A simple derivation of the Overlap Dirac Operator

Abstract

We derive the vector-like four dimensional overlap Dirac operator starting from a five dimensional Dirac action in the presence of a delta-function space-time defect. The effective operator is obtained by first integrating out all the fermionic modes in the fixed gauge background, and then identifying the contribution from the localized modes as the determinant of an operator in one dimension less. We define physically relevant degrees of freedom on the defect by introducing an auxiliary defect-bound fermion field and integrating out the original five dimensional bulk field.

9 pages, LaTeX

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Cited by in corpus (7)

• On the decoupling of mirror fermions
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Lattice chirality, anomaly matching, and more on the (non)decoupling of mirror fermions
• Dynamical Casimir effect from fermions in an oscillating bag in 1+1 dimensions
• A Dual Path Integral Representation for Finite Temperature Quantum Field Theory
• Chiral anomaly, induced current, and vacuum polarization tensor for a Dirac field in the presence of a defect