D=5 super Yang-Mills theory (changes) in nLab

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Contents

Idea

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

Properties

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.

• D=4 super Yang-Mills theory

• D=5D=5 super Yang-Mills theory

  • D=5 Yang-Mills theory

  • D=5 Maxwell theory

  • D=5 Einstein-Maxwell theory

• D=6 super Yang-Mills theory

• D=10 super Yang-Mills theory

dd	NN	superconformal super Lie algebra	R-symmetry	black 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 D=3 SYM 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
A5A\phantom{A}5\phantom{A}	A1A\phantom{A}1\phantom{A}	AF(4)A\phantom{A}F(4)\phantom{A}	ASO(3)A\phantom{A}SO(3)\phantom{A}	D4-brane D=5 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)

References

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 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)

instantons:

• Dongsu Bak, Andreas Gustavsson, One dyonic instanton in 5d maximal SYM theory (arXiv:1305.3637)

On Yang-Mills solitons in 5d as Yang-Mills instantons in 4d:

• Constantinos Papageorgakis, Andrew B. Royston: Instanton-soliton loops in 5D super-Yang-Mills, Proc. Symp. Pure Math. 88 (2014) 351-360 [[arXiv:1409.4093](https://arxiv.org/abs/1409.4093), doi:10.1090/pspum/088, spire:1336668]

topological twists:

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

The perturbation theory is considered in

• Zvi Bern, John Joseph Carrasco, Lance Dixon, Michael Douglas, Matt von Hippel, Henrik Johansson, D=5D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops (arXiv:1210.7709)

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):

• Nathan Seiberg, Sec. 7 of Notes on Theories with 16 Supercharges, Nucl. Phys. Proc. Suppl. 67:158-171, 1998 (arXiv:hep-th/9705117)

• Michael Douglas, On D=5 super Yang-Mills theory and (2,0) theory, JHEP 1102:011, 2011 (arXiv:1012.2880)

• Neil Lambert, Constantinos Papageorgakis, Maximilian Schmidt-Sommerfeld, M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills, JHEP 1101:083, 2011 (arXiv:1012.2882)

• Edward Witten, Sections 4 and 5 of Fivebranes and Knots (arXiv:1101.3216)

• Moritz McGarrie, 5D Maximally Supersymmetric Yang-Mills in 4D Superspace: Applications (arXiv:1303.4534)

• Yuji Tachikawa, Section 6.4 of: 𝒩=2\mathcal{N}=2 supersymmetric dynamics for pedestrians, Lecture Notes in Physics, vol. 890, 2014 (arXiv:1312.2684, doi:10.1007/978-3-319-08822-8, web version)

• Chris Hull, Neil Lambert, Emergent Time and the M5-Brane, JHEP06(2014)016 (arXiv:1403.4532)

• Chiung Hwang, Joonho Kim, Seok Kim, Jaemo Park, Section 3.4.2 of: General instanton counting and 5d SCFT (arxiv:1406.6793)

• Andreas Gustavsson, Five-dimensional Super-Yang-Mills and its Kaluza-Klein tower. JHEP01(2019)222 (arXiv:1812.01897)

• Neil Lambert, Sec. 3.1 and 3.4.3. of Lessons from M2’s and Hopes for M5’s, Proceedings of the LMS-EPSRC Durham Symposium: Higher Structures in M-Theory, August 2018 Fortschritte der Physik, 2019 (arXiv:1903.02825, slides pdf, video recording)

• Lakshya Bhardwaj, Patrick Jefferson, Hee-Cheol Kim, Houri-Christina Tarazi, Cumrun Vafa, Twisted Circle Compactification of 6d SCFTs (arXiv:1909.11666)

• Lakshya Bhardwaj, More 5d KK theories (arXiv:2005.01722)

• Max Hubner, 5d SCFTs from (E n,E m)(E_n, E_m) Conformal Matter (arXiv:2006.01694)

• Lakshya Bhardwaj, Flavor Symmetry of 5d SCFTs, Part 1: General Setup (arXiv:2010.13230)

• Lakshya Bhardwaj, Flavor Symmetry of 5d SCFTs, Part 2: Applications (arXiv:2010.13235)

• Hirotaka Hayashi, Hee-Cheol Kim, Kantaro Ohmori, 6d/5d exceptional gauge theories from web diagrams (arXiv:2103.02799)

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:

• Ofer Aharony, Amihay Hanany, Branes, Superpotentials and Superconformal Fixed Points, Nucl. Phys. B504:239-271, 1997 (arXiv:hep-th/9704170)

• Ofer Aharony, Amihay Hanany, Barak Kol, Webs of (p,q)(p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams, JHEP 9801:002,1998 (arXiv:hep-th/9710116)

• Oren Bergman, Gabi Zafrir, Lifting 4d dualities to 5d, JHEP04 (2015) 141 (arXiv:1410.2806)

Further developments:

• Taro Kimura, Rui-Dong Zhu, Section 2 of Web Construction of ABCDEFG and Affine Quiver Gauge Theories (arXiv:1907.02382)