Chiral matter and transitions in heterotic string models

G. Curio

TL;DR

The paper develops a spectral-cover framework for heterotic string compactifications on elliptically fibered Calabi–Yau threefolds with SU(n) bundles to compute the massless chiral spectrum. It derives the net generation number as $\frac{1}{2} c_3(V) = \lambda \eta (\eta - n c_1)$, tying the result to a discrete gamma modulus and to an F-theory four-flux analogue. The work also analyzes matter localized on base curves, constructs numerous 3-generation models with unbroken gauge groups SU(5), SO(10), E6, and studies heterotic 5-brane/instanton transitions alongside their F-theory 3-brane counterparts via Hecke transforms. It concludes with an interpretation in terms of intersections of 7-branes in F-theory, where the four-flux twisting along intersection curves governs the chiral matter content. Overall, the paper builds a bridge between heterotic spectral-cover constructions and F-theory flux phenomenology, enabling explicit 3-generation model-building and a unified view of chirality-changing transitions.

Abstract

In the framework of N=1 supersymmetric string models given by the heterotic string on an elliptic Calabi-Yau $π:Z\ra B$ together with a SU(n) bundle we compute the chiral matter content of the massless spectrum. For this purpose the net generation number, i.e. half the third Chern class, is computed from data related to the heterotic vector bundle in the spectral cover description; a non-technical introduction to that method is supplied. This invariant is, in the class of bundles considered, shown to be related to a discrete modulus which is the heterotic analogue of the $F$-theory four-flux. We consider also the relevant matter which is supported along certain curves in the base $B$ and derive the net generation number again from the independent matter-related computation. We then illustrate these considerations with two applications. First we show that the construction leads to numerous 3 generation models of unbroken gauge group $SU(5), SO(10)$ or $E_6$. Secondly we discuss the closely related issue of the heterotic 5-brane/instanton transition resp. the F-theoretic 3-brane/instanton transition. The extra chiral matter in these transitions is related to the Hecke transform of the direct sum of the original bundle and the dissolved 5-brane along the intersection of their spectral covers. Finally we point to the corresponding $F$-theory interpretation of chiral matter from the intersection of 7-branes where the influence of four-flux on the twisting along the intersection curve plays a crucial role.

Chiral matter and transitions in heterotic string models

TL;DR

The paper develops a spectral-cover framework for heterotic string compactifications on elliptically fibered Calabi–Yau threefolds with SU(n) bundles to compute the massless chiral spectrum. It derives the net generation number as

, tying the result to a discrete gamma modulus and to an F-theory four-flux analogue. The work also analyzes matter localized on base curves, constructs numerous 3-generation models with unbroken gauge groups SU(5), SO(10), E6, and studies heterotic 5-brane/instanton transitions alongside their F-theory 3-brane counterparts via Hecke transforms. It concludes with an interpretation in terms of intersections of 7-branes in F-theory, where the four-flux twisting along intersection curves governs the chiral matter content. Overall, the paper builds a bridge between heterotic spectral-cover constructions and F-theory flux phenomenology, enabling explicit 3-generation model-building and a unified view of chirality-changing transitions.

Abstract

In the framework of N=1 supersymmetric string models given by the heterotic string on an elliptic Calabi-Yau

together with a SU(n) bundle we compute the chiral matter content of the massless spectrum. For this purpose the net generation number, i.e. half the third Chern class, is computed from data related to the heterotic vector bundle in the spectral cover description; a non-technical introduction to that method is supplied. This invariant is, in the class of bundles considered, shown to be related to a discrete modulus which is the heterotic analogue of the

-theory four-flux. We consider also the relevant matter which is supported along certain curves in the base

and derive the net generation number again from the independent matter-related computation. We then illustrate these considerations with two applications. First we show that the construction leads to numerous 3 generation models of unbroken gauge group

or

. Secondly we discuss the closely related issue of the heterotic 5-brane/instanton transition resp. the F-theoretic 3-brane/instanton transition. The extra chiral matter in these transitions is related to the Hecke transform of the direct sum of the original bundle and the dissolved 5-brane along the intersection of their spectral covers. Finally we point to the corresponding

-theory interpretation of chiral matter from the intersection of 7-branes where the influence of four-flux on the twisting along the intersection curve plays a crucial role.