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D=4 N=1 super Yang-Mills theory
Contents
Contents
Idea
super Yang-Mills theory on a 4-dimensional spacetime with N = 1 N = 1 supersymmetry .
d d N N superconformal super Lie algebra R-symmetry black brane worldvolume superconformal field theory via AdS-CFT A 3 A \phantom{A}3\phantom{A} A 2 k + 1 A \phantom{A}2k+1\phantom{A} A B ( k , 2 ) ≃ \phantom{A}B(k,2) \simeq osp ( 2 k + 1 | 4 ) A (2k+1 \vert 4)\phantom{A} A SO ( 2 k + 1 ) A \phantom{A}SO(2k+1)\phantom{A}
A 3 A \phantom{A}3\phantom{A} A 2 k A \phantom{A}2k\phantom{A} A D ( k , 2 ) ≃ \phantom{A}D(k,2)\simeq osp ( 2 k | 4 ) A (2k \vert 4)\phantom{A} A SO ( 2 k ) A \phantom{A}SO(2k)\phantom{A} M2-brane D=3 SYM BLG model ABJM model
A 4 A \phantom{A}4\phantom{A} A k + 1 A \phantom{A}k+1\phantom{A} A A ( 3 , k ) ≃ 𝔰𝔩 ( 4 | k + 1 ) A \phantom{A}A(3,k)\simeq \mathfrak{sl}(4 \vert k+1)\phantom{A} A U ( 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
A 5 A \phantom{A}5\phantom{A} A 1 A \phantom{A}1\phantom{A} A F ( 4 ) A \phantom{A}F(4)\phantom{A} A SO ( 3 ) A \phantom{A}SO(3)\phantom{A} D4-brane D=5 SYM
A 6 A \phantom{A}6\phantom{A} A k A \phantom{A}k\phantom{A} A D ( 4 , k ) ≃ \phantom{A}D(4,k) \simeq osp ( 8 | 2 k ) A (8 \vert 2k)\phantom{A} A Sp ( 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 )
d d N N superconformal super Lie algebra R-symmetry black brane worldvolume superconformal field theory via AdS-CFT A 3 A \phantom{A}3\phantom{A} A 2 k + 1 A \phantom{A}2k+1\phantom{A} A B ( k , 2 ) ≃ \phantom{A}B(k,2) \simeq osp ( 2 k + 1 | 4 ) A (2k+1 \vert 4)\phantom{A} A SO ( 2 k + 1 ) A \phantom{A}SO(2k+1)\phantom{A}
A 3 A \phantom{A}3\phantom{A} A 2 k A \phantom{A}2k\phantom{A} A D ( k , 2 ) ≃ \phantom{A}D(k,2)\simeq osp ( 2 k | 4 ) A (2k \vert 4)\phantom{A} A SO ( 2 k ) A \phantom{A}SO(2k)\phantom{A} M2-brane D=3 SYM BLG model ABJM model
A 4 A \phantom{A}4\phantom{A} A k + 1 A \phantom{A}k+1\phantom{A} A A ( 3 , k ) ≃ 𝔰𝔩 ( 4 | k + 1 ) A \phantom{A}A(3,k)\simeq \mathfrak{sl}(4 \vert k+1)\phantom{A} A U ( 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
A 5 A \phantom{A}5\phantom{A} A 1 A \phantom{A}1\phantom{A} A F ( 4 ) A \phantom{A}F(4)\phantom{A} A SO ( 3 ) A \phantom{A}SO(3)\phantom{A} D4-brane D=5 SYM
A 6 A \phantom{A}6\phantom{A} A k A \phantom{A}k\phantom{A} A D ( 4 , k ) ≃ \phantom{A}D(4,k) \simeq osp ( 8 | 2 k ) A (8 \vert 2k)\phantom{A} A Sp ( 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
Original articles:
Review:
Yuji Tachikawa, Lectures on 4 d 4d N = 1 N=1 dynamics and related topics (arXiv:1812.08946 )
See also at N=2 D=4 super Yang-Mills theory .
The KK-compactification of the D=6 N=(1,0) SCFT (on M5-branes ) 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, 4 d 4d 𝒩 = 1 \mathcal{N} = 1 from 6 d ( 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, 4 d 4d 𝒩 = 1 \mathcal{N}=1 from 6 d 6d 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 )
Via D3 branes at resolved orbifold singularities and invoking a generalized McKay correspondence :
Pietro G. Fré , Lectures on resolutions à la Kronheimer of orbifold singularities, McKay quivers for Gauge Theories on D3 branes, and the issue of Ricci flat metrics on the resolved three-folds [arXiv:2308.14022 ]
The Witten index :
Leonardo Rastelli , Shlomo S. Razamat, The supersymmetric index in four dimensions , Journal of Physics A: Mathematical and Theoretical, Volume 50, Number 44 (arXiv:1608.02965 )
Last revised on June 28, 2024 at 13:30:23.
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