nLab 4d superconformal gauge field theory

There exists superconformal field theories/super Yang-Mills theories in 4 dimensions:

• N=1 D=4 super Yang-Mills theory

• N=2 D=4 super Yang-Mills theory

• N=4 D=4 super Yang-Mills theory

and by topological twisting these give rise to

• topologically twisted D=4 super Yang-Mills theory

according to the classification of superconformal symmetry…

$d$	$N$	superconformal super Lie algebra	R-symmetry	black brane worldvolume superconformal field theory via AdS-CFT
$\phantom{A}3\phantom{A}$	$\phantom{A}2k+1\phantom{A}$	$\phantom{A}B(k,2) \simeq$ 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)