Strongly γ -Deformed N=4 Supersymmetric Yang-Mills Theory as an Integrable Conformal Field Theory

Abstract

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.

O(N) model in 4<d<6 : Instantons and complex CFTs

“…A simple argument for the exponential suppression of the imaginary parts is that on the sphere S d , or cylinder S d−1 × R, the conformal coupling to curvature adds a positive quadratic term to the scalar potential, making the perturbative vacuum metastable. We demonstrate the smallness of imaginary parts explicitly by computing, at large N , the sphere The fact that the imaginary parts are very small for large N , makes the O(N ) models in 4 < d < 6 similar to the robust examples [35][36][37][38][39][40][41][42] of complex CFTs corresponding to the walking RG flows and weakly first-order phase transitions. In d = 5, for large enough N the imaginary parts of scaling dimensions can be made so small that the numerical bootstrap studies cannot distinguish such complex CFTs from the regular CFTs.…”

Twistor fishnets

“…The fact that {Z i } enter only through the projective delta functions makes it clear that V 4 is compactly supported. Finally,∂V 4 = 0 sincē 12) and the integrand of (4.11) is otherwise holomorphic. This establishes that…”

“…These are given by writing twistor vertices which generate the double trace interactions appearing in the divergences: There is now considerable perturbative evidence that the β-functions for the couplings α 1 , α 2 have two fixed points, for which FCFT is a true (non-unitary) CFT. For α 2 , the β-function can be computed exactly [11,12], and vanishes for α 2 2 = ξ 2 . The β-function for α 1 has been computed up to seven loops [12], where it vanishes at the values…”

“…For α 2 , the β-function can be computed exactly [11,12], and vanishes for α 2 2 = ξ 2 . The β-function for α 1 has been computed up to seven loops [12], where it vanishes at the values…”

“…Anomalous dimensions, certain correlation functions and scattering amplitudes have all been determined exactly as functions of the coupling in FCFT [12,[18][19][20][21]. In addition, FCFT appears to admit a holographic description in terms of a discretized string-like model [22][23][24][25], and provides a first example of a non-supersymmetric 4d QFT with spontaneously broken conformal invariance [26].…”