M5-brane charge




Where D-brane charge is the charge in K-theory carried by D-branes and computed as the partition function/index of the “superparticles” on the D-brane being the boundary field theory of the open superstring ending on them, so open M2-branes ending on M5-branes should induced a charge given by the partition function of their bounding self-dual strings (“M-strings”), which is now an elliptic genus. Hence M5-brane charge should be in elliptic cohomology (Sati 10).

partition functions in quantum field theory as indices/genera/orientations in generalized cohomology theory:

ddpartition function in dd-dimensional QFTsuperchargeindex in cohomology theorygenuslogarithmic coefficients of Hirzebruch series
0push-forward in ordinary cohomology: integration of differential formsorientation
1spinning particleDirac operatorKO-theory indexA-hat genusBernoulli numbersAtiyah-Bott-Shapiro orientation MSpinKOM Spin \to KO
endpoint of 2d Poisson-Chern-Simons theory stringSpin^c Dirac operator twisted by prequantum line bundlespace of quantum states of boundary phase space/Poisson manifoldTodd genusBernoulli numbersAtiyah-Bott-Shapiro orientation MSpin cKUM Spin^c \to KU
endpoint of type II superstringSpin^c Dirac operator twisted by Chan-Paton gauge fieldD-brane chargeTodd genusBernoulli numbersAtiyah-Bott-Shapiro orientation MSpin cKUM Spin^c \to KU
2type II superstringDirac-Ramond operatorsuperstring partition function in NS-R sectorOchanine elliptic genusSO orientation of elliptic cohomology
heterotic superstringDirac-Ramond operatorsuperstring partition functionWitten genusEisenstein seriesstring orientation of tmf
self-dual stringM5-brane charge
3w4-orientation of EO(2)-theory


That the elliptic genus of the self-dual string on the M5-brane should be the M5-brane charge in elliptic cohomology in higher analogy to D-brane charge in K-theory is due to

Discussion of computation of the elliptic genus/Witten genus of the self-dual string on the M5-brane includes

  • Stefan Hohenegger, Amer Iqbal, M-strings, Elliptic Genera and N=4 String Amplitudes (arXiv:1310.1325)

Last revised on January 2, 2021 at 11:50:52. See the history of this page for a list of all contributions to it.