Abstract
In this letter the fractional fermion number of thick domain walls is computed. The analysis is achieved by developing the heat kernel expansion of the spectral eta function of the Dirac Hamiltonian governing the fermionic fluctuations around the domain wall. A formula is derived showing that a non null fermion number is always accompanied by a Hall conductivity induced on the wall. In the limit of thin and impenetrable walls the chiral bag boundary conditions arise, and the Hall conductivity is computed for this case as well.
Highlights
The possibility of a fractional fermion number of solitons was first noted by Jackiw and Rebbi in 1976 [1]
An efficient method for calculation of the fractional charge based on a resummation of the heat kernel expansion was suggested recently in [7]
The fermion number fractionization is connected with quantum anomalies and with the parity anomaly [8,9] in particular
Summary
The possibility of a fractional fermion number of solitons was first noted by Jackiw and Rebbi in 1976 [1]. The resummation method of [7] works straightforwardly and relatively easy in this case and produces a nice formula for the fractional charge in terms of the total magnetic flux and of the chiral angle of scalar fields in the asymptotic regions. The fermion number fractionization is connected with quantum anomalies and with the parity anomaly [8,9] in particular It was believed for a long time that there cannot be a parity anomaly in (3 + 1) dimensions. Our results on the fermion number allow to fix the induced Chern-Simons action for domain walls. Since chiral bag boundary conditions may be obtained as a strong coupling limit of domain walls, we are able to compute the Chern-Simons term on the boundaries as well
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