Anomalous dimensions for ϕ n in scale invariant d = 3 theory

We study the O(2N) model at criticality in three dimensions in the double scaling limit of large N and large charge. We show that the large-charge expansion is an asymptotic series, and we use resurgence techniques to study the non-perturbative corrections and to extend the validity of the eft to any value of the charge. We conjecture the general form of the non-perturbative behavior of the conformal dimensions for any value of N and find very good agreement with previous lattice data.

Section: Discussionmentioning

confidence: 99%

Section: Jhep05(2021)035mentioning

confidence: 99%

Resurgence of the large-charge expansion

Dondi

Kalogerakis

Orlando

et al. 2021

“…This typically endows, for UV free theories, perturbative infrared fixed points. Interestingly, the charge expansion captures higher orders in the ordinary perturbative coupling corrections [28][29][30][31][32]. The reason being that the presence of a small parameter allows studying the fixed-charge sectors of a CFT by defining a 't Hooft-like coupling A = Q in which one can take the limit → 0 while maintaining A fixed.…”

Section: Jhep12(2021)204mentioning

confidence: 99%

“…Later on the O(N ) model was also investigated via the semiclassical approach at large N in various dimensions in [34,35]. The O(N ) model in 3 − dimensions was investigated [32,36]. The study of the quite involved U(N ) × U(M ) model in 4 − dimensions appeared in [31,37].…”

Section: Jhep12(2021)204mentioning

confidence: 99%

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More on the weak gravity conjecture via convexity of charged operators

Antipin

Bersini

Sannino

et al. 2021

The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy. Because of the dual conformal field theory (CFT) formulation in the anti-de Sitter space, the conformal dimension ∆(Q) of the lowest-dimension operator with charge Q under some global U(1) symmetry must be a convex function of Q. This property has been conjectured to hold for any (unitary) conformal field theory and generalized to larger global symmetry groups. Here we refine and further test the convex charge conjecture via semiclassical computations for fixed charge sectors of different theories in various dimensions. We analyze the convexity properties of the leading and next-to-leading order terms stemming from the semiclassical computation, de facto, extending previous tests beyond the leading perturbative contributions and to arbitrary charges. In particular, the leading contribution is sufficient to test convexity in the semiclassical computations. We also consider intriguing cases in which the models feature a transition from real to complex conformal dimensions either as a function of the charge or number of matter fields. As a relevant example of the first kind, we investigate the O(N) model in 4 + ϵ dimensions. As an example of the second type, we consider the U(N) × U(M) model in 4 − ϵ dimensions. Both models display a rich dynamics where, by changing the number of matter fields and/or charge, one can achieve dramatically different physical regimes. We discover that whenever a complex conformal dimension appears, the real part satisfies the convexity property.

RG flows and fixed points of O(N)r models

Jepsen,

2024

By means of ϵ and large N expansions, we study generalizations of the O(N) model where the fundamental fields are tensors of rank r rather than vectors, and where the global symmetry (up to additional discrete symmetries and quotients) is O(N)r, focusing on the cases r ≤ 5. Owing to the distinct ways of performing index contractions, these theories contain multiple quartic operators, which mix under the RG flow. At all large N fixed points, melonic operators are absent and the leading Feynman diagrams are bubble diagrams, so that all perturbative fixed points can be readily matched to full large N solutions obtained from Hubbard-Stratonovich transformations. The family of fixed points we uncover extend to arbitrary higher values of r, and as their number grows superexponentially with r, these theories offer a vast generalization of the critical O(N) model.We also study sextic O(N)r theories, whose large N limits are obscured by the fact that the dominant Feynman diagrams are not restricted to melonic or bubble diagrams. For these theories the large N dynamics differ qualitatively across different values of r, and we demonstrate that the RG flows possess a numerous and diverse set of perturbative fixed points beginning at rank four.