On the UV completion of the O(N) model in 6 − ϵ dimensions: a stable large-charge sector

Abstract

We study large charge sectors in the O(N) model in 6 − ϵ dimensions. For 4 < d < 6, in perturbation theory, the quartic O(N) theory has a UV stable fixed point at large N . It was recently argued that this fixed point can be described in terms of an IR fixed point of a cubic O(N) model. By considering a double scaling limit of large charge and weak couplings, we compute two-point and all “extremal” higher-point correlation functions for large charge operators and find a precise equivalence between both pictures. Instanton instabilities are found to be exponentially suppressed at large charge. We also consider correlation function of U(1)-invariant meson operators in the O(2N) ⊃ U(1) × SU(N) theory, as a first step towards tests of (higher spin) AdS/CFT.

Supersymmetry breaking deformations and phase transitions in five dimensions

“…A still open question is whether non-supersymmetric ones exist. Investigations in this direction have been done mostly using the -expansion approach and bootstrap techniques [36][37][38][39][40][41][42][43][44], but it is fair to say that we are still far from having any clear picture about the existence of interacting conformal field theories (CFT) in five dimensions.…”

Resurgence of the large-charge expansion

“…Even-and odddimensional spheres are known to behave differently [43] (the heat kernel trace is convergent in odd dimensions) and it would be interesting to see how this reflects in the resurgence analysis at large charge. Another possibility is to build on the results of a different doublescaling limit, studying the Wilson-Fisher point at large charge in the ε-expansion [26,[50][51][52][53][54][55][56][57][58][59][60]. In the same spirit, it would be interesting to perform a resurgence analysis of supersymmetric systems, both at large R-charge and in the double-scaling limit g → 0, Q → ∞ [18][19][20][21].…”

“…where the coefficients f n cannot be computed within the eft: they enter as an input and have to be computed independently, e.g. in a double-scaling limit [26,[49][50][51][52][53][54][55][56][57][58][59][60] or on the lattice [4,5]. In our double-scaling limit, the quantities that we have studied above correspond to the minimal energy configuration for this action.…”

On the large charge sector in the critical O(N) model at large N

“…Asĵ is increased, the two solutions get closer and "collide" atĵ 0.052, and then move off to the complex plane forĵ > 0.052. This mechanism is 10 The scaling dimensions of large charge operators in the IR fixed point of the cubic model in d = 6 − were recently studied in [29]. However, that work focuses on the regime j √ fixed, which corresponds to small j .…”