Triples, Fluxes, and Strings

TL;DR

This work maps the rich, highly structured moduli space of string compactifications preserving sixteen supercharges, emphasizing discrete, non-perturbative components realized across heterotic, type I, orientifold, M-, and F-theory frameworks. It develops a gauge-bundle, Narain- and asymmetric-orbifold perspective that reveals new 7D components labeled by ${\\mathbb Z}_m$, including CHL-like theories and novel dualities between spaces with different singular geometries and fluxes. A central theme is the interplay between fluxes (RR, one- and three-form) and singularities, explored through equivariant K-theory, del Pezzo automorphisms, and M-theory 3-forms, with frozen or partially frozen singularities emerging as key ingredients. The paper also develops a geometric–topological language (lattices, centralizers, and Nikulin classifications) to connect moduli, dualities, and degeneration limits, offering a framework to reinterpret M/theory 3-form data and its holographic descriptions in CHL-like vacua. Overall, the results suggest a tightly constrained web of dualities that links diverse compactifications and flux configurations, deepening our understanding of non-perturbative string vacua and their geometric underpinnings.

Abstract

We study string compactifications with sixteen supersymmetries. The moduli space for these compactifications becomes quite intricate in lower dimensions, partly because there are many different irreducible components. We focus primarily, but not exclusively, on compactifications to seven or more dimensions. These vacua can be realized in a number ways: the perturbative constructions we study include toroidal compactifications of the heterotic/type I strings, asymmetric orbifolds, and orientifolds. In addition, we describe less conventional M and F theory compactifications on smooth spaces. The last class of vacua considered are compactifications on singular spaces with non-trivial discrete fluxes. We find a number of new components in the string moduli space. Contained in some of these components are M theory compactifications with novel kinds of ``frozen'' singularities. We are naturally led to conjecture the existence of new dualities relating spaces with different singular geometries and fluxes. As our study of these vacua unfolds, we also learn about additional topics including: F theory on spaces without section, automorphisms of del Pezzo surfaces, and novel physics (and puzzles) from equivariant K-theory. Lastly, we comment on how the data we gain about the M theory three-form might be interpreted.

Figures (8)

• Figure 1: The extended Dynkin diagram of $E_{8}$. The integers are the (co)root integers associated to the respective nodes.
• Figure 2: The extended Dynkin diagram of $D_{16}$ ($Spin(32)$). The integers are the (co)root integers associated to the respective nodes.
• Figure 3: The singular fibers on $Z/G$.
• Figure 4: The singular fibers for F theory on $\widetilde{Z/G}$.
• Figure 5: Cell decomposition of $S^2$.