Rationality of the 2d SCFT on BPS strings provides a consistency criterion that uniquely determines the elliptic genus and global gauge group in a class of 6d supergravity models without tensor multiplets.
Algebroids, Heterotic Moduli Spaces and the Strominger System
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abstract
In this paper we study compactifications of heterotic string theory on manifolds satisfying the ddbar-lemma. We consider the Strominger system description of the low energy supergravity to first order in alpha' and show that the moduli of such compactifications are subspaces of familiar cohomology groups such as H^1(TX), H^1(TX*), H^1(End_0(V)) and H^1(End_0(TX)). These groups encode the complex structure, Kahler moduli, bundle moduli and perturbations of the spin connection respectively in the case of a Calabi-Yau compactification. We investigate the fluctuations of only a subset of the conditions of the Strominger system (expected to correspond physically to F-term constraints in the effective theory). The full physical moduli space is, therefore, given by a further restriction on these degrees of freedom which we discuss but do not explicitly provide. This paper is complementary to a previous tree-level worldsheet analysis of such moduli and agrees with that discussion in the limit of vanishing alpha'. The structure we present can be interpreted in terms of recent work in Atiyah and Courant algebroids, and we conjecture links with aspects of Hitchin's generalized geometry to heterotic moduli.
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Deforming holomorphic Chern-Simons theory produces rescaling-invariant instantons and anomaly-free theories on End(TX) for Morse-classified directions in deformation space.
Fibering heterotic compactification data over moduli space organizes deformations as components of universal curvatures and incorporates α'^2 supersymmetry corrections.
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Rational points in the 6d supergravity landscape and simple current extensions
Rationality of the 2d SCFT on BPS strings provides a consistency criterion that uniquely determines the elliptic genus and global gauge group in a class of 6d supergravity models without tensor multiplets.
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On a Deformed Holomorphic Chern-Simons Theory
Deforming holomorphic Chern-Simons theory produces rescaling-invariant instantons and anomaly-free theories on End(TX) for Morse-classified directions in deformation space.
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Universal geometry as an organising principle for heterotic moduli
Fibering heterotic compactification data over moduli space organizes deformations as components of universal curvatures and incorporates α'^2 supersymmetry corrections.