A new SU(2) anomaly
Name
1810.00844.pdf
Description
Accepted version
Size
622.81 KB
Format
Unknown
Checksum (MD5)
efb93c604855e70d8697379705d0ccf8
Author(s)
Wang, Juven
Wen, Xiao-Gang
Witten, Edward
Date Issued
2019
Journal
Journal of Mathematical Physics
Publisher
AIP Publishing
Version
Author's final manuscript
Abstract
© 2019 Author(s). A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more generally in representations of spin 2r + 1/2, is inconsistent. We describe here a more subtle anomaly that can affect SU(2) gauge theory in four dimensions under the condition that fermions transform with half-integer spin under SU(2) and bosons transform with integer spin. Such a theory, formulated in a way that requires no choice of spin structure, and with an odd number of fermion multiplets in representations of spin 4r + 3/2, is inconsistent. The theory is consistent if one picks a spin or spin c structure. Under Higgsing to U(1), the new SU(2) anomaly reduces to a known anomaly of "all-fermion electrodynamics." Like that theory, an SU(2) theory with an odd number of fermion multiplets in representations of spin 4r + 3/2 can provide a boundary state for a five-dimensional gapped theory whose partition function on a closed five-manifold Y is (-1)-Yw2w3. All statements have analogs with SU(2) replaced by Sp(2N). There is also an analog in five dimensions.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1063/1.5082852
