Towards a bootstrap approach to higher orders of epsilon expansion

Abstract

We employ a hybrid approach in determining the anomalous dimension and OPE coefficient of higher spin operators in the Wilson-Fisher theory. First we do a large spin analysis for CFT data where we use results obtained from the usual and the Mellin Bootstrap and also from Feynman diagram literature. This gives new predictions at O( 4 ) and O( 5 ) for anomalous dimensions and OPE coefficients, and also provides a cross-check for the results from Mellin Bootstrap. These higher orders get contributions from all higher spin operators in the crossed channel. We also use the Bootstrap in Mellin space method for φ 3 in d = 6 − CFT where we calculate general higher spin OPE data. We demonstrate a higher loop order calculation in this approach by summing over contributions from higher spin operators of the crossed channel in the same spirit as before. * parijatdey@iisc.ac.in

Three ways to solve critical ϕ4 theory on 4 − 𝜖 dimensional real projective space: Perturbation, bootstrap, and Schwinger–Dyson equation

“…Thus, to make progress in analytic approach, we need a certain organizing principle or a resummation to deal with it. In the flat space-time, such techniques have been developed by using the Mellin space formalism in [9][10] [11][12] [13] as well as in the large spin perturbation theory in [18]. We would like to see if a similar technique can be applied to the CFTs on RP d or on more non-trivial manifold.…”

Holographic four-point functions in the (2, 0) theory

“…(4.1) 11 For other applications and recent developments, see [1,[37][38][39][40][41][42][43][44][45][46][47][48]).…”

On the Polyakov-Mellin bootstrap

“…In this paper we have elaborated on the crossing symmetric formalism introduced by Polyakov and recast in Mellin space in [14,15] (and further applied in several contexts [16,17,27,28]). In the process, we have enormously simplified the key ingredients in the approach.…”

“…quantities not yet computed, in general, even with Feynman diagrams. These results have since also been generalised to the case with O(N ) symmetry [16], for a leading order perturbative proof for non-existence of CFTs beyond 6 dimensions [27] as well as to study the epsilon expansion in the large spin limit [28].…”