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M-theory on S1/G_HW times H/G_ADE

Contents

Contents

Idea

The KK-compactification of M-theory on fibers

S 1G HW×G ADE S^1 \!\sslash\! G_{HW} \times \mathbb{H}\!\sslash\! G_{ADE}

which are, locally, the Cartesian product of

  1. the circle orientifolded by G HW 2G_{HW} \simeq \mathbb{Z}_2 as in Horava-Witten theory;

  2. the quaternions orbifolded by a finite subgroup of SU(2) G ADEG_{ADE}.

graphics grabbed from HSS18, Example 2.2.7

Depending on whether the circle fiber for duality between M-theory and type IIA string theory is taken to be along the orbit of G HWG_{HW} or of nG ADE\mathbb{Z}_{n} \subset G_{ADE} this is

For G ADE= 2G_{ADE} = \mathbb{Z}_2 this subsumes M-theory on K3 times S 1G HWS^1 \sslash G_{HW} (Seiberg-Witten 96)


Relation to D=6D = 6 N=(1,0)N=(1,0) SCFT

Gives rise to D=6 N=(1,0) SCFT ( DHTV 14, Section 6, Gaiotto-Tomasiello 14, HKLY 15)

Dual perspectives

HET on ADE-singularities

(…)

Type I’ with D6s ending on 12\tfrac{1}{2} NS5-branes

from GKSTY 02

If in addition the black NS5-brane sits at an O8-plane, hence at the orientifold fixed point-locus, then in the ordinary /2\mathbb{Z}/2-quotient it appears as a “half-brane” with only one copy of D6-branes ending on it:

from GKSTY 02

(In Hanany-Zaffaroni 99 this is interpreted in terms of the 't Hooft-Polyakov monopole.)

The lift to M-theory of this situation is an M5-brane intersecting an M9-brane (see at M-theory on S1/G_HW times H/G_ADE):

from GKSTY 02

Alternatively the O8-plane may intersect the black D6-branes away from the black NS5-brane:

from HKLY 15

In general, some of the NS5 sit away from the O8-plane, while some sit on top of it:

from Hanany-Zaffaroni 98

KK-compactification of M-theory

References

General

Type II/I’ perspective

On S 1G HW×K 3S^1 \sslash G_{HW} \times K_3

Last revised on July 15, 2019 at 12:59:33. See the history of this page for a list of all contributions to it.