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Eigenvalue inequalities for fermions in gauge theories

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Abstract

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.

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Authors and Affiliations

  1. Joseph Henry Laboratories, Princeton University, 08544, Princeton, NJ, USA

    Cumrun Vafa & Edward Witten

  2. Institute for Advanced Study, 08540, Princeton, NJ, USA

    Edward Witten

Authors
  1. Cumrun Vafa
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  2. Edward Witten
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Additional information

Communicated by A. Jaffe

Supported in part by the National Science Foundation Grant No. PHY80-19754

Supported in part by DOE Grant No. DE-AC02-76ER02220

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Vafa, C., Witten, E. Eigenvalue inequalities for fermions in gauge theories. Commun.Math. Phys. 95, 257–276 (1984). https://doi.org/10.1007/BF01212397

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  • DOI: https://doi.org/10.1007/BF01212397

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