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Local/Short-range conformal field theories from long-range perturbation theory
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We show that by imposing the conformal Wald identity, one can extract conformal data of the corresponding short-range/local CFT from the long-range perturbation theory. We first apply this to the O(N) vector model. We demonstrate that by properly re-sum the perturbative series, one gets reasonable estimations of the critical exponents of the local/short-range CFTs. We then apply this method to study fermionic models with four-fermion interactions. In 2+1 dimensions, the model has the Gross-Neveu coupling and the Thirring coupling. We also consider a 4+1 dimensional theory with a generalized Thirring coupling.
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1d Ising model with $1/r^{1.99}$ interaction
The authors propose a weakly coupled dual field theory for the 1D long-range Ising CFT near s = 1, derive an exact spectrum at s = 1, and find matching perturbative CFT data from RG and bootstrap calculations.
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