nLab Diaconescu-Moore-Witten anomaly

Idea

A potential quantum anomaly in M-theory/type IIA string theory.

References

General

The anomaly was found in

• Duiliu-Emanuel Diaconescu, Gregory Moore, Edward Witten, $E_8$ Gauge Theory, and a Derivation of K-Theory from M-Theory, Adv.Theor.Math.Phys.6:1031-1134 (2003) [arXiv:hep-th/0005090]

while mostly assuming vanishing NS-fields (the B-field). The non-vanishing B-field in this context was considered in

• Gregory Moore, Natalia Saulina, T-Duality, and the K-Theoretic Partition Function of TypeIIA Superstring Theory, Nucl.Phys. B670 (2003) 27-89 (arXiv:hep-th/0206092)

where however the anomaly as such is not discussed. This was then put together in

• Varghese Mathai, Hisham Sati, Some Relations between Twisted K-theory and E8 Gauge Theory, JHEP 0403:016 (2004) [arXiv:hep-th/0312033]

which hence discusses the anomaly for twisted K-theory.

Interpretaton via second integral Morava K-theory

An interpretation of the phenomenon in terms of orientation in second integral Morava K-theory is in

• Igor Kriz, Hisham Sati, M-theory, type IIA superstrings, and elliptic cohomology, Adv. Theor. Math. Phys. 8 (2004), no. 2, 345–394 (Euclid, 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) (spire:899170)

Interpretation via tangentially twisted Cohomotopy

Interpretation of the anomaly cancellation as a consequence of flux quantization in tangentiall twisted Cohomotopy:

• Domenico Fiorenza, Hisham Sati, Urs Schreiber: Twisted Cohomotopy implies M-theory anomaly cancellation, Communications in Mathematical Physics 377 (2020) 1961-2025 [arXiv:1904.10207, doi:10.1007/s00220-020-03707-2]

Interpretation via $tmf$ with level structure

Interpretation via an analogue of the string orientation of tmf but for tmf with level structure:

• Arun Debray, Matthew Yu: Type IIA String Theory and tmf with Level Structure [arXiv:2411.07299]

Review:

• Matthew Yu: A new tangential structure for type IIA string theory, talk at CQTS (May 2025) [slides:pdf]

Related concepts

chromatic level	generalized cohomology theory / E-∞ ring	obstruction to orientation in generalized cohomology	generalized orientation/polarization	quantization	incarnation as quantum anomaly in higher gauge theory
1	complex K-theory $KU$	third integral SW class $W_3$	spinᶜ structure	K-theoretic geometric quantization	Freed-Witten anomaly
2	EO(n)	Stiefel-Whitney class $w_4$
2	integral Morava K-theory $\tilde K(2)$	seventh integral SW class $W_7$			Diaconescu-Moore-Witten anomaly in Kriz-Sati interpretation