Tensionless String in the Notoph Background

TL;DR

This paper investigates how tensionless strings interact with antisymmetric background fields using spinor formalism, identifying the notoph field as the key degree of freedom influencing the interaction.

Contribution

It introduces a geometric condition for null string-background interaction and links the notoph field to a specific gauge-invariant degree of freedom.

Findings

Only one gauge-invariant degree of freedom of B_{ab} does not satisfy the interaction condition.

The interaction reduces to a single derivation coefficient identified with the notoph field.

The complex system of equations simplifies to linear differential equations for spinor basis functions.

Abstract

We study the interaction between a tensionless (null) string and an antisymmetric background field B_{ab} using a 2-component spinor formalism. A geometric condition for the absence of such an interaction is formulated. We show that only one gauge-invariant degree of freedom of the field B_{ab} does not satisfy this condition. Identification of this degree of freedom with the notoph field \phi of Ogievetskii-Polubarinov-Kalb-Ramond is suggested. Application of a two-component spinor formalism allows us a reduction of the complete system of non-linear partial differential equations and constraints governing the interacting null string dynamics to a system of linear differential equations for the basis spinors of the spin-frame. We find that total effect of the interaction is contained in a single derivation coefficient which is identified with the notoph field.