Abstract
We study 3d CFTs with an $O(N)$ global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension $O(N)$ vector $\phi_i$ and the lowest dimension $O(N)$ singlet $s$, assumed to be the only relevant operators in their symmetry representations. The constraints of crossing symmetry and unitarity for these four-point functions force the scaling dimensions $(\Delta_\phi, \Delta_s)$ to lie inside small islands. We also make rigorous determinations of current two-point functions in the $O(2)$ and $O(3)$ models, with applications to transport in condensed matter systems.
Highlights
Ising correlator bootstrap leads to a small and isolated allowed region in operator dimension space consistent with the known dimensions in the 3d Ising CFT
Filip Kos,a David Poland,a David Simmons-Duffinb and Alessandro Vichic aDepartment of Physics, Yale University, New Haven, CT 06520, U.S.A. bSchool of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A. cTheory Division, CERN, Geneva, Switzerland E-mail: filip.kos@yale.edu, dpoland@gmail.com, davidsd@gmail.com, alessandro.vichi@cern.ch Abstract: We study 3d CFTs with an O(N ) global symmetry using the conformal bootstrap for a system of mixed correlators
In this work we focus on 3d CFTs with O(N ) global symmetry, previously studied using numerical bootstrap techniques in [15, 22]
Summary
Ising correlator bootstrap leads to a small and isolated allowed region in operator dimension space consistent with the known dimensions in the 3d Ising CFT. The immediate question is whether the same approach can be used to rigorously isolate and precisely determine spectra in the zoo of other known (and perhaps unknown) CFTs, those with physical importance. We will show that the CFTs known as the O(N ) vector models can be isolated using a system of mixed correlators containing the leading O(N ) vector φi and singlet s, assumed to be the only relevant operators in their symmetry representations. We make precise determinations of the current central charge JJ ∝ CJ for N = 2, 3 This coefficient is interesting because it describes conductivity properties of materials in the vicinity of their critical point [54].
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