Strongly $\gamma$-Deformed $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory as an Integrable Conformal Field Theory

David Grabner , Nikolay Gromov , Vladimir Kazakov (1, 2) , Gregory Korchemsky (3)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
2 UPMC - Université Pierre et Marie Curie - Paris 6
3 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We demonstrate by explicit multiloop calculation that γ-deformed planar N=4 supersymmetric Yang-Mills (SYM) theory, supplemented with a set of double-trace counterterms, has two nontrivial fixed points in the recently proposed double scaling limit, combining vanishing ’t Hooft coupling and large imaginary deformation parameter. We provide evidence that, at the fixed points, the theory is described by an integrable nonunitary four-dimensional conformal field theory. We find a closed expression for the four-point correlation function of the simplest protected operators and use it to compute the exact conformal data of operators with arbitrary Lorentz spin. We conjecture that both conformal symmetry and integrability should survive in γ-deformed planar N=4 SYM theory for arbitrary values of the deformation parameters.

Mots clés: field theory: conformal; field theory: integrability; supersymmetry: 4; deformation; fixed point; scaling: approximation; n-point function: 4; symmetry: conformal; operator product expansion

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]

David Grabner, Nikolay Gromov, Vladimir Kazakov, Gregory Korchemsky. Strongly $\gamma$-Deformed $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory as an Integrable Conformal Field Theory. Physical Review Letters, 2018, 120 (11), pp.111601. ⟨10.1103/PhysRevLett.120.111601⟩. ⟨hal-01758325⟩