Contents

# Contents

## Idea

super Yang-Mills theory on a 4-dimensional spacetime with $N = 1$ supersymmetry.

$d$$N$superconformal super Lie algebraR-symmetryblack brane worldvolume
superconformal field theory
$\phantom{A}3\phantom{A}$$\phantom{A}2k+1\phantom{A}$$\phantom{A}B(k,2) \simeq$ osp$(2k+1 \vert 4)\phantom{A}$$\phantom{A}SO(2k+1)\phantom{A}$
$\phantom{A}3\phantom{A}$$\phantom{A}2k\phantom{A}$$\phantom{A}D(k,2)\simeq$ osp$(2k \vert 4)\phantom{A}$$\phantom{A}SO(2k)\phantom{A}$M2-brane
D=3 SYM
BLG model
ABJM model
$\phantom{A}4\phantom{A}$$\phantom{A}k+1\phantom{A}$$\phantom{A}A(3,k)\simeq \mathfrak{sl}(4 \vert k+1)\phantom{A}$$\phantom{A}U(k+1)\phantom{A}$D3-brane
D=4 N=4 SYM
D=4 N=2 SYM
D=4 N=1 SYM
$\phantom{A}5\phantom{A}$$\phantom{A}1\phantom{A}$$\phantom{A}F(4)\phantom{A}$$\phantom{A}SO(3)\phantom{A}$D4-brane
D=5 SYM
$\phantom{A}6\phantom{A}$$\phantom{A}k\phantom{A}$$\phantom{A}D(4,k) \simeq$ osp$(8 \vert 2k)\phantom{A}$$\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$$N$superconformal super Lie algebraR-symmetryblack brane worldvolume
superconformal field theory
$\phantom{A}3\phantom{A}$$\phantom{A}2k+1\phantom{A}$$\phantom{A}B(k,2) \simeq$ osp$(2k+1 \vert 4)\phantom{A}$$\phantom{A}SO(2k+1)\phantom{A}$
$\phantom{A}3\phantom{A}$$\phantom{A}2k\phantom{A}$$\phantom{A}D(k,2)\simeq$ osp$(2k \vert 4)\phantom{A}$$\phantom{A}SO(2k)\phantom{A}$M2-brane
D=3 SYM
BLG model
ABJM model
$\phantom{A}4\phantom{A}$$\phantom{A}k+1\phantom{A}$$\phantom{A}A(3,k)\simeq \mathfrak{sl}(4 \vert k+1)\phantom{A}$$\phantom{A}U(k+1)\phantom{A}$D3-brane
D=4 N=4 SYM
D=4 N=2 SYM
D=4 N=1 SYM
$\phantom{A}5\phantom{A}$$\phantom{A}1\phantom{A}$$\phantom{A}F(4)\phantom{A}$$\phantom{A}SO(3)\phantom{A}$D4-brane
D=5 SYM
$\phantom{A}6\phantom{A}$$\phantom{A}k\phantom{A}$$\phantom{A}D(4,k) \simeq$ osp$(8 \vert 2k)\phantom{A}$$\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:

• Hugh Osborn, $\mathcal{N}=1$ Superconformal Symmetry in Four Dimensional Quantum Field Theory, Annals Phys. 272:243-294, 1999 (arXiv:hep-th/9808041)

Review:

• Yuji Tachikawa, Lectures on $4d$ $N=1$ dynamics and related topics (arXiv:1812.08946)

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, $4d$ $\mathcal{N} = 1$ from $6d (1,0)$, J. High Energ. Phys. (2017) 2017: 64 (arXiv:1610.09178)

• Ibrahima Bah, Amihay Hanany, Kazunobu Maruyoshi, Shlomo S. Razamat, Yuji Tachikawa, Gabi Zafrir, $4d$ $\mathcal{N}=1$ from $6d$ $\mathcal{N}=(1,0)$ 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)

### Witten index

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 January 15, 2020 at 03:25:46. See the history of this page for a list of all contributions to it.