Adjoint fermion zero-modes for SU(N) calorons

Understand

We derive analytic formulas for the zero-modes of the Dirac equation in the adjoint representation in the background field of Q=1 SU(N) calorons.

• Solutions with various boundary conditions are obtained, including the physically most relevant cases of periodic and antiperiodic ones.
• The latter are essential ingredients in a semiclassical treatment of finite temperature supersymmetric Yang-Mills theory.
• A detailed discussion of adjoint zero-modes in several other contexts is also presented.