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.
main page – abbreviations – journals – comments – other
sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 1
nov 2009