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Charting the space of 3D CFTs with a continuous global symmetry | | Anatoly Dymarsky
; Joao Penedones
; Emilio Trevisani
; Alessandro Vichi
; | | Date: |
11 May 2017 | | Abstract: | We study correlation functions of a conserved spin-1 current $J_mu$ in three
dimensional Conformal Field Theories (CFTs). We investigate the constraints
imposed by permutation symmetry and current conservation on the form of three
point functions $langle J_mu J_
u mathcal O_{Delta,ell}
angle $ and the
four point function $langle J_mu J_
u J_
ho J_sigma
angle $ and identify
the minimal set of independent crossing symmetry conditions. We obtain a
recurrence relation for conformal blocks for generic spin-1 operators in three
dimensions. In the process, we improve several technical points, facilitating
the use of recurrence relations. By applying the machinery of the numerical
conformal bootstrap we obtain universal bounds on the dimensions of certain
light operators as well as the central charge. Highlights of our results
include numerical evidence for the conformal collider bound and new constraints
on the parameters of the critical $O(2)$ model. The results obtained in this
work apply to any unitary, parity-preserving three dimensional CFT. | | Source: | arXiv, 1705.4278 | | Services: | Forum | Review | PDF | Favorites | |
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