Kauffman knot invariant from SO(N) or Sp(N) Chern-Simons theory and the Potts model

Journal Article · Tue Jun 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.125026· OSTI ID:21408116

Astorino, Marco ^[1]

---

1. Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Valdivia, Chile and Centro de Estudios Cientificos (CECS), Valdivia (Chile)

The expectation value of Wilson loop operators in three-dimensional SO(N) Chern-Simons gauge theory gives a known knot invariant: the Kauffman polynomial. Here this result is derived, at the first order, via a simple variational method. With the same procedure the skein relation for Sp(N) are also obtained. Jones polynomial arises as special cases: Sp(2), SO(-2), and SL(2,R). These results are confirmed and extended up to the second order, by means of perturbation theory, which moreover let us establish a duality relation between SO({+-}N) and Sp({+-}N) invariants. A correspondence between the first orders in perturbation theory of SO(-2), Sp(2) or SU(2) Chern-Simons quantum holonomy's traces and the partition function of the Q=4 Potts model is built.

• OSTI ID: 21408116
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 12; Other Information: DOI: 10.1103/PhysRevD.81.125026; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPUTERIZED SIMULATION
DUALITY
GAUGE INVARIANCE
PARTITION FUNCTIONS
PERTURBATION THEORY
POLYNOMIALS
QUANTUM FIELD THEORY
SO GROUPS
THREE-DIMENSIONAL CALCULATIONS
VARIATIONAL METHODS
WILSON LOOP
CALCULATION METHODS
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
SIMULATION
SYMMETRY GROUPS