Conformal superalgebras, massless representations, and hidden symmetries

Journal Article · Tue Jul 15 00:00:00 EDT 1986 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.34.525· OSTI ID:5411926

Binegar, B

In this paper we study the massless representations of the conformal superalgebras u(2,2/N-italic), su(2,2/N-italic), pu(2,2/4), and psu(2,2/4). It is argued that they are the only unitary representations of conformal supersymmetry that have a realistic (i.e., finite) particle spectrum. We show that the massless unitary irreducible representations (UIR's) of an N-italic-extended conformal supersymmetry symmetry restrict to irreducible representations of the N-italic-extended super-Poincare-acute-accent algebra and prove that the massless UIR's of the N-italic-extended super-Poincare-acute-accent algebra have unique extensions to massless UIR's of su(2,2/N-italic) if N-italicnot =4, or to massless UIR's of pu(2,2/4) if N-italic = 4. These facts suggest that the hidden U(N-italic) symmetries found in N-italic-extended supersymmetric gauge theories may be, in fact, only a subalgebra of an overall N-italic-extended conformal superalgebra. An explicit construction of all the massless representations of su(2,2/N-italicnot =4) and pu(2,2/4) is given. It is seen that the adjoint representation of the internal su(N-italic) subalgebra never appears in a massless representation of N-italic-extended conformal supersymmetry.

• Research Organization: Physique Mathe-acute-accentmatique, Faculte-acute-accent des Sciences, Mirande, Universite-acute-accent de Dijon, 21000 Dijon, France
• OSTI ID: 5411926
• Journal Information: Phys. Rev. D; (United States), Vol. 34:2
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
MASSLESS PARTICLES
SUPERSYMMETRY
ALGORITHMS
FIELD EQUATIONS
GAUGE INVARIANCE
POINCARE GROUPS
SU GROUPS
U GROUPS
ELEMENTARY PARTICLES
EQUATIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL LOGIC
SYMMETRY
SYMMETRY GROUPS
645301* - High Energy Physics- Particle Invariance Principles & Symmetries- General- (-1987)
645400 - High Energy Physics- Field Theory