Mellin space bootstrap for global symmetry
@article{Dey2016MellinSB, title={Mellin space bootstrap for global symmetry}, author={Parijat Dey and Apratim Kaviraj and Aninda Sinha}, journal={Journal of High Energy Physics}, year={2016}, volume={2017}, pages={1-46} }
A bstractWe apply analytic conformal bootstrap ideas in Mellin space to conformal field theories with O(N) symmetry and cubic anisotropy. We write down the conditions arising from the consistency between the operator product expansion and crossing symmetry in Mellin space. We solve the constraint equations to compute the anomalous dimension and the OPE coefficients of all operators quadratic in the fields in the epsilon expansion. We reproduce known results and derive new results up to O(ϵ3…
102 Citations
Simplifying large spin bootstrap in Mellin space
- Mathematics
- 2017
A bstractWe set up the conventional conformal bootstrap equations in Mellin space and analyse the anomalous dimensions and OPE coefficients of large spin double trace operators. By decomposing the…
Simplifying large spin bootstrap in Mellin space
- MathematicsJournal of High Energy Physics
- 2018
We set up the conventional conformal bootstrap equations in Mellin space and analyse the anomalous dimensions and OPE coefficients of large spin double trace operators. By decomposing the equations…
Analytic bootstrap for logarithmic CFT
- Mathematics, PhysicsJournal of High Energy Physics
- 2019
We study logarithmic conformal field theory (LogCFT) in four dimensions using conformal bootstrap techniques in the large spin limit. We focus on the constraints imposed by conformal symmetry on the…
Mellin bootstrap for scalars in generic dimension
- PhysicsJournal of High Energy Physics
- 2018
A bstractWe use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossing-symmetric Mellin space…
A Mellin space approach to the conformal bootstrap
- Mathematics
- 2016
A bstractWe describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of CFTd four point functions and expands them in terms of crossing symmetric…
Mellin bootstrap for scalars in generic dimension
- PhysicsJournal of High Energy Physics
- 2018
We use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossing-symmetric Mellin space formulation of…
Analytic bootstrap of mixed correlators in the O(n) CFT
- MathematicsJournal of High Energy Physics
- 2022
We use large spin perturbation theory and the Lorentzian inversion formula to compute order-ϵ corrections to mixed correlators in the O(n) Wilson-Fisher CFT in 4 − ϵ dimensions. In particular, we…
Inverse bootstrapping conformal field theories
- Computer Science
- 2017
It turns out that the free scalar theory, the 2d minimal model CFTs, the ϕ4 Wilson-Fisher CFT, the Lee-Yang CFT and the Ising CFT are consistent with the universal relations from the minimal fusion rule.
On the Polyakov-Mellin bootstrap
- MathematicsJournal of High Energy Physics
- 2018
A bstractWe elaborate on some general aspects of the crossing symmetric approach of Polyakov to the conformal bootstrap, as recently formulated in Mellin space. This approach uses, as building…
Polyakov-Mellin bootstrap for AdS loops
- MathematicsJournal of High Energy Physics
- 2020
Using Polyakov-Mellin bootstrap to extract the CFT data of all operators, including scalars, till O(1/N4), and compute the loop amplitude in AdS which corresponds to non-planar correlators of in CFT, the paper fixes the AdS bubble diagram and the triangle diagram for the general case.
References
SHOWING 1-10 OF 128 REFERENCES
Conformal Bootstrap in Mellin Space.
- MathematicsPhysical review letters
- 2017
This work proposes a new approach towards analytically solving for the dynamical content of conformal field theories (CFTs) using the bootstrap philosophy, and illustrates the power of this method in the ε expansion of the Wilson-Fisher fixed point by reproducing anomalous dimensions and obtaining OPE coefficients to higher orders in ε than currently available using other analytic techniques.
Large spin systematics in CFT
- Physics
- 2015
A bstractUsing conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin…
A Mellin space approach to the conformal bootstrap
- Mathematics
- 2016
A bstractWe describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of CFTd four point functions and expands them in terms of crossing symmetric…
OPE Convergence in Conformal Field Theory
- Mathematics
- 2012
We clarify questions related to the convergence of the OPE and conformal block decomposition in unitary Conformal Field Theories (for any number of spacetime dimensions). In particular, we explain…
More constraining conformal bootstrap
- Physics
- 2013
Recently an efficient numerical method has been developed to implement the constraints of crossing symmetry and unitarity on the operator dimensions and OPE coefficients of conformal field theories…
Analytic bootstrap at large spin
- Physics, Mathematics
- 2015
A bstractWe use analytic conformal bootstrap methods to determine the anomalous dimensions and OPE coefficients for large spin operators in general conformal field theories in four dimensions…
Anomalous dimensions in CFT with weakly broken higher spin symmetry
- Mathematics
- 2016
A bstractIn a conformal field theory with weakly broken higher spin symmetry, the leading order anomalous dimensions of the broken currents can be efficiently determined from the structure of the…
Bootstrapping 3D fermions
- Physics
- 2015
A bstractWe study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in…
Universal anomalous dimensions at large spin and large twist
- Physics
- 2015
A bstractIn this paper we consider anomalous dimensions of double trace operators at large spin (ℓ) and large twist (τ) in CFTs in arbitrary dimensions (d ≥ 3). Using analytic conformal bootstrap…
Spinning conformal correlators
- Computer Science
- 2011
A bstractWe develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an indexfree notation where tensors…