Manifold Compactifications Research Articles

On TCS G2 manifolds and 4D emergent strings

In this note, we study the Swampland Distance Conjecture in TCS G2 manifold compactifications of M-theory. In particular, we are interested in testing a refined version — the Emergent String Conjecture, in settings with 4d N = 1 supersymmetry. We find that a weakly coupled, tensionless fundamental heterotic string does emerge at the infinite distance limit characterized by shrinking the K3-fiber in a TCS G2 manifold. Such a fundamental tensionless string leads to the parametrically leading infinite tower of asymptotically massless states, which is in line with the Emergent String Conjecture. The tensionless string, however, receives quantum corrections. We check that these quantum corrections do modify the volume of the shrinking K3-fiber via string duality and hence make the string regain a non-vanishing tension at the quantum level, leading to a decompactification. Geometrically, the quantum corrections modify the metric of the classical moduli space and are expected to obstruct the infinite distance limit. We also comment on another possible type of infinite distance limit in TCS G2 compactifications, which might lead to a weakly coupled fundamental type II string theory.

Stringy dyonic solutions and clifford structures

Using the toroidal compactification of string theory on [Formula: see text]-dimensional tori, [Formula: see text], we investigate dyonic objects in arbitrary dimensions. First, we present a class of dyonic black solutions formed by two different D-branes using a correspondence between toroidal cycles and objects possessing both magnetic and electric charges, belonging to [Formula: see text] dyonic gauge symmetry. This symmetry could be associated with electrically charged magnetic monopole solutions in stringy model buildings of the standard model (SM) extensions. Then, we consider in some detail such black hole classes obtained from even-dimensional toroidal compactifications, and we find that they are linked to [Formula: see text] Clifford algebras using the vee product. It is believed that this analysis could be extended to dyonic objects which can be obtained from local Calabi–Yau manifold compactifications.

Cascade of special holonomy manifolds and heterotic string theory

We investigate heterotic string theory on special holonomy manifolds including exceptional holonomy G 2 and Spin(7) manifolds. The gauge symmetry is F 4 in a G 2 manifold compactification, and so(9) in a Spin(7) manifold compactification. We also study the cascade of the holonomies: so(8)⊃ Spin(7)⊃ G 2⊃ su(3)⊃ su(2). The differences of adjoining groups are described by Ising, tricritical Ising, 3-state Potts and u(1) models. These theories are essential for spacetime supersymmetries and gauge group enhancements. As concrete examples, we construct the modular invariant partition functions and analyze their massless spectra for G 2 and Spin(7) orbifolds. We obtain the relation between topological numbers of the manifolds and multiplicities of matters in specific representations.

Methods of holonomy theory for Ricci-flat Riemannian manifolds

Compact, Ricci-flat Riemannian manifolds often arise in physical applications, either as a technical device or as models of ‘‘internal’’ space. The idea of extending the holonomy group of such a manifold to a larger gauge group (‘‘embedding the connection in the gauge group’’) plays a fundamental role in the ‘‘manifold compactification’’ approach to superstring phenomenology, and the work of Gepner suggests that this idea may have equally fundamental analogs in other approaches. The holonomy theory of simply connected Ricci-flat manifolds has recently been the subject of much mathematical work, but physicists are mainly interested in the case of multiply connected manifolds. The purpose of this paper is to present some techniques for understanding the holonomy theory of compact, multiply connected Ricci-flat manifolds. These lead to a general classification theorem.

Flipped SU(5) from manifold compactification of the ten-dimensional heterotic string

We show that a recently proposed flipped SU(5)×U(1) GUT cannot be obtained from a conventional SO(10) GUT, nor from the heterotic string by Hosotani gauge symmetry breaking of E 6 on a manifold with (2,2) world-sheet supersymmetry. It can in principle be obtained by Hosotani gauge symmetry breaking of SO(10) on a manifold with (1,2) world-sheet supersymmetry. We identify the topological conditions under which the required chiral matter generations, Higgs multiplets, and gauge singlet fields can be light. In particular we show that non-perturbative world-sheet instanton effects neither destabilize the manifold nor give masses to the gauge singlets. The required Yukawa couplings are not forbidden by any known selection rules.

Calabi-Yau manifold compactification in the heterotic string and N=1 supersymmetry in four dimensions

We examine whether a torsion-free Calabi-Yau manifold with the SU(3) holonomy group embedded in E 8×E 8 satisfies the classical field equations with O(α' 3) heterotic string corrections. In general, the torsion-freedom is lost and the exact embedding condition is modified at O(α' 3), but the N=1 supersymmetry in four dimensions is still preserved even at O(α' 3). Allowing some local field redefinitions, however, we can restore the exact embedding of the SU(3) holonomy into E 8×E 8→E 6×SU(3)×E 8, maintaining also the D=4, N=1 symmetry. Our results are based on the dual (type IB) superspace formulation, which guarantees the on-shell closure of supersymmetry.

Accidental degeneracies in string compactification

The equivalence of the torus and group manifold compactification of strings is established. Accidental degeneracies are shown to occur for a large class of compactifications. This way many examples are obtained in which modular invariance does not uniquely fix the representation content of the spectrum.