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

Contents

Context

Duality in string theory

String theory

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 5,1×( 5 refl 2)\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)(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 2\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.