# Contents

## Idea

In type IIB supergravity the dilaton/string coupling ${g}_{s}$ and the degree-1 RR-field ${C}_{0}$ combine into a complex function

$\tau :={C}_{0}+i{g}_{2}$\tau := C_0 + i g_2

which transforms under the $\mathrm{SL}\left(2,ℤ\right)$ S-duality $\subset$ U-duality as

$\left(\begin{array}{cc}a& b\\ c& d\end{array}\right):\tau ↦\frac{a\tau +b}{c\tau +d}\phantom{\rule{thinmathspace}{0ex}}.$\left( \array{ a & b \\ c & d } \right) : \tau \mapsto \frac{a \tau + b}{c \tau + d} \,.

This combined field is also called the axio-dilaton.

## Properties

Created on February 24, 2012 12:21:44 by Urs Schreiber (82.113.119.226)