Supersymmetric Gauge Theories |

**In General** > s.a. lattice gauge theory;
non-commutative theories; twistors;
types of gauge theories.

* __Motivation__: It is
a beautiful theory; It reduces the quantum field theory divergences,
*N* = 4 global supersymmetric gauge theory appears to be finite;
It seems to give a vanishing cosmological constant; Energy becomes
non-negative.

* __Superpotential__:
It can be at most cubic in the fields, for renormalizability.

* __Particle content__:
Need at least two Higgs superdoublets to give masses to quarks and
leptons (and other reasons); The mass of the lightest Higgs must be
≤ 150 GeV; The minimal supersymmetric standard model (MSSM) has

- Gauge bosons, *g*,
*W*^{ ±}, *Z*,
*γ*, with partners \(\tilde g\), \(\tilde W{}^\pm\),
\(\tilde Z\), \(\tilde\gamma\).

- Quarks and leptons, *q* and
*l*, with corresponding sfermions, \(\tilde q\) and \(\tilde l\).

- Higgs fermion doublets, (\(\tilde
h{}^0\), \(\tilde h{}^-\)) and (\(\tilde{\bar h}{}^-\), \(\tilde{\bar h}{}^0\)),
with Higgs boson partners (*h*^{0},
*h*^{−}) and (\(\bar h{}^-\),
\(\bar h{}^0\)).

* __R-parity__: A symmetry invoked
to explain conservation of baryon and lepton numbers, despite the couplings;
It implies that supersymmetric partners are produced in pairs.

* __And the cosmological constant__:
Λ may not be zero, but it is with R symmetry or strings.

* __Experimentally__: The mass
of leptonic partners must be at least 45 GeV, from LEP experiments with
*Z*s.

**References**
> s.a. particle physics; supersymmetry
in field theory [including modified supersymmetric theories and curved spacetime].

@ __General__:
Caicedo & Gambini PRD(89);
Fucito ht/97-conf [supersymmetric-Yang-Mills];
Hübsch NPB(00) [coexistence of supersymmetry and gauge];
Strassler in(04)ht/03-TASI01 [and scaling];
Mateos a1602-ln.

@ __Books, intros, reviews__: Gières 88;
Bailin & Love 94 [III];
Piguet ht/97-ln;
Gates ht/98-ln;
Bellucci et al ed-06
[r CQG(07)];
Binétruy 06;
Aitchison 07;
Cecotti 15.

@ __Wilson loops__: Erickson et al NPB(00)ht;
Zarembo NPB(02)ht;
Lunin JHEP(06)ht.

@ __Diffeomorphism-invariant__: Husain PRD(96)ht;
Piguet CQG(00) [vector supersymmetry].

> __Related topics__: see duality;
Division Algebras.

**Standard Model and Related Theories** > s.a. yang-mills theory.

* __Motivation__: It seems to
lead to better gauge coupling constant unification, at about 2 ×
10^{16} GeV; It reduces the number of
parameters of the theory; All fermions are embedded in a few supermultiplets;
It solves the hierarchy problem, because *μ* has no renormalization
(all terms cancel), if at least *N* = 1 supersymmetry is unbroken down
to a few × 100 GeV; It provides particle masses (breaking and Higgs
mechanism); It provides a compelling candidate particle for the dark matter.

@ __Standard model__:
Csáki MPLA(96) [MSSM review];
Kong IJMPA(04);
López-Fogliani & Muñoz PRL(06);
Cai et al PRL(08)
[proposal of spin-1 top and bottom quark superpartners];
Berger et al JHEP(09) [MSSM and experiments];
Ma MPLA(09) [axionic extensions];
Rodriguez IJMPA(10) [history];
Maniatis IJMPA(10),
Ellwanger et al PRP(10) [next-to-minimal susy extension];
Antoniadis et al NPB(10)-a1006 [non-linear MSSM];
> s.a. inflationary scenarios.

@ __Supersymmetric Yang-Mills theory__: Arnsdorf & Smolin ht/01 [duality for superconformal Yang-Mills];
Sethi JHEP(04);
Bossard et al PLB(09)-a0908 [maximally supersymmetric, UV behavior];
Fokken a1701-PhD
[\({\cal N} = 4\) SYM theory and its deformations].

@ __GUTs__: López et al RNC(94);
Jeannerot et al PRD(03)hp [cosmic strings].

@ __Related topics__: Dienes & Thomas PRD(10)-a0911 [Fayet-Iliopoulos terms, inconsistency in supergravity];
Kobakhidze & Talia a1508 [deviations from MSSM, effective field theory framework];
Bajc et al JHEP(18)-a1709 [asymptotically safe scenario].

> __Related topics__: see 3D gravity;
modified QED; monopoles;
poincaré group [continuous-spin theories].

main page
– abbreviations
– journals – comments
– other sites – acknowledgements

send feedback and suggestions to bombelli at olemiss.edu – modified 1 jan 2020