Summary: A note on positive energy theorem for spaces
with asymptotic SUSY compactification
Xianzhe Dai
Mathematics, University of California Santa Barbara, Santa Barbara, California 93106
Received 22 November 2004; accepted 5 January 2005; published online 23 March 2005
We extend the higher dimensional positive mass theorem in Dai, X., Commun.
Math. Phys. 244, 335­345 2004 to the Lorentzian setting. This includes the
original higher dimensional positive energy theorem whose spinor proof is given in
Witten, E., Commun. Math. Phys. 80, 381­402 1981 and Parker, T., and
Taubes, C., Commun. Math. Phys. 84, 223­238 1982 for dimension 4 and in
Zhang, X., J. Math. Phys. 40, 3540­3552 1999 for dimension 5. © 2005
American Institute of Physics. DOI: 10.1063/1.1862095
I. INTRODUCTION AND STATEMENT OF THE RESULT
In this note, we formulate and prove the Lorentzian version of the positive mass theorem in
Ref. 4. There we prove a positive mass theorem for spaces of any dimension which asymptotically
approach the product of a flat Euclidean space with a compact manifold which admits a nonzero
parallel spinor such as a Calabi­Yau manifold or any special honolomy manifold except the
quaternionic Kähler manifold . This is motivated by string theory, especially the recent work in
Ref. 7. The application of the positive mass theorem of Ref. 4 to the study of stability of Ricci flat
manifolds is discussed in Ref. 5.

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

Collections: Mathematics