nLab Geometric and topological structures related to M-branes

This entry provides hyperlinked keywords and further pointers to the literature for the articles

• Hisham Sati, Geometric and topological structures related to M-branes ,

  part I, Proc. Symp. Pure Math. 81 (2010), 181-236 (arXiv:1001.5020),

  part II: Twisted $String$ and $String^c$ structures, J. Australian Math. Soc. 90 (2011), 93-108 (arXiv:1007.5419);

  part III: Twisted higher structures, Int. J. Geom. Meth. Mod. Phys. 8 (2011), 1097-1116 (arXiv:1008.1755)

on phenomena of higher geometry and generalized cohomology encountered in string theory and specifically when going towards M-theory.

Apart from original work this provides an exhaustive bibliography of the relevant existing literature, which we reproduce hyperlinked below.

Abstract

We consider the topological and geometric structures associated with cohomological and homological objects in M-theory. For the latter, we have M2-branes and M5-branes, the analysis of which requires the underlying spacetime to admit a String structure and a Fivebrane structure, respectively. For the former, we study how the fields in M-theory are associated with the above structures, with homotopy algebras, with twisted cohomology, and with generalized cohomology. We also explain how the corresponding charges should take values in topological modular forms. We survey background material and related results in the process.

Higher cohomological charges

Discussion of elliptic cohomology and Morava K-theory as the home for higher analogs of D-brane charges (M5-brane charge, M9-brane charge…) and the corresponding orientation in generalized cohomology as higher quantum anomaly conditions (such as the Diaconescu-Moore-Witten anomaly):

• Hisham Sati, Craig Westerland, Twisted Morava K-theory and E-theory (arXiv:1109.3867)

• Igor Kriz, Hisham Sati, M-theory, type IIA superstrings, and elliptic cohomology, Adv. Theor.

  Math. Phys. 8 (2004), no. 2, 345–394 (arXiv:hep-th/0404013)

• Lukas Buhné, Properties of Integral Morava K-Theory and the Asserted Application to the Diaconescu-Moore-Witten Anomaly, Diploma thesis Hamburg (2011)

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category: reference