A generalized positive energy theorem for spaces with asymptotic SUSY compactification

In this short note, we prove a generalized positive energy theorem for spaces with asymptotic SUSY compactification involving non-symmetric data. This work is motivated by the work of Dai [A positive mass theorem for spaces with asymptotic SUSY compactification, Comm. Math. Phys. 244 (2004) 335-345; A note on positive energy theorem for spaces with asymptotic SUSY compactification, 2004. arXiv:math-ph/0406006], Hertog-Horowitz-Maeda [Negative energy density in Calabi-Yau compactifications, JHEP 0305 (2003) 060], and Zhang [Angular momentum and positive mass theorem, Comm. Math. Phys. 206 (1999) 137-155].