Contents

supersymmetry

# Contents

## Idea

super Yang-Mills theory on spacetimes of dimension $D=5$, hence the supersymmetric version of D=5 Yang-Mills theory.

## Properties

### As the worldvolume theory of the D4-brane

$D = 5$ SYM may be regarded as the worldvolume field theory on the D4-brane in type II string theory.

### Via reduction from the M5-brane / $D=6$ SCFT

For relation to the D=6 N=(2,0) SCFT via KK-compactification on a circle fiber, hence as worldvolume theory of the double dimensional reduction of the M5-brane (see also at Perry-Schwarz Lagrangian), see the references below.

$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)

### General

• Nathan Seiberg, Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics, Phys. Lett. B388:753-760, 1996 (arXiv:hep-th/9608111)

• Arthur Hebecker, 5D Super Yang-Mills Theory in 4D Superspace, Superfield Brane Operators, and Applications to Orbifold GUTs (arXiv:hep-ph/0112230)

• Clay Cordova, Daniel Jafferis, Five-Dimensional Maximally Supersymmetric Yang-Mills in Supergravity Backgrounds (arXiv:1305.2886)

• Shuichi Yokoyama, Supersymmetry Algebra in Super Yang-Mills Theories, JHEP09(2015)211 (arXiv:1506.03522)

• I.L. Buchbinder, E.A. Ivanov, I.B. Samsonov, Low-energy effective action in $5D$, $\mathcal{N}=2$ supersymmetric gauge theory, Nuclear Physics B Volume 940, March 2019, Pages 54-62 (arXiv:1812.07206)

• Lakshya Bhardwaj, On the classification of 5d SCFTs (arXiv:1909.09635)

• Louise Anderson, Five-dimensional topologically twisted maximally supersymmetric Yang-Mills theory (arXiv:1212.5019)

The perturbation theory is considered in

### From $D = 6$ SCFT

Relation to the D=6 N=(2,0) SCFT via KK-compactification on a circle fiber, hence as worldvolume theory of the D4-brane double dimensional reduction of the M5-brane (see also at Perry-Schwarz Lagrangian):

### From M-theory on Calabi-Yau 3-folds

• Cyril Closset, Michele Del Zotto, Vivek Saxena, Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective (arXiv:1812.10451)

• Vivek Saxena, Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study, High Energ. Phys. 2020, 198 (2020) (arXiv:1911.09574)

### Realization on $(p,q)$5-brane webs

Realization (geometric engineering) on (p,q)5-brane webs:

Further developments: