Finite and Infinite Symmetries in (2+1)-Dimensional Field Theory

Abstract

These days, Franco Iachello is {\it the\/} eminent practitioner applying classical and finite groups to physics. In this he is following a tradition at Yale, established by the late Feza Gursey, and succeeding Gursey in the Gibbs chair; Gursey in turn, had Pauli as a mentor. Iachello's striking achievement has been to find an actual realization of arcane supersymmetry within mundane adjacent even-odd nuclei. Thus far this is the only {\it physical\/} use of supersymmetry, and its fans surely must be surprised at the venue. Here we describe the role of $SO(2,1)$ conformal symmetry in non-relativistic Chern--Simons theory: how it acts, how it controls the nature of solutions, how it expands to an infinite group on the manifold of static solutions thereby rendering the static problem completely integrable. Since Iachello has also used the $SO(2,1)$ group in various contexts, this essay is presented to him on the occasion of his fiftieth birthday.

23 double-spaced pages

References in corpus (4)

• Scattering at Planckian Energies
• Extended Superconformal Galilean Symmetry in Chern-Simons Matter Systems
• Electromagnetic fields of a massless particle and the eikonal
• Chern-Simons Solitons, Toda Theories and the Chiral Model

Cited by in corpus (11)

• Gravity duals for non-relativistic CFTs
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Nonrelativistic conformal field theories
• Conformal Symmetry of Relativistic and Nonrelativistic Systems and AdS/CFT Correspondence
• Non-Relativistic M2-brane Gauge Theory and New Superconformal Algebra
• Non-Abelian Chern-Simons Particles and their Quantization
• Symmetries of fluid dynamics with polytropic exponent
• A Nonrelativistic Chiral Soliton in One Dimension
• OPE convergence in non-relativistic conformal field theories
• Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
• Extended Non Linear Conformal Symmetry and DSR Velocities on the Physical Surface