nLab
MO5

Contents

Contents

Idea

The MO5 (Dasgupta-Mukhil 95, Sec. 2FFurther, Witten 95, Sec. 3.3) is one of the types of 12\tfrac{1}{2} BPS orientifold fixed loci in M-theory/on D=11 N=1 super-spacetime. Locally on super Minkowski spacetime it is the super-orientifold ℝ 10,1|32β«½β„€ 2 Ξ“ 56789\mathbb{R}^{10,1\vert \mathbf{32}} \sslash \mathbb{Z}^{\Gamma^{56789}}_2 given by the global orbifold quotient by the group of order 2 which is generated by the Clifford algebra-element Ξ“ 5Ξ“ 6Ξ“ 7Ξ“ 8Ξ“ 9∈Pin +(10,1)\Gamma_5 \Gamma_6 \Gamma_7 \Gamma_8 \Gamma_9 \in Pin^+(10,1) in the positive pin group (for precise details see HSS 18, Lemma 4.12).

Properties

Charge, anomaly cancellation and duality to O4-planes

Under duality between M-theory and type IIA string theory, for KK-compactification along a circle-fiber parallel to the MO5, a plain MO5 becomes the O4-plane, specifically the O βˆ’4O^- 4-plane, while an MO5 with an M5-brane on top of it becomes the O +4O^+ 4-plane (Gimon 9, Sec. III8,Hanany-Kol 00, Sec. 3.1).

Hence the spacetime dimensions of the MO5 is the same that of the black M5-brane, but its charge as an O-plane is βˆ’12- \tfrac{1}{2} that of a single M5-brane (Dasgupta-Mukhil 95, Sec. 2, Witten 95, 3.3, Hori 98, 2.1), so that am M-theoretic lift of RR-field tadpole cancellation requires the presence of 16 M5-branes in an toroidal MO5-type orientifold 𝕋 5 sgnβ«½β„€ 2\mathbb{T}^{\mathbf{5}_{sgn}} \!\sslash\! \mathbb{Z}_2.

As a sector of heterotic M-theory on ADE-singularities

By the classification of MFF 12, Sec. 8.3, the MO5-plane is not in fact a 12\tfrac{1}{2} BPS solution of D=11 N=1 supergravity. But the intersection of an MK6 with an MO9-plane is a 14\tfrac{1}{4} BPS solution to D=11 N=1 supergravity.

graphics grabbed from HSS18, Example 2.2.7

Thus, heterotic M-theory on ADE-orbifolds the MO5-plane becomes the fixed locus of the diagonal β„€ 2β†ͺdiagβ„€ 2Γ—G DE\mathbb{Z}_2 \overset{ diag }{\hookrightarrow } \mathbb{Z}_2 \times G^{DE}, hence the intersection of an MO9 with an MK6 DE{}_{DE} (FLO 99, Sec. 4), also called the βˆ’12M5-\tfrac{1}{2}M5, since under duality between M-theory and type IIA string theory this becomes the half NS5-brane of type I' string theory.

As geometric engineering of D=6D=6 𝒩=(2,0)\mathcal{N} = (2,0) SCFTs

Coincident M5-branes on an MO5-plane are supposed to geometrically engineer D=6 N=(2,0) SCFTs with D-series gauge groups (AKY 98, Sec. IIB).

But if these are really βˆ’12M5=MK6∩MO9-\tfrac{1}{2} M5 = MK6 \cap MO9-branes of heterotic M-theory on ADE-orbifolds, then they will geometrically engineer D=6 N=(1,0) SCFTs, instead, see there.

References

General

The original articles are

Classification view of rational equivariant Cohomotopy of super-spacetime:

As a sector of the βˆ’12M5-\tfrac{1}{2}M5 in heterotic M-theory at ADE-singularities

Discussion in the more general context of heterotic M-theory on ADE-orbifolds is in

and in view of super-embeddings of M5-branes in

Relation to O4-planes

Relation of the MO5 to the O4-plane under duality between M-theory and type IIA string theory:

Geometric engineering of orthogonal D=6D=6, 𝒩=(2,0)\mathcal{N}=(2,0) SCFTs

As geometric engineering of D=6 N=(2,0) SCFTs with D-series gauge groups:

  • Changhyun Ahn, Hoil Kim, Hyun Seok Yang, SO(2N)SO(2N) (0,2)(0,2) SCFT and M Theory on AdS 7×ℝP 4AdS_7 \times \mathbb{R}P^4, Phys.Rev. D59 (1999) 106002 (arXiv:hep-th/9808182)

Last revised on September 14, 2019 at 15:02:07. See the history of this page for a list of all contributions to it.