nLab w4-orientation of EO(2)-theory

Idea

The real form $EO(2)$ of ER-theory (i.e. real oriented Morava E-theory) is oriented by Spin structure combined with w4-structure, hence by trivialization of the Stiefel-Whitney classes $w_1$, $w_2$ and $w_4$. (Kriz-Sati 04, section 5.2, esp. p. 29).

Related concepts

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

$d$	partition function in $d$-dimensional QFT	supercharge	index in cohomology theory	genus	logarithmic coefficients of Hirzebruch series
0			push-forward in ordinary cohomology: integration of differential forms			orientation
1	spinning particle	Dirac operator	KO-theory index	A-hat genus	Bernoulli numbers	Atiyah-Bott-Shapiro orientation $M Spin \to KO$
	endpoint of 2d Poisson-Chern-Simons theory string	Spin^c Dirac operator twisted by prequantum line bundle	space of quantum states of boundary phase space/Poisson manifold	Todd genus	Bernoulli numbers	Atiyah-Bott-Shapiro orientation $M Spin^c \to KU$
	endpoint of type II superstring	Spin^c Dirac operator twisted by Chan-Paton gauge field	D-brane charge	Todd genus	Bernoulli numbers	Atiyah-Bott-Shapiro orientation $M Spin^c \to KU$
2	type II superstring	Dirac-Ramond operator	superstring partition function in NS-R sector	Ochanine elliptic genus		SO orientation of elliptic cohomology
	heterotic superstring	Dirac-Ramond operator	superstring partition function	Witten genus	Eisenstein series	string orientation of tmf
	self-dual string		M5-brane charge
3						w4-orientation of EO(2)-theory

References

• Igor Kriz, Hisham Sati, M Theory, Type IIA Superstrings, and Elliptic Cohomology, Adv.Theor.Math.Phys. 8 (2004) 345-395 (arXiv:hep-th/0404013)