This is not the latest version of this item. The latest version can be found here.
A new SU(2) anomaly
Name
1810.00844.pdf
Description
Accepted version
Size
622.81 KB
Format
Adobe PDF
Checksum (MD5)
efb93c604855e70d8697379705d0ccf8
Author(s)
Wang, Juven
Wen, Xiao-Gang
Witten, Edward
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.
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
10.1063/1.5082852
