Conformal QEDd, F-theorem and the expansion

Simone Giombi, Igor R. Klebanov, Grigory Tarnopolsky

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We calculate the free energies F for U(1) gauge theories on the d dimensional sphere of radius R. For the theory with free Maxwell action we find the exact result as a function of d; it contains the term consistent with the lack of conformal invariance in dimensions other than 4. When the U(1) gauge theory is coupled to a sufficient number N f of massless four-component fermions, it acquires an interacting conformal phase, which in describes the long distance behavior of the model. The conformal phase can be studied using large N f methods. Generalizing the d = 3 calculation in arXiv:1112.5342, we compute its sphere free energy as a function of d, ignoring the terms of order and higher. For finite N f, following arXiv:1409.1937 and arXiv:1507.01960, we develop the expansion for the sphere free energy of conformal QEDd. Its extrapolation to d = 3 shows very good agreement with the large N f approximation for Nf > 3. For N f at or below some critical value , the symmetric conformal phase of QED3 is expected to disappear or become unstable. By using the F-theorem and comparing the sphere free energies in the conformal and broken symmetry phases, we show that . As another application of our results, we calculate the one loop beta function in conformal QED6, where the gauge field has a four-derivative kinetic term. We show that this theory coupled to N f massless fermions is asymptotically free.

Original languageEnglish (US)
Article number135403
JournalJournal of Physics A: Mathematical and Theoretical
Issue number13
StatePublished - Feb 19 2016

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


  • F-theorem
  • conformal field theory
  • renormalization group


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