Supersymmetric Theories  

Types of Theories > s.a. [types of field theories]; boundaries in field theory; modified quantum mechanics [supersymmetric].
* Wess-Zumino model: The simplest model of global supersymmetry, with Lagrangian

L = – (a A)2 – (a B)2 –  * ( · ) ,

with A a scalar, B a pseudoscalar, of spin-1/2, *:= 4.
@ Wess-Zumino: Wess & Zumino NPB(74); Girotti et al NPB(00)ht [non-commutative]; Britto & Feng PRL(03) [N = 1/2 is renormalizable]; Ritter CMP(04)ht/03 [vacuum geometry]; Synatschke et al a0909 [phase diagram]; > s.a. supersymmetry breaking.
@ Wess-Zumino-Witten: Witten NPB(83), CMP(84); Gawedzki ht/99-ln; Lugo PLB(01), Moreno & Schaposnik NPB(01) [non-commutative]; Gawedzki et al CMP(04)ht/01 [boundary theory, canonical quantization]; Arcioni et al JGP(04) [on random Regge triangulations]; Liao PRD(06) [in odd-dimensional spacetime]; > s.a. bundle [gerbes].
@ Diffeomorphism-invariant, generally covariant: Gamboa & Zanelli AP(88); Husain PRD(96)ht; Piguet CQG(00)ht [vector supersymmetry], ht/00-in [and ghost field equations].
@ And minisuperspace: D'Eath & Hughes PLB(88).
@ Supersymmetric extension of local Lorentz symmetry: Abe & Nakanishi IJMPA(89), IJMPA(90).
@ And gravity: Tung PLA(00)gq/99; > s.a. brans-dicke theory; Hypergravity; quantum cosmology; semiclassical quantum gravity; supergravity.
@ Other theories: Metz et al PRL(99) + pn(99)aug [nuclear physics]; Jackiw & Polychronakos PRD(00)ht [fluid dynamics]; Rupp et al NPB(01) [non-linear realizations]; Requardt IJGMP(05)mp/04 [on graphs/networks]; Ho & Tanaka AP(06) [Schrödinger, Pauli, Dirac equations]; Correa & Plyushchay AP(07) [hidden supersymmetry in bosonic systems]; news pw(08)mar [in ultracold atoms, proposal]; Kagan & Young NPB(08) [spin chains]; > s.a. sigma model.

Supersymmetric Gauge Theories > s.a. lattice gauge theory; non-commutative theories; twistors; types of gauge theories; yang-mills theory.
* Motivation, in general: It is a beautiful theory; Reduces the quantum field theory divergences, N = 4 global supersymmetric gauge theory appears to be finite; Seems to give a vanishing cosmological constant; Energy becomes non-negative.
* Motivation, standard model: Seems to lead to better gauge coupling constant unification, at about 2 × 1016 GeV; Reduces the number of parameters of the theory; Fermions all embedded in few supermultiplets; Solves the hierarchy problem, because has no renormalization (all terms cancel), if at least N = 1 supersymmetry is unbroken down to a few × 100 GeV; Provides particle masses (breaking and Higgs mechanism); Provides a compelling candidate particle for the dark matter.
* Superpotential: It can be at most cubic in the fields, for renormalizability.
* Particle content: Need at least two Higgs superdoublets to give masses to q's and l's (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, , with partners \tilde g, \tilde W +/–, \tilde Z, \tilde .
- Quarks and leptons, q and l, with corresponding sfermions, \tilde q and \tilde l.
- Higgs fermion doublets, (\tilde h0, \tilde h–) and (\tilde\bar h–, \tilde\bar h0), with Higgs boson partners (h0, h–) and (\bar h–, \bar h0).
* 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: 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.
@ 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]; > s.a. inflationary scenarios.
@ Supersymmetric Yang-Mills theory: Arnsdorf & Smolin ht/01 [duality for superconformal Yang-Mills]; Sethi JHEP(04); Bossard et al a0908 [maximally supersymmetric, UV behavior].
@ GUTs: López et al RNC(94); Jeannerot et al PRD(03)hp [cosmic strings].
> Related topics: see monopoles.

References > s.a. particle physics; supersymmetry in field theory [including modified supersymmetric theories].
@ General: Caicedo & Gambini PRD(89); Fucito ht/97-in [supersymmetric-Yang-Mills]; Hübsch NPB(00) [coexistence of supersymmetry and gauge]; Lee cm/06 [emergence at a quantum critical point].
@ Books, intros, reviews: Gières 88; Bailin & Love 94 [III]; Piguet ht/97-ln; Gates ht/98-ln; Strassler ht/03-ln [and scaling]; Bellucci et al ed-06 [r CQG(07)]; Binétruy 06; Aitchison 07.
@ 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.

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