Background constraints in the infinite tension limit of the heterotic string

In this work we investigate the classical constraints imposed on the supergravity and super Yang-Mills backgrounds in the ${\alpha }^{\mathrm{\prime }}\to 0$ limit of the heterotic string using the pure spinor formalism. Guided by the recently observed sectorization of the model, we show that all the ten-dimensional constraints are elegantly obtained from the single condition of nilpotency of the BRST charge.