# nLab duality between M-theory on Z2-orbifolds and type IIB string theory on K3-fibrations

Contents

### Context

#### Duality in string theory

duality in string theory

general mechanisms

string-fivebrane duality

string-string dualities

M-theory

F-theory

string-QFT duality

QFT-QFT duality:

# Contents

## Idea

One of the conjectured dualities in string theory:

M-theory in a configuration whose low-energy super spacetime is an orbifold locally of the form $\mathbb{R}^{5,1} \times (\mathbb{R}^5\sslash_{refl} \mathbb{Z}_2)$ is argued to be equivalent to KK-compactifications of type IIB string theory on K3-surfaces.

(Either this refers to the perturbation series-limit of M-theory, or else, more generally, to non-perturbative type IIB theory, now also known as F-theory.)

This was originally argued in (Dasgupta-Mukhil 96, section 2) and (Witten 95b, Sen 96, top. of p .5).

## Properties

### Geometric engineering of the 6d $(2,0)$-superconformal QFT

On either side of the duality, this is the setup that exhibits geometric engineering of the 6d (2,0)-superconformal QFT in the ADE-classification:

On the type IIB-side this is argued in (Witten95a, section 1), for ADE singularities in the K3-surface.

On the M-theory side, (Witten 95b, p. 9-10) identifies the $\mathbb{Z}_2$-orbifold singularity with the worldvolume of M5-branes. Placing this furthermore inside the ADE singularity locus of a MK6-brane should be the corresponding setup (any reference saying this explicitly, i.e. speaking about M5 $\cap$ (MK6 at ADE) ?)

## References

The expected relation to the 6d (2,0)-superconformal QFT is discussed in

Last revised on May 15, 2019 at 08:24:50. See the history of this page for a list of all contributions to it.