Abstract
We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum G2 manifolds. For a given G2 manifold, we discuss evidence for the existence of mirror symmetries of two kinds: one is an autoequivalence for a given Type II superstring on a mirror pair of G2 manifolds, the other is a duality between Type II strings with different chiralities for another pair of mirror manifolds. We clarify the role of the B-field in the construction, and check that the corresponding massless spectra are respected by the generalized mirror maps. We discuss hints towards a homological version based on BPS spectroscopy. We provide several novel examples of smooth, as well as singular, mirror G2 backgrounds via pairs of dual projecting tops. We test our conjectures against a Joyce orbifold example, where we reproduce, using our geometrical methods, the known mirror maps that arise from the SCFT worldsheet perspective. Along the way, we discuss non-Abelian gauge symmetries, and argue for the generation of the Affleck-Harvey-Witten superpotential in the pure SYM case.
Highlights
One of the most important features of superstring theory and M/F-theory are string dualities, which relate compactified string theories to one another, often making the very concept of space-time geometry ambiguous.1 The subject of string dualities has been vastly explored in the past two decades, and most results obtained in this context about toroidal compactifications and Calabi-Yau (CY) geometries are textbook material
We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum G2 manifolds
For a given G2 manifold, we discuss evidence for the existence of mirror symmetries of two kinds: one is an autoequivalence for a given Type II superstring on a mirror pair of G2 manifolds, the other is a duality between Type II strings with different chiralities for another pair of mirror manifolds
Summary
One of the most important features of superstring theory and M/F-theory are string dualities, which relate compactified string theories to one another, often making the very concept of space-time geometry ambiguous. The subject of string dualities has been vastly explored in the past two decades, and most results obtained in this context about toroidal compactifications and Calabi-Yau (CY) geometries are textbook material. About 50 million novel examples of compact G2 manifolds have been obtained as twisted connected sums (TCS) of pairs of asymptotically cylindrical CY three-folds [12,13,14] This is a result with interesting implications in the context of compactifications of superstring theories and M-theory [15,16,17,18,19]. Notice that by placing a D2-brane along the flat R2,1 component of the ten-dimensional background R2,1 × J, we obtain a worldvolume theory on the brane which has N = 1 in three dimensions Under the duality this configuration of branes is mapped to a D5-brane in Type IIB which is wrapped along the T 3 fiber. We discuss explicit examples of the mirror manifolds which arises from this construction and revisit the examples discussed in [17], emphasizing the role played by G2-manifolds with singularities
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