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RG flow from ϕ[superscript 4] theory to the 2D Ising model

Author(s)
Anand, Nikhil; Katz, Emanuel; Khandker, Zuhair U.; Walters, Matthew T.; Genest, Vincent
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Abstract
We study 1+1 dimensional ϕ[superscript 4] theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, C. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with C ≤ C[subscript max], we numerically diagonalize the Hamiltonian at strong coupling and study the resulting IR dynamics. We compute non-perturbative spectral densities of several local operators, which are equivalent to real-time, infinite-volume correlation functions. These spectral densities, which include the Zamolodchikov C-function along the full RG flow, are calculable at any value of the coupling. Near criticality, our numerical results reproduce correlation functions in the 2D Ising model. Keywords: Conformal Field Theory, Field Theories in Lower Dimensions, Nonperturbative Effects, Renormalization Group
Date issued
2017-08
URI
http://hdl.handle.net/1721.1/113406
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Anand, Nikhil, et al. “RG Flow from ϕ[superscript 4] Theory to the 2D Ising Model.” Journal of High Energy Physics, vol. 2017, no. 8, Aug. 2017.
Version: Final published version
ISSN
1029-8479
1126-6708

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