Some $\mathbf{Z}_2$-invariant Variables: Constructed of the Scalars Dilaton and Axion

TL;DR

This paper constructs Z2-invariant scalars and forms from dilaton and axion fields, enabling the formulation of invariant actions in 10 dimensions, and analyzes their independence and properties.

Contribution

It introduces a set of Z2-invariant scalars and forms from dilaton and axion fields, facilitating the creation of invariant actions in higher-dimensional theories.

Findings

Identified Z2-invariant scalars and forms from dilaton and axion fields.

Established various 10-dimensional invariant actions using these invariants.

Analyzed independence of the constructed invariants.

Abstract

Using the dilaton scalar and axion pseudoscalar fields we construct a number of scalars and differential forms which are symmetric under the $\mathbf{Z}_2$-subgroup of the group $SL(2, \mathbf{R})$. These invariants enable us to establish various 10-dimensional invariant actions. Other invariants which are not independent from the previous ones will be detached.