Supersymmetric Theories  

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

L = − \(1\over2\)(∂a A)2 − \(1\over2\)(∂a B)2 − \(1\over2\)λ* (γ · ∂) λ,

with A a scalar, B a pseudoscalar, λ of spin-1/2, λ*:= λ γ4.
@ General references: Haber & Haskins TASI(18)-a1712 [intro].
@ Wess-Zumino model: 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-proc [phase diagram]; Dimitrijević et al PRD(10)-a1001 [deformed]; Yu & Yang PRL(10) [simulation with cold atom-molecule mixtures in 2D optical lattices]; Frasca JNMP(13)-a1308 [massless, classical solutions]; > s.a. supersymmetry breaking.
@ Wess-Zumino-Witten model: 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].
@ Supersymmetric extension of local Lorentz symmetry: Abe & Nakanishi IJMPA(89), IJMPA(90).
@ Emergent supersymmetry: Jackiw & Polychronakos PRD(00)ht [fluid dynamics]; Goh et al JHEP(05)ht/03, JHEP(06); Lee PRB(07)cm/06 [in a lattice model at a quantum critical point]; Lee a1009-ln [in condensed-matter systems]; Huijse et al PRL(15)-a1403 [1+1 dimensional models]; Gao & Liu JHEP(18)-a1701; Zhao & Liu npjQM(19)-a1706 [supersymmetry (non-)emergence at a quantum critical point].
@ Spin chains: Kagan & Young NPB(08); Hagendorf JSP(13)-a1207 [with dynamical lattice supersymmetry].
@ 3D theories: Awad & Faizal JHEP(15)-a1503 [3D scalar field theories]; Cottrell et al JHEP(16)-a1509 [and their gravity duals].
@ Other theories: Andreev JRLR(92) [2-level systems]; Metz et al PRL(99) + pn(99)aug [nuclear physics]; 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]; Horváthy et al PRD(10)-a1004 [between Jackiw-Nair and Dirac-Majorana anyons]; Fendley & Hagendorf JSM(11)-a1011 [fermion chain, ground state]; Fan et al JHEP(12) [stealth supersymmetry]; Wu et al a1812 [fermion-boson symmetry]; > s.a. higher-spin theories; sigma models; stochastic quantum mechanics.
> Related topics : see Axinos; boundaries in field theory.

Modified Supersymmetric Theories > s.a. types of quantum field theories.
* Pseudo-supersymmetry: It arises in brane world models, where two branes preserve different halves of the bulk supersymmetry; Supersymmetry is broken, although each sector of the model is separately supersymmetric.
@ Fractional supersymmetry: Mohammedi MPLA(95); de Azcárraga & Macfarlane JMP(96)ht/95; Dunne et al IJMPA(97).
@ Parasupersymmetry: Tanaka AP(07) [quantum many-body systems]; > s.a. fock space [parasupersymmetric system].
@ Non-linear realizations: Clark & Love PRD(04)ht [Goldstino and R-axion]; Love MPLA(05).
@ Non-commutative geometry: Hussain & Thompson PLB(91), PLB(91); Chamseddine PLB(94); Terashima PLB(00)ht; Habara PTP(03)ht/02; Beenakker et al a1409 [almost commutative geometries], a1409 [supersymmetry breaking].
@ Non-commutative supersymmetric Yang-Mills: Kalau & Walze JGP(97); Hashimoto & Itzhaki PLB(99)ht [AdS-cft], JHEP(99)ht [and ordinary].
@ Moyal-Weyl deformed: Ferrara & Lledó JHEP(00)ht.
@ Without Grassmann variables: Cahill JHEP(01)ht.
@ In curved spaces: Kehagias & Russo NPB(13)-a1211 [d-dimensional]; Dumitrescu a1608-in [intro].
@ Other generalizations: Devchand & Nuyts AIP(98)ht [Lorentz-covariant generalizations]; Maumary & Ojima mp/00 [and homotopy]; Klein PRD(02)ht, PRD(03)ht/02, ht/02-conf [pseudo-supersymmetry]; Besnard mp/04 [number-operator algebras]; Frampton MPLA(06)ht/05 [misaligned supersymmetry]; Álvarez et al PLB(14)-a1306, Symm(21)-a2104 [unconventional representation, without supersymmetric partners]; Ho a1506 [off-shell supersymmetry]; Meyer et al JHEP(17)-a1703 [non-relativistic supersymmetric field theories]; > s.a. Supersymmetry [non-associative].

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