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Full Maurer–Cartan equation for heterotic SU(3) deformations

Derive the full Maurer–Cartan equation governing deformations of solutions to the heterotic SU(3) (Hull–Strominger) system formulated via the operator \bar D acting on the bundle Q = (T^{1,0}X)^* \oplus End(E) \oplus T^{1,0}X, thereby making precise the deformation theory beyond the identification of potential obstructions in H^{0,2}_{\bar D}(Q).

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Background

The paper reviews prior physics-based deformation theory where infinitesimal deformations lie in H{0,1}_{\bar D}(Q) and potential obstructions in H{0,2}_{\bar D}(Q), but it emphasizes that a complete Maurer–Cartan formulation remains missing.

A complete Maurer–Cartan equation would encode the non-linear deformation theory and clarify how obstructions arise and interact, thus refining the moduli space description beyond the linearized setting.

References

Moreover, though the full Maurer--Cartan equation for deformations is yet to be worked out, it is shown that the potential obstructions lie in H{0,2}_{\bar{D}(Q), which is defined in a similar manner.

— Local descriptions of the heterotic SU(3) moduli space (2409.04382 - Lázari et al., 6 Sep 2024) in Section 1, Results