A new SU(2) anomaly

Juven Wang, Xiao Gang Wen, Edward Witten

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

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 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.

Original languageEnglish (US)
Article number052301
JournalJournal of Mathematical Physics
Volume60
Issue number5
DOIs
StatePublished - May 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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