Perturbative and instanton corrections to the OPE of CPOs in

On non-supersymmetric conformal manifolds: field theory and holography

“…This looks like a generic phenomenon which has been proposed in [32,33] to be related to the presence of tachyonic instabilities in the gravity dual [34]. 12 In this context, the only model we are aware of which evades this problem, is a non-tachyonic orientifold of Type 0B string theory, discussed in [36]. However, it turns out that the absence of tachyons is not dual to the existence of fixed points in the dangerous double-trace operator running, but rather to the absence of such operators, at least at leading order in 1/N [37].…”

“…We thank Chris Herzog for making us aware of this possibility. 12 Eventually, these problems might also be connected with recent claims about the non-perturbative instability of non-supersymmetric AdS vacua [35].…”

“…As an example, one can consider the D-component (in N = 1 language) of the Konishi multiplet, K = Tr X i X i , which is marginal at g Y M = 0 and becomes marginally irrelevant in the interacting theory. Its anomalous dimensions is known [12,13] and one could then give a prediction, via (2.21), on the behaviour of C OOK , where O is the marginal operator dual to the (complexified) gauge coupling. However, due to a U(1) bonus symmetry enjoyed by N = 4 SYM and a corresponding selection rule [14], such OPE coefficient is predicted to vanish.…”

Conjectures for large N superconformal chiral primary four point functions

“…This is as expected since these operators are absent in the large N limit, their dimensions are proportional to λ 1 4 as λ → ∞ [27] so that they decouple from the spectrum revealed by the large N operator product expansion. This is different from the perturbative expansion about free field theory when such operators are present for any ℓ (ℓ = 0 is the Konishi scalar) and have a leading anomalous dimension proportional to λ, which is therefore not suppressed by 1/N , whereas multi-trace operators have anomalous dimensions which are O(λ/N 2 ) [28]. The disappearance of twist two operators belonging to long multiplets in the strong coupling limit λ → ∞ requires in the operator product calculations in [23] a non trivial cancellation between the free field O(1/N 2 ) contributions and also the leading non ln u terms from the dynamical D-functions.…”

Resurgence of the dressing phase for AdS5 × S5

“…From the purely perturbative point of view, the three-loop coefficient is also distinguished because only starting from three-loops the odd coefficients produce contributions to the dressing phase which satisfy the homogeneous crossing equation, while this is not the case for the one-loop perturbative coefficients or the even ones. For the non-perturbative contributions it might be that there is a protection mechanism based on vanishing of the zero mode contributions, forcing perturbation theory on top of these new non-perturbative saddles to start from three-loops, in the same spirit to what has been observed for the case of the instanton corrections for the anomalous dimension of the Konishi operator [24,25].…”