Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry

Marc-Antoine Fiset

Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry

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arxiv 1809.06376 v1 pith:5D4VDZOE submitted 2018-09-17 hep-th math.QA

Marc-Antoine Fiset This is my paper · ORCID

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keywords algebrasconnectedmanifoldsmirrorsuperconformaltwistedalgebraanalogues

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abstract

We realise the Shatashvili-Vafa superconformal algebra for $G_2$ string compactifications by combining Odake and free conformal algebras following closely the recent mathematical construction of twisted connected sum $G_2$ holonomy manifolds. By considering automorphisms of this realisation, we identify stringy analogues of two mirror maps proposed by Braun and Del Zotto for these manifolds.

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For G2 and SU(3) string backgrounds with NS flux, the scalar torsion class controls the first-order deformation of the worldsheet super W-algebra couplings away from special holonomy.

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