Monopole operators from the 4 − ϵ expansion

Shai M. Chester, Márk Mezei, Silviu S. Pufu, Itamar Yaakov

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25 Scopus citations


Three-dimensional quantum electrodynamics with N charged fermions contains monopole operators that have been studied perturbatively at large N. Here, we initiate the study of these monopole operators in the 4 − ϵ expansion by generalizing them to codimension-3 defect operators in d = 4−ϵ spacetime dimensions. Assuming the infrared dynamics is described by an interacting CFT, we define the “conformal weight” of these operators in terms of the free energy density on S2× ℍ 2 − ϵ in the presence of magnetic flux through the S2, and calculate this quantity to next-to-leading order in ϵ. Extrapolating the conformal weight to ϵ = 1 gives an estimate of the scaling dimension of the monopole operators in d = 3 that does not rely on the 1/N expansion. We also perform the computation of the conformal weight in the large N expansion for any d and find agreement between the large N and the small ϵ expansions in their overlapping regime of validity.

Original languageEnglish (US)
Article number15
JournalJournal of High Energy Physics
Issue number12
StatePublished - Dec 1 2016

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • Conformal Field Theory
  • Solitons Monopoles and Instantons


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