Strings versus Anti Strings in the inversion invariant or proper volume formulation

TL;DR

This paper explores a modified measure formulation of strings and branes where tension is a dynamical variable, revealing conditions for positive and negative tensions that correspond to strings, anti-strings, and their pair creation in background fields.

Contribution

It introduces a signed reparametrization invariant volume element formulation allowing dynamical tension to produce both positive and negative tensions, modeling strings and anti-strings.

Findings

Anti strings occur when scalar time runs opposite to world sheet time.

Dynamical tension can be positive or negative, corresponding to strings or anti-strings.

String anti-string pair creation is analogous to QED pair creation in an external field.

Abstract

The specific model studied is in the context of the modified measure formulation the string or branes where tension appear as an additional dynamical degree of freedom . We then consider the signed reparametrization invariant volume element formulation of dynamical strings and branes and find that the dynamical tension can produce positive tensions or negative tensions, corresponding exactly to strings and branes and anti strings and anti branes respectively. The anti strings are realized when a scalar time that defines the modified measure runs in the opposite direction to the world sheet time. For strings with positive tension, both times run in the same direction. The situation resembles the situation in Relativistic Quantum Mechanics with positive and negative energies, proper time of particles running forward with respect of coordinate time , while for anti particles proper tome runs opposite of coordinate time. An example where string anti string pair creation takes place in analogy to the pair creation in an external electric field in QED background field, this time in the presence of a background scalar field that couples to the strings and locally changes the tension, the tension field.