Gauge invariance in Chern-Simons theory on a torus

Journal Article · Mon Jun 12 00:00:00 EDT 1989 · Phys. Rev. Lett.; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.62.2785· OSTI ID:5897136

Hosotani, Y

In the Chern-Simons gauge theory on a manifold /ital T//sup 2//times/R/sup 1/ (two-torus/times/time) the unitary operators, which induce large gauge transformations shifting the nonintegrable phases of the two dinstinct Wilson-line integrals on the torus by multiples of 2..pi.., do not commute with each other unless the coefficient of the Chern-Simons term is quantized. In U(1) theory this condition gives the statistics phase theta=..pi..//ital n/ (/ital n/ an integer). The condition coincides with the one previously derived on a manifold /ital S//sup 3/ (three-sphere) for SU(/ital N/greater than or equal to3) theory but differs by a factor 2 for SU(2) theory. The requirement of the /ital Z//sub /ital N// invariance in pure SU(/ital N/) gauge theory imposes a stronger constraint.

• Research Organization: Institute for Advanced Study, Princeton, New Jersey 08540(US)
• OSTI ID: 5897136
• Journal Information: Phys. Rev. Lett.; (United States), Vol. 62:24
• Country of Publication: United States
• Language: English

Related Subjects

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