Sigma-model anomalies in compact type IIB orientifolds and Fayet-Iliopoulos terms

TL;DR

This work shows that in compact $D=4$, $N=1$ Type IIB orientifolds, sigma-model (modular) anomalies for planes rotated by all twists can be canceled by a generalized Green-Schwarz mechanism mediated by twisted RR fields, with crucial mixing between twisted and untwisted moduli. Gravitational sigma-model anomalies additionally involve the dilaton through one-loop mixing with untwisted moduli, paralleling heterotic dual logic but via twisted sectors in the orientifold context. Moreover, Fayet-Iliopoulos terms acquire an untwisted-modulus dependent piece at tree level due to this moduli mixing, altering their vacuum structure and potential matching to heterotic duals. The results reveal a rich, non-universal GS structure in Type IIB orientifolds and emphasize the central role of twisted/untwisted moduli interplay in the low-energy effective action.

Abstract

Compact Type IIB D=4, N=1 orientifolds have certain U(1) sigma model symmetries at the level of the effective Lagrangian. These symmetries are generically anomalous. We study the particular case of $Z_N$ orientifolds and find that these anomalies may be cancelled by a generalized Green-Schwarz mechanism. This mechanism works by the exchange of twisted RR-fields associated to the orbifold singularities and it requires the mixing between twisted and untwisted moduli of the orbifold. As a consequence, the Fayet-Iliopoulos terms which are present for the gauged anomalous U(1)'s of the models get an additional untwisted modulus dependent piece at the tree level.

Figures (7)

• Figure 1: The string theory diagrams contributing to the three point amplitude corresponding to the field theory anomaly.
• Figure 2: The string theory diagram in figure 1c in the closed string channel. This contribution provides the GS counterterms which cancel the anomaly from the triangle diagrams. Closed string twisted models propagate in the closed string channel and mediate the GS mechanism.
• Figure 3: There are only two string theory diagrams which contribute to the scattering amplitude of one $U(1)$ gauge boson and two gravitons. Thus factorization is not as manifest as in the example in figure 1.
• Figure 4: This figures shows the limits where the string theory diagrams give field theory contributions. The first two are point-particle limits in the open string channel and give the usual triangle anomaly. The third is a point-particle limit in the closed string channel and represents the exchange of closed string twisted modes. Notice that the cylinder diagram in figure \ref{['diagrav']} generates two different field-theory contributions.
• Figure 5: The two string theory diagrams contributing to the coupling of the $\sigma$-model composite connection with two non-abelian gauge bosons.