Structure in the heterotic matter field Kähler potential

It has long been known that superpotential couplings in heterotic theories often vanish despite the absence of any known symmetry that would forbid them. We show that such structure is also exhibited by the matter field Kähler potential of these compactifications. We give an analytical analysis which provides some simple conditions under which certain terms, which would be expected to be present in the Kähler potential, vanish. Explicit examples of this phenomenon are provided, some of which are verifiable by other methods and some of which can only currently be accessed by these techniques. By studying the interplay of the structure we find with Higgsing transitions, we are able to show that this vanishing of Kähler potential terms can extend to all orders in a perturbative expansion in the matter fields.