Eigenvalue inequalities for fermions in gauge theories

Cumrun Vafa, Edward Witten

Research output: Contribution to journalArticlepeer-review

147 Scopus citations


We show that QCD with a sufficient number of fermions of zero bare mass has physical massless particles. That result also follows from triangle anomalies, so only our method is novel. Our method involves proving special cases of recently conjectured paramagnetic inequalities for fermions. The proofs are simple applications of the Atiyah-Patodi-Singer theorem on spectral flow.

Original languageEnglish (US)
Pages (from-to)257-276
Number of pages20
JournalCommunications In Mathematical Physics
Issue number3
StatePublished - Sep 1984

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Eigenvalue inequalities for fermions in gauge theories'. Together they form a unique fingerprint.

Cite this