# Contents

## Idea

In type IIB supergravity the dilaton/string coupling $g_s$ and the degree-1 RR-field $C_0$ of the D(-1)-brane combine into a complex function

$\tau := C_0 + i g_2$

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

$\left( \array{ a & b \\ c & d } \right) : \tau \mapsto \frac{a \tau + b}{c \tau + d} \,.$

This combined field is also called the axio-dilaton.

## Properties

Revised on May 7, 2014 23:26:03 by Urs Schreiber (88.128.80.30)