# Contents

## Idea

Whatever it is otherwise, string theory turns out to be an organizational principle that subsumes a wealth of effective quantum field theories together with hints for their UV-completion. As such, string theory reveals a multitude of equivalences between superficially very different-looking (classes of) quantum field theories, or between various limits (notably strong/weak coupling limits) of various different-looking quantum field theories. Large classes of these equivalences go by the name of “dualities”:

There is also

## Overview

under construction

reduction from 11delectric σ-modelweak/strong coupling dualitymagnetic σ-model
M2-brane in 11d sugra EFT$←$electric-magnetic duality$\to$M5-brane in 11d sugra EFT
HW reduction
$↓$ on orientifold K3$×{S}^{1}//{ℤ}_{2}$$↓$ on orientifold K3$×{S}^{1}//{ℤ}_{2}$
F1-brane in heterotic supergravity$←$S-duality$\to$black string in heterotic sugra
HW reduction
$↓$ on orientifold T4$×{S}^{1}//{ℤ}_{2}$$↓$ on orientifold T4$×{S}^{1}//{ℤ}_{2}$
F1-brane in heterotic supergravity$←$S-duality$\to$black string in type IIA sugra
KK reduction
$↓$ on K3$×{S}^{1}$$↓$ on K3$×{S}^{1}$
F1-brane in IIA sugra$←$S-duality$\to$black string in heterotic sugra
KK reduction
$↓$ on ${T}^{4}×{S}^{1}$$↓$ on ${T}^{4}×{S}^{1}$
F1-brane in IIA sugra$←$S-duality$\to$black string in type IIA sugra
F-reduction$↕$ T-duality on ${S}^{1}$
F1-brane in IIB sugra$←$S-duality$\to$D1-brane in 10d IIB sugra
U-duality$↕$ T-duality on ${T}^{2}$
D3-brane in IIB sugra$←$S-duality$\to$D3-brane in IIB sugra

## References

### Original articles

The original article suggesting the relation of 11d sugra to string theory is

An original article collecting all the weak/strong electric/magnetic dualities is

### Surveys and lecture notes

A detailed discussion of dualities induced on K3-compactifications is in

Revised on October 14, 2012 14:55:03 by Urs Schreiber (89.204.130.129)