$D$-term and $F$-term potential of non-Abelian D7-branes in IIB Calabi-Yau orientifolds

RESUMO

We derive the 4d $D$-term and $F$-term potential generated by a D7-brane stack in Calabi-Yau orientifold compactifications of type IIB string theory, taking into account the effect of worldvolume and ISD bulk fluxes and the non-Abelian nature of the brane fields. This potential is an important ingredient for moduli stabilization in IIB, e.g., in de Sitter scenarios using a T-brane uplift. While aspects of the $D$-term and $F$-term parts of the potential have been inferred before with various arguments, we provide here a unified first-principles derivation of the full potential by dimensionally reducing the non-Abelian DBI action of the D7-branes. Our result generalizes previous expressions and agrees with them where applicable, thus confirming the mutual consistency of the various approaches. Moreover, we provide a thorough discussion of corrections from integrating out KK modes and argue that demanding control over such corrections implies bounds on the Calabi-Yau volume and the brane fields. Aside from these various results for the 4d effective action, our calculation also shows how bulk fluxes correct the potential and the BPS equations in the 8d worldvolume theory that governs the microscopic dynamics of non-Abelian branes.