Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (I): Heterotic F^6 Terms at Two Loops

TL;DR

This work analyzes two-loop heterotic $F^6$ interactions in $D=10$ with gauge group $SO(32)$ and tests their relationship to Type I via duality. By employing genus-2 correlators, Fay trisecant and generalized Riemann identities, the authors constrain the effective action within a single-trace non-Abelian Born-Infeld ansatz, revealing a marked difference from BI expectations. In the Abelian Cartan sector, the two-loop coefficients satisfy $h=0$ and $s=-4l$, deviating from the Born-Infeld values and signaling nontrivial supersymmetric constraints beyond BPS saturation. For the full non-Abelian theory, many constraints reduce the initial 31 coefficients to a 12-parameter family, with three independent triangle terms, and the amplitudes exhibit non-topological left-right mover couplings, underscoring subtlety in duality for higher-derivative, non-BPS amplitudes.

Abstract

We study the two-loop F^6 interactions in SO(32) heterotic superstring theory in D=10. By using the generalized Riemann identity we are able to determine the single-trace part of the effective action up to a few constants which are related to certain scattering amplitudes. This two-loop heterotic result is related by duality to Type I interactions at the tree level. However, it turns out to be completely different from any sort of non-Abelian generalization of Born-Infeld theory. We offer an explanation of this discrepancy.

Figures (8)

• Figure 1: Diagrammatic representation of the four terms in Eq.(\ref{['f4']}).
• Figure 2: Diagrammatic representation of the three terms in Eq.(\ref{['f6ab']}).
• Figure 3: Diagrams representing three purely non-Abelian terms. Their coefficients are, from left to right, $t(1)$, $t(2)$ and $t(3)$.
• Figure 4: The diagrams of Fig.3 are dressed with circles which label the two antisymmetrization sets.
• Figure 5: Diagrammatic representation of ${\cal L}_{6l}$, Eq.(\ref{['ltot']}).