A bstract In this paper we study compactifications of heterotic string theory on manifolds satisfying the ? ? ˉ $$ partial overline{partial} $$ -lemma. We consider the Strominger system description of the low energy supergravity to first order in α ′ 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, K?hler 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 α ′. 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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