nLab D=5 super Yang-Mills theory



Quantum Field Theory

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



field theory:

Lagrangian field theory


quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization



States and observables

Operator algebra

Local QFT

Perturbative QFT




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


As the worldvolume theory of the D4-brane

D=5D = 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=6D=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.

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
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
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)



  • 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 5D5D, 𝒩=2\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)


topological twists:

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

The perturbation theory is considered in

From D=6D = 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

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)(p,q)5-brane webs

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

Further developments:

Last revised on August 8, 2021 at 13:47:52. See the history of this page for a list of all contributions to it.