Abstract
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.
Highlights
Further conjectured as O(1) in the Refined SDC [15, 16]
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
We have claimed that a weakly coupled, tensionless fundamental heterotic string emerges at the infinite distance limit (3.1), of which the stringy excitations furnish an infinite tower of the asymptotically light states at this limit, which is in line with the Emergent String Conjecture [23]
Summary
We give an overview of the effective theories from G2 compactifications of M-theory and set the background for the later discussions in this note. A G2 manifold is a real seven-dimensional Riemannian manifold X with a Riemannian metric g such that the holonomy group Hol(X) ⊆ G2. Speaking, with such a holonomy group Hol(X) ⊆ G2, it leads to a global covariantly constant spinor η as the spinor representation 8 of SO(7) decomposes as 8 → 7 + 1. The compactifications of M-theory on G2 manifolds typically lead to theories of 4d N = 1 supergravity, which can be determined by three functions: a F-term superpotential W , a Kahler potential K and a gauge-kinetic coupling function fαβ.
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