nLab
axio-dilaton

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 $\mathrm{SL}(2,\mathbb{Z})$ S-duality $\subset$ U-duality as

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

• In F-theory the variation of the axio-dilaton determines an elliptic fibration which encodes non-perturbative vacua of type IIB string theory.