On M-Theory and the Symmetries of Type II String Effective Actions

TL;DR

This paper explores the dimensional reduction of M-theory to derive type II string effective actions, emphasizing symmetries like T-duality and S-duality, and clarifying their origins in lower-dimensional theories.

Contribution

It provides a detailed analysis of how T-duality and S-duality symmetries emerge from M-theory compactifications and their implications for type II string theories.

Findings

Demonstrates the O(1,1) invariance of the NS-NS sector in nine dimensions.

Shows the exact mapping between type IIA and type IIB theories via T-duality in nine dimensions.

Provides a dynamical argument linking S-duality in type IIA to M-theory compactified on a T-dual torus.

Abstract

We study the ``ordinary'' Scherk-Schwarz dimensional reduction of the bosonic sector of the low energy effective action of a hypothetical M-theory on $S^1 \times S^1 \cong T^2$. We thus obtain the low energy effective actions of type IIA string theory in both ten and nine space-time dimensions. We point out how to obtain the O(1, 1) invariance of the NS-NS sector of the string effective action correctly in nine dimensions. We dimensionally reduce the type IIB string effective action on $S^1$ and show that the resulting nine dimensional theory can be mapped, purely from the bosonic consideration, exactly to the type IIA theory by an O(1, 1) or Buscher's T-duality transformations. We then give a dynamical argument, in analogy with that for the type IIB theory in ten dimensions, to show how an S-duality in the type IIA theory can be understood from the underlying nine dimensional theory by compactifying M-theory on a T-dual torus $\tilde {T}^2$.