FERMIONIC THETA-VACUA AND LONG-NECKED REMNANTS

We study a vacuum polarization effect in the background of a certain dilatonic extremal black hole, known as the cornucopion. Whenever charged fermions are of any nonzero mass, the gravitational back reaction to a generic value of a CP-nonconserving vacuum angle theta is shown to be important owing to a vacuum energy density which does not vanish deep inside the cornucopion. When the vacuum energy density is positive, this effect creates an extremal horizon at finite physical distance, closing off the infinite neck. We study the geometry of this horizon in some detail and find different physical interpretations for small and large fermion mass. Also, we argue that the conclusion is qualitatively correct despite the inevitable strong coupling.