Establish the complete messenger-induced vacuum orientation in degenerate-mass ISS

Determine whether the one-loop messenger Coleman–Weinberg logarithm completely determines the vacuum orientation of the ISS metastable supersymmetry-breaking vacuum when the electric quark masses are degenerate or nearly degenerate, including the effects of higher-loop corrections, finite contributions, and magnetic-instanton orientation dependence, and establish whether these effects induce spontaneous CP violation.

Background

For non-degenerate electric quark masses, the ISS supersymmetry-breaking order parameter is uniquely aligned and real in a CP-invariant basis. In the exactly degenerate limit, the ISS sector has a continuous vacuum-orientation degeneracy described by a complex Grassmannian.

Messenger loops lift this degeneracy through a potential proportional to the magnitude of the messenger-induced auxiliary coupling. An antisymmetric component of the messenger portal can favor a complex projector and thereby generate an order-one phase in the gluino mass.

The paper derives the leading one-loop logarithmic contribution but explicitly leaves unresolved whether it is the full orientation-dependent effect. Higher-loop terms, finite parts, and magnetic-instanton contributions could alter the selected orientation and hence the CP properties of the vacuum, particularly for exactly or nearly degenerate masses.