The Type IIA Flux Potential, 4-forms and Freed-Witten anomalies

Alvaro Herraez; Luis E. Ibanez; Fernando Marchesano; Gianluca Zoccarato

doi:10.1007/JHEP09(2018)018

paper

The Type IIA Flux Potential, 4-forms and Freed-Witten anomalies

arXiv:1802.05771 · doi:10.1007/JHEP09(2018)018

Abstract

We compute the full classical 4d scalar potential of type IIA Calabi-Yau orientifolds in the presence of fluxes and D6-branes. We show that it can be written as a bilinear form $V = Z^{A B} ρ_{A} ρ_{B}$ , where the $ρ_{A}$ are in one-to-one correspondence with the 4-form fluxes of the 4d effective theory. The $ρ_{A}$ only depend on the internal fluxes, the axions and the topological data of the compactification, and are fully determined by the Freed-Witten anomalies of branes that appear as 4d string defects. The quadratic form $Z^{A B}$ only depends on the saxionic partners of these axions. In general, the $ρ_{A}$ can be seen as the basic invariants under the discrete shift symmetries of the 4d effective theory, and therefore the building blocks of any flux-dependent quantity. All these polynomials may be obtained by derivation from one of them, associated to a universal 4-form. The standard N=1 supergravity flux superpotential is uniquely determined from this {\it master polynomial}, and vice versa.

arXiv comment75 pages, one figure; v2 minor corrections

The Type IIA Flux Potential, 4-forms and Freed-Witten anomalies

Abstract

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