An algebraic approach to the analytic bootstrap

By L. Alday, A. Zhiboedov. 2015

155 citations recorded by the source corpus.

A bstractWe develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion relations. We compute corrections to the anomalous dimension of large spin operators due to the exchange of a primary and its descendants in the crossed channel and show that this leads to a Borel-summable expansion. We analyse higher order corrections to the microscopic CFT data in the direct channel and its matching to infinite towers of operators in the crossed channel. We apply this method to the critical O(N ) model. At large N we reproduce the first few terms in the large spin expansion of the known two-loop anomalous dimensions of higher spin currents in the traceless symmetric representation of O(N ) and make further predictions. At small N we present the results for the truncated large spin expansion series of anomalous dimensions of higher spin currents.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e0f2e708815c99721626d33ff09ce4fc7c94e81a

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Citations in the corpus

Gravitational S-matrix from CFT dispersion relations (2017, background): “rresponding to non-integer or negative p. This is relevant to compute the contribution to the CFT data due to an exchanged operator, in the dual channel, of arbitrary twist. This case was analysed in [7] for leading twist operators from the point of view of large spin expansions. The formula above f”
Loops in AdS from conformal field theory (2016, methodology): “Expressions and an algorithm for computing g (m) ∆,` (v) can be found in [53].”
The lightcone bootstrap and the spectrum of the 3d Ising CFT (2016, methodology): “where c0,1(τO, `O) are the coefficients computed in [1] and given in equation (2.”
EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions (2016, background): “For recent work in this direction, see [54, 55].”