The transition towards a low-carbon economy is an epoch-defining goal. However, this transition develops following traditional patterns of business that are intrinsically environmentally harmful as they rest upon profit-oriented strategies of commodifying natural resources. By taking the anthropological notion of "corporate sovereignty", this contribution discusses the unsustainability of private corporates' property a-like structures of power over natural resources and frames them within forms of economic governmentality. The paper concludes by stressing the need for a cultural change to occur to back the transition towards a novel model of sustainable business, i.e. of "business within the Heart's limits".