Application of Kawaguchi Lagrangian formulation to string theory

TL;DR

This paper explores the Kawaguchi Lagrangian formulation's ability to demonstrate dualities in string theory, including string-scalar and membrane-scalar dualities, by leveraging its unique symmetry between fields and parameters.

Contribution

It introduces the application of Kawaguchi Lagrangian formulation to string theory, revealing simple relations between dual theories and demonstrating role exchanges between fields and parameters.

Findings

Dualities are proved using Kawaguchi metrics.

A relation between dual theories' metrics is established.

Exchange of roles between fermionic fields and parameters is demonstrated.

Abstract

String-scalar duality proposed by Y. Hosotani and membrane-scalar duality by A. Sugamoto are reexamined in the context of Kawaguchi Lagrangian formulation. The characteristic feature of this formulation is the indifferent nature of fields and parameters. Therefore even the exchange of roles between fields and parameters is possible. In this manner, dualities above can be proved easily. Between Kawaguchi metrics of the dually related theories, a simple relation is found. As an example of the exchange between fermionic fields and parameters, a replacement of the role of Grassmann parameters of the 2-dimensional superspace by the 9th component of Neveu-Schwarz-Ramond (NSR) fermions is studied in superstring model. Compactification is also discussed in this model.