A new SU(2) anomaly
Abstract
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 halfinteger 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 "allfermion 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 fivedimensional gapped theory whose partition function on a closed fivemanifold Y is (1^{) ∫Yw2w3}. All statements have analogs with SU(2) replaced by Sp(2N). There is also an analog in five dimensions.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 May 2019
 DOI:
 10.1063/1.5082852
 arXiv:
 arXiv:1810.00844
 Bibcode:
 2019JMP....60e2301W
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons;
 Mathematical Physics
 EPrint:
 39 pp, added references and minor typos corrected, added comment on dynamics, updated reference in this version