We apply analytic bootstrap techniques to the four-point correlator of fundamental fields in the Wilson-Fisher model. In an -expansion crossing symmetry fixes the double discontinuity of the correlator in terms of CFT data at lower orders. Large spin perturbation theory, or equivalently the recently proposed Froissart-Gribov inversion integral, then allows one to reconstruct the CFT data of intermediate operators of any spin. We use this method to compute the anomalous dimensions and OPE coefficients of leading twist operators. To cubic order in the double discontinuity arises solely from the identity operator and the scalar bilinear operator, making the computation straightforward. At higher orders the double discontinuity receives contributions from infinite towers of higher spin operators. At fourth order, the structure of perturbation theory leads to a proposal in terms of functions of certain degree of transcendentality, which can then be fixed by symmetries. This leads to the full determination of the CFT data for leading twist operators to fourth order.

We compute, using the method of large spin perturbation theory, the anomalous dimensions and OPE coefficients of all leading twist operators in the critical O(N ) model, to fourth order in the -expansion. This is done fully within a bootstrap framework, and generalizes a recent result for the CFT-data of the Wilson-Fisher model. The anomalous dimensions we obtain for the O(N ) singlet operators agree with the literature values, obtained by diagrammatic techniques, while the anomalous dimensions for operators in other representations, as well as all OPE coefficients, are new. From the results for the OPE coefficients, we derive the 4 corrections to the central charges C T and C J , which are found to be compatible with the known large N expansions. Predictions for the central charge in the strongly coupled 3d model, including the 3d Ising model, are made for various values of N , which compare favourably with numerical results and previous predictions. 34 , (2.2) and where G ijkl (z,z) satisfies crossing symmetry: 1 − z z ∆ϕ G ijkl (z,z) = z 1 −z ∆ϕ G kjil (1 −z, 1 − z).(2.3)

We apply the methods of modern analytic bootstrap to the critical O(N ) model in a 1/N expansion. At infinite N the model possesses higher spin symmetry which is weakly broken as we turn on 1/N . By studying consistency conditions for the correlator of four fundamental fields we derive the CFT-data for all the (broken) currents to order 1/N , and the CFT-data for the non-singlet currents to order 1/N 2 . To order 1/N our results are in perfect agreement with those in the literature. To order 1/N 2 we reproduce known results for anomalous dimensions and obtain a variety of new results for structure constants, including the global symmetry central charge C J to this order.

We explore aspects of the correspondence between Seifert 3-manifolds and 3d N = 2 supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d N = 2 theories constructed from boundary conditions and interfaces in a 4d N = 2 * theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-'t Hooft loops in the 4d N = 2 * theory. In the presence of a mass parameter for the distinguished flavour symmetry, we recover aspects of refined Chern-Simons theory with complex gauge group, and in particular construct an analytic continuation of the S-matrix of refined Chern-Simons theory.

Abstract:We apply the method of the large spin bootstrap to analyse fermionic conformal field theories with weakly broken higher spin symmetry. Through the study of correlators of composite operators, we find the anomalous dimensions and OPE coefficients in the GrossNeveu model in d = 2 + ε dimensions and the Gross-Neveu-Yukawa model in d = 4 − ε dimensions, based only on crossing symmetry. Furthermore a non-trivial solution in the d = 2 + ε expansion is found for a fermionic theory in which the fundamental field is not part of the spectrum. The results are perturbative in ε and valid to all orders in the spin, reproducing known results for operator dimensions and providing some new results for operator dimensions and OPE coefficients.