| 研究実績の概要 |
Our research plan for FY 2017 was to exploit our existing computational tools for computation in strongly coupled conformal field theories at in the middle of theory space, far from extreme limits where conventional perturbation theory could be used. Over the course of this project, we have developed a set of tools based on the "large quantum-number expansion", where observables are computed in states carrying large quantum number under some symmetry, such as an abelian or nonabelian global charge.In the previous years of the project, we have applied these techniques to generic but isolated cases. In these theories, we have derived precise sum rules on operator dimensions that cannot be accessed by other methods.This year we have expanded our techniques to draw conclusions about large families of strongly-coupled three- and four-dimensional CFT, and compared with independent calculations.This year we have completed three papers: (1) For operator dimensions, the large-J perturbation theory reproduces the spectrum of semi-short scalar operators; (2) for OPE coefficients, the large-J expansion in N=2 D=4 superconformal theories of rank one, can compute the OPE coefficients for Coulomb branch chiral primaries and agrees with values computed by localization and bootstrap calculations. (3) We have also analyzed more complicated nonsupersymmetric CFT at large charge, such as the O(4) Wilson-Fisher model, finding dramatic predictions for large-charge correlation functions.
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