Euclidean Actions, Instantons, Solitons and Supersymmetry

Understand

Theories with axionic scalars admit three different Euclidean formulations, obtained by Wick rotation, Wick rotation combined with analytic continuation of the axionic scalars, and Wick rotation combined with Hodge dualization.

• We investigate the relation between these formulations for a class of theories which contains the sigma models of N=2 vector multiplets as a special case.
• It is shown that semi-classical amplitudes can be expressed equivalently using the two types of axionic actions, while the Hodge dualized version gives a different value for the instanton action unless the integration constants associated with the axion fields are chosen in a particular way.
• With this choice the instanton action is equal to the mass of the soliton or black hole obtained by dimensional lifting with respect to time.