Monopole operators from the 4 - ɛ expansion
Abstract
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 - ɛ expansion by generalizing them to codimension-3 defect operators in d = 4- ɛ 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 {S}^2× {H}^{2-ɛ} in the presence of magnetic flux through the S 2, and calculate this quantity to next-to-leading order in ɛ. Extrapolating the conformal weight to ɛ = 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 ɛ expansions in their overlapping regime of validity.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- December 2016
- DOI:
- 10.1007/JHEP12(2016)015
- arXiv:
- arXiv:1511.07108
- Bibcode:
- 2016JHEP...12..015C
- Keywords:
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- Conformal Field Theory;
- Solitons Monopoles and Instantons;
- High Energy Physics - Theory
- E-Print:
- 45 pages, 3 figures, version accepted by journal