2,763 research outputs found
Index Theorems and Loop Space Geometry
We investigate the evaluation of the Dirac index using symplectic geometry in
the loop space of the corresponding supersymmetric quantum mechanical model. In
particular, we find that if we impose a simple first class constraint, we can
evaluate the Callias index of an odd dimensional Dirac operator directly from
the quantum mechanical model which yields the Atiyah-Singer index of an even
dimensional Dirac operator in one more dimension. The effective action obtained
by BRST quantization of this constrained system can be interpreted in terms of
loop space symplectic geometry, and the corresponding path integral for the
index can be evaluated exactly using the recently developed localization
techniques.Comment: 15 pages, report CERN-TH-6471 and HU-TFT-92-1
BRST extension of the Faddeev model
The Faddeev model is a second class constrained system. Here we construct its
nilpotent BRST operator and derive the ensuing manifestly BRST invariant
Lagrangian. Our construction employs the structure of Stuckelberg fields in a
nontrivial fashion.Comment: 4 pages, new references adde
Dual Superconductors and SU(2) Yang-Mills
We propose that the SU(2) Yang-Mills theory can be interpreted as a two-band
dual superconductor with an interband Josephson coupling. We discuss various
consequences of this interpretation including electric flux quantization,
confinement of vortices with fractional flux, and the possibility that a closed
vortex loop exhibits exotic exchange statistics
Anomaly-Induced Magnetic Screening in 2+1 dimensional QED at Finite Density
We show that in 2+1 dimensional Quantum Electrodynamics an external magnetic
field applied to a finite density of massless fermions is screened, due to a
-dimensional realization of the underlying -dimensional axial anomaly
of the space components of the electric current. This is shown to imply
screening of the magnetic field, i.e., the Meissner effect. We discuss the
physical implications of this result.Comment: 8 pages, DFTT-93-10 [ Eq.(15) and (16) were scrambled in previous
version
Fixed Charge Ensembles and Parity Breaking Terms
Recently derived results for the exact induced parity-breaking term in 2+1
dimensions at finite temperature are shown to be relevant to the determination
of the free energy for fixed-charge ensembles. The partition functions for
fixed total charge corresponding to massive fermions in the presence of Abelian
and non-Abelian magnetic fields are discussed. We show that the presence of the
induced Chern-Simons term manifests itself in that the free energy depends
strongly on the relation between the external magnetic flux and the value of
the fixed charge.Comment: 10 pages, Revte
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