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 (h⁰, 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 Zs.

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 × 10¹⁶ 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].

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