Loop-Corrected Compactifications of the Heterotic String with Line Bundles

TL;DR

This work develops a systematic framework for heterotic compactifications with line bundles on Calabi–Yau manifolds, showing that multiple anomalous U(1)s are canceled via a generalized Green–Schwarz mechanism and that Fayet–Iliopoulos terms receive a one-loop, stringy correction that effectively freezes combinations of the dilaton and Kähler moduli through a corrected Donaldson–Uhlenbeck–Yau condition. The authors derive holomorphic gauge kinetic functions with one-loop threshold corrections, construct explicit monad-style bundles with SU(N) × U(1)^M structure, and present concrete tadpole-free examples including models with Standard Model gauge symmetry. Their results highlight non-universal U(1) couplings and moduli stabilization patterns that parallel Type I constructions and expand the heterotic landscape with viable line-bundle models. This provides a concrete path toward realistic heterotic vacua and demonstrates rich gauge-enhancement possibilities and global symmetry structures arising from abelian fluxes.

Abstract

We consider the E8 x E8 heterotic string theory compactified on Calabi-Yau manifolds with bundles containing abelian factors in their structure group. Generic low energy consequences such as the generalised Green-Schwarz mechanism for the multiple anomalous abelian gauge groups are studied. We also compute the holomorphic gauge couplings and induced Fayet-Iliopoulos terms up to one-loop order, where the latter are interpreted as stringy one-loop corrections to the Donaldson-Uhlenbeck-Yau condition. Such models generically have frozen combinations of Kaehler and dilaton moduli. We study concrete bundles with structure group SU(N) x U(1)^M yielding quasi-realistic gauge groups with chiral matter given by certain bundle cohomology classes. We also provide a number of explicit tadpole free examples of bundles defined by exact sequences of sums of line bundles over complete intersection Calabi-Yau spaces. This includes one example with precisely the Standard Model gauge symmetry.

Figures (5)

• Figure 1: Green-Schwarz counterterm for the mixed gauge anomaly.
• Figure 2: The plot shows the Kähler moduli $(r_1,r_2)$ for the values $4g_s\in\{0,0.1,0.2,0.3,0.4,0.5\}$ of the string coupling constant.
• Figure 3: Gauge symmetry enhancement for bundles with structure group $SU(4)\times U(1)^2$. On generic lines through the origin the gauge symmetry is enhanced to $SU(3)\times SU(2)\times U(1)$ while for the specific values shown one gets even non-abelian enhancement. The left image shows the loci of non-abelian enhancement in the $(c_1(L_2),c_1(L_1))$-plane for $SU(4)\times U(1)^2$ and the right image for $U(4)\times U(1)^2$.
• Figure 4: Gauge symmetry enhancement for $SU(3)\times U(1)^3$ bundles. The picture shows the projection of the various planes defined in Table \ref{['enhance1']} into the planes $l_i \equiv c_1(L_i)=1$. At the point $l_i=0$ for $i=1,2,3$, the observable gauge group is $E_6$.
• Figure 5: The plot shows the Kähler moduli $(r_1,r_2)$ for the values $4 g_s\in\{0,0.1,0.2,0.3,0.4,0.5\}$ of the string coupling constant.