RG stability of integrable fishnet models

107

191

We study the O(N ) and Gross-Neveu models at large N on AdS d+1 background.Thanks to the isometries of AdS, the observables in these theories are constrained by the SO(d, 2) conformal group even in the presence of mass deformations, as was discussed by Callan and Wilczek [1], and provide an interesting two-parameter family of quantities which interpolate between the S-matrices in flat space and the correlators in CFT with a boundary. For the actual computation, we judiciously use the spectral representation to resum loop diagrams in the bulk. After the resummation, the AdS 4-particle scattering amplitude is given in terms of a single unknown function of the spectral parameter. We then "bootstrap" the unknown function by requiring the absence of double-trace operators in the boundary OPE. Our results are at leading nontrivial order in 1 N , and include the full dependence on the quartic coupling, the mass parameters, and the AdS radius. In the bosonic O(N ) model we study both the massive phase and the symmetry-breaking phase, which exists even in AdS 2 evading Coleman's theorem, and identify the AdS analogue of a resonance in flat space. We then propose that symmetry breaking in AdS implies the existence of a conformal manifold in the boundary conformal theory. We also provide evidence for the existence of a critical point with bulk conformal symmetry, matching existing results and finding new ones for the conformal boundary conditions of the critical theories. For the Gross-Neveu model we find a bound state, which interpolates between the familiar bound state in flat space and the displacement operator at the critical point.

Section: Goldstone Bosons and Conformal Manifoldmentioning

confidence: 99%

A study of quantum field theories in AdS at finite coupling

Carmi

Pietro

Komatsu

2019

107

191

“…The planar limit corresponds to sending N → ∞ at fixed g 2 and the theory is conformal for any g 2 . In particular, no double-trace interactions are needed here [72]. The simplest single-trace operator is the BMN vacuum operator…”

Section: D Fishnet Graphsmentioning

confidence: 99%

Continuum limit of fishnet graphs and AdS sigma model

Basso

Zhong

2019

We consider the continuum limit of 4d planar fishnet diagrams using integrable spin chain methods borrowed from the N = 4 Super-Yang-Mills theory. These techniques give us control on the scaling dimensions of single-trace operators for all values of the coupling constant in the fishnet theory. We use them to study the thermodynamical limit of the BMN operator corresponding to the spin chain ferromagnetic vacuum. We find that its scaling dimension exhibits a critical behaviour when the coupling constant approaches Zamolodchikov's critical coupling. Analysis close to that point suggests that the continuum limit of the fishnet graphs is controlled by the two-dimensional AdS 5 non-linear sigma model. More generally, we present evidence that the fishnet diagrams define an integrable lattice regularization of the AdS 5 model. A system of massless TBA equations is derived for the tachyon energy by dualizing the TBA equations of the weakly coupled planar N = 4 SYM theory.arXiv:1806.04105v1 [hep-th]

“…These models, although not being unitary, are interesting in many respect, but they also share the presence of double-trace operators in the effective action which spoil conformal invariance at leading order in 1/N . In a more recent work [40], it was suggested that a suitable refinement of these models (that is, introducing an extra flavor structure for the component fields) could project out the double-trace operators, at least at leading order in 1/N , similarly to [37]. And that also three and six-dimensional versions of the same model are not plagued by double-trace operator running, at large N .…”

Section: Jhep11(2017)167mentioning

confidence: 99%

On non-supersymmetric conformal manifolds: field theory and holography

Bashmakov

Bertolini

Raj

2017

Abstract:We discuss the constraints that a conformal field theory should enjoy to admit exactly marginal deformations, i.e. to be part of a conformal manifold. In particular, using tools from conformal perturbation theory, we derive a sum rule from which one can extract restrictions on the spectrum of low spin operators and on the behavior of OPE coefficients involving nearly marginal operators. We then focus on conformal field theories admitting a gravity dual description, and as such a large-N expansion. We discuss the relation between conformal perturbation theory and loop expansion in the bulk, and show how such connection could help in the search for conformal manifolds beyond the planar limit. Our results do not rely on supersymmetry, and therefore apply also outside the realm of superconformal field theories.