DR

This paper introduces a twistor-based action principle for null strings in 4D Minkowski space, providing a reparametrization invariant formulation that derives evolution equations and includes non-geodesic cases.

Contribution

It presents a novel twistor action functional for null 2-surfaces that is constraint-free and reparametrization invariant, advancing the theoretical understanding of null string dynamics.

Findings

Derivation of evolution equations for null strings.

Inclusion of non-geodesic null strings in the formalism.

Discussion on minimality and potential extensions to time-like and space-like surfaces.

Abstract

I present a twistor action functional for null 2-surfaces (null strings) in 4D Minkowski spacetime. The proposed formulation is reparametrization invariant and free of algebraic and differential constraints. Proposed approach results in derivation of evolution equations for the null strings. It is shown that non-geodesic null strings are contained in the presented formalism. A discussion of the problem of minimality for 2-surfaces with degenerate induced metric is given. I also speculate on the possible description of strings (time-like 2-surfaces) and conventional (space-like) 2-surfaces.