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

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

• Keshav Dasgupta, Sunil Mukhi, Orbifolds of M-theory, Nucl.Phys. B465 (1996) 399-412 (arXiv:hep-th/9512196)

• Edward Witten, Five-branes And M-Theory On An Orbifold, Nucl.Phys.B463:383-397, 1996 (arXiv:hep-th/9512219)

• Ashoke Sen, Orbifolds of M-Theory and String Theory, Mod.Phys.Lett.A11:1339-1348, 1996 (arXiv:hep-th/9603113)

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

• Edward Witten, Some Comments On String Dynamics (arXiv:hep-th/9507121)