Communications in Mathematical Physics

, Volume 95, Issue 3, pp 257–276 | Cite as

Eigenvalue inequalities for fermions in gauge theories

  • Cumrun Vafa
  • Edward Witten


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.


Neural Network Statistical Physic Complex System Gauge Theory Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Cumrun Vafa
    • 1
  • Edward Witten
    • 1
    • 2
  1. 1.Joseph Henry LaboratoriesPrinceton UniversityPrincetonUSA
  2. 2.Institute for Advanced StudyPrincetonUSA

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