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D=6 N=(1,0) SCFT

Contents

Context

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

superconformal field theory in dimension 6 with number of supersymmetries equal to 1.

Arises from

(…)

ddNNsuperconformal super Lie algebraR-symmetryblack brane worldvolume
superconformal field theory
via AdS-CFT
A3A\phantom{A}3\phantom{A}A2k+1A\phantom{A}2k+1\phantom{A}AB(k,2)\phantom{A}B(k,2) \simeq osp(2k+1|4)A(2k+1 \vert 4)\phantom{A}ASO(2k+1)A\phantom{A}SO(2k+1)\phantom{A}
A3A\phantom{A}3\phantom{A}A2kA\phantom{A}2k\phantom{A}AD(k,2)\phantom{A}D(k,2)\simeq osp(2k|4)A(2k \vert 4)\phantom{A}ASO(2k)A\phantom{A}SO(2k)\phantom{A}M2-brane
D=3 SYM
BLG model
ABJM model
A4A\phantom{A}4\phantom{A}Ak+1A\phantom{A}k+1\phantom{A}AA(3,k)𝔰𝔩(4|k+1)A\phantom{A}A(3,k)\simeq \mathfrak{sl}(4 \vert k+1)\phantom{A}AU(k+1)A\phantom{A}U(k+1)\phantom{A}D3-brane
D=4 N=4 SYM
D=4 N=2 SYM
D=4 N=1 SYM
A5A\phantom{A}5\phantom{A}A1A\phantom{A}1\phantom{A}AF(4)A\phantom{A}F(4)\phantom{A}ASO(3)A\phantom{A}SO(3)\phantom{A}D4-brane
D=5 SYM
A6A\phantom{A}6\phantom{A}AkA\phantom{A}k\phantom{A}AD(4,k)\phantom{A}D(4,k) \simeq osp(8|2k)A(8 \vert 2k)\phantom{A}ASp(k)A\phantom{A}Sp(k)\phantom{A}M5-brane
D=6 N=(2,0) SCFT
D=6 N=(1,0) SCFT

(Shnider 88, also Nahm 78, see Minwalla 98, section 4.2)

References

General

Anomaly cancellation

Discussion of anomaly cancellation and Green-Schwarz mechanism:

Lagrangian description

A class of Lagrangian densities for D=6 N=(1,0) SCFTs with non-abelian gauge group has been proposed in

reviewed in

An attempt to understand the SSW 11-models as higher gauge theories for gauge-L-infinity algebras which are variants of the string Lie 2-algebra is due to:

Geometric engineering on 5-branes

On D=6 N=(1,0) SCFTs via geometric engineering on M5-branes/NS5-branes at D-, E-type ADE-singularities, notably from M-theory on S1/G_HW times H/G_ADE, hence from orbifolds of type I' string theory (see at half NS5-brane):

KK-Compactification to D=4D=4 𝒩=1\mathcal{N} = 1 SYM

The KK-compactification specifically of the D=6 N=(1,0) SCFT to D=4 N=1 super Yang-Mills:

  • Ibrahima Bah, Christopher Beem, Nikolay Bobev, Brian Wecht, Four-Dimensional SCFTs from M5-Branes (arXiv:1203.0303)

  • Shlomo S. Razamat, Cumrun Vafa, Gabi Zafrir, 4d4d 𝒩=1\mathcal{N} = 1 from 6d(1,0)6d (1,0), J. High Energ. Phys. (2017) 2017: 64 (arXiv:1610.09178)

  • Ibrahima Bah, Amihay Hanany, Kazunobu Maruyoshi, Shlomo S. Razamat, Yuji Tachikawa, Gabi Zafrir, 4d4d 𝒩=1\mathcal{N}=1 from 6d6d 𝒩=(1,0)\mathcal{N}=(1,0) on a torus with fluxes (arXiv:1702.04740)

  • Hee-Cheol Kim, Shlomo S. Razamat, Cumrun Vafa, Gabi Zafrir, E-String Theory on Riemann Surfaces, Fortsch. Phys. (arXiv:1709.02496)

  • Hee-Cheol Kim, Shlomo S. Razamat, Cumrun Vafa, Gabi Zafrir, D-type Conformal Matter and SU/USp Quivers, JHEP06(2018)058 (arXiv:1802.00620)

  • Hee-Cheol Kim, Shlomo S. Razamat, Cumrun Vafa, Gabi Zafrir, Compactifications of ADE conformal matter on a torus, JHEP09(2018)110 (arXiv:1806.07620)

  • Shlomo S. Razamat, Gabi Zafrir, Compactification of 6d minimal SCFTs on Riemann surfaces, Phys. Rev. D 98, 066006 (2018) (arXiv:1806.09196)

  • Jin Chen, Babak Haghighat, Shuwei Liu, Marcus Sperling, 4d N=1 from 6d D-type N=(1,0) (arXiv:1907.00536)

SU(2)SU(2)-flavor symmetry on heterotic M5-branes

Emergence of SU(2) flavor-symmetry on single M5-branes in heterotic M-theory on ADE-orbifolds (in the D=6 N=(1,0) SCFT on small instantons in heterotic string theory):

Argument for this by translation under duality between M-theory and type IIA string theory to half NS5-brane/D6/D8-brane bound state systems in type I' string theory:

Reviewed in:

  • Santiago Cabrera, Amihay Hanany, Marcus Sperling, Section 2.3 of: Magnetic Quivers, Higgs Branches, and 6d 𝒩=(1,0)\mathcal{N}=(1,0) Theories, JHEP06(2019)071, JHEP07(2019)137 (arXiv:1904.12293)

The emergence of flavor in these half NS5-brane/D6/D8-brane bound state systems, due to the semi-infinite extension of the D6-branes making them act as flavor branes:

Reviewed in:

  • Fabio Apruzzi, Marco Fazzi, Section 2.1 of: AdS 7/CFT 6AdS_7/CFT_6 with orientifolds, J. High Energ. Phys. (2018) 2018: 124 (arXiv:1712.03235)

See also:

Last revised on November 15, 2020 at 09:39:10. See the history of this page for a list of all contributions to it.