arXiv subjects

Oleg Antipin

Publications and source records attributed to Oleg Antipin.

At least 19 recordsLinked to original sources

arXiv2026

Semiclassical Canovaccio for Composite Operators

We present a novel semiclassical framework tailored to determine the scaling dimensions of heavy neutral composite operators in conformal field theories (CFTs) which are inaccessible with other current methodologies. It utilizes the state-operator correspondence to map the desired scaling dimensions to the semiclassical energy spectrum of periodic homogeneous field configurations on a cylinder. As concrete applications, we provide detailed analyses for the $ϕ^4$ theory near four dimensions and $ϕ^6$ near three dimensions, semiclassically determining the full spectrum of neutral operators in the traceless symmetric Lorentz representations. Our methodology is presented pedagogically and is readily applicable to a vast class of CFTs.

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arXiv2025

Exact Results for the Spectrum of the Ising Conformal Field Theory

We develop a semiclassical framework to determine scaling dimensions of neutral composite operators in scalar conformal field theories. For the critical Ising $λϕ^4$ theory in $d=4-ε$, we obtain the full spectrum of composite operators built out of $n$ fields transforming in the traceless-symmetric Lorentz representations to next-to-leading order in the double-scaling limit $n\rightarrow \infty$ and $λ\rightarrow 0$ with $λn$ fixed. At any given order the semiclassical expansion resums an infinite number of Feynman diagrams. Combining our results with existing perturbative computations further yields the complete five-loop scaling dimensions in the $ε$-expansion for the family of $ϕ^n$ operators. Finally, in three dimensions the next-to-leading order semiclassical results supersede any other existing methodology for $n \gtrsim \mathcal{O}(10)$.

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arXiv2025

Consistency Relation for Fixed Point Dynamics

We gain insight on the fixed point dynamics of $d$ dimensional quantum field theories by exploiting the critical behavior of the $d-ε$ sister theories. To this end we first derive a self-consistent relation between the $d-ε$ scaling exponents and the associated $d$ dimensional beta functions. We then demonstrate that to account for an interacting fixed point in the original theory the related $d-ε$ scaling exponent must be multi-valued in $ε$. We elucidate our findings by discussing several examples such as the QCD Banks-Zaks infrared fixed point, QCD at large number of flavors, as well as the O(N) model in four dimensions. For the latter, we show that although the $1/N$ corrections prevent the reconstruction of the renormalization group flow, this is possible when adding the $1/N^2$ contributions.

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arXiv2024

Exact Results for Scaling Dimensions of Neutral Operators in scalar CFTs

We determine the scaling dimension $Δ_n$ for the class of composite operators $ϕ^n$ in the $λϕ^4$ theory in $d=4-ε$ taking the double scaling limit $n\rightarrow \infty$ and $λ\rightarrow 0$ with fixed $λn$ via a semiclassical approach. Our results resum the leading power of $n$ at any loop order. In the small $λn$ regime we reproduce the known diagrammatic results and predict the infinite series of higher-order terms. For intermediate values of $λn$ we find that $Δ_n/n$ increases monotonically approaching a $(λn)^{1/3}$ behavior in the $λn \to \infty$ limit. We further generalize our results to neutral operators in the $ϕ^4$ in $d=4-ε$, $ϕ^3$ in $d=6-ε$, and $ϕ^6$ in $d=3-ε$ theories with $O(N)$ symmetry.

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arXiv2023

Infinite order results for charged sectors of the Standard Model

We determine anomalous dimensions of a family of fixed hypercharge operators in the Standard Model featuring the general Cabibbo-Kobayashi-Maskawa structure. The results are obtained at infinite orders in the couplings and to leading and subleading orders in the charge. The computed anomalous dimensions are shown to agree with the maximum known order in perturbation theory. We further show that the large hypercharge sector of the Standard Model is characterised by a non-Abelian vector condensation phase.

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arXiv2023

Gauge Invariance at Large Charge

Quantum field theories with global symmetries simplify considerably in the large-charge limit allowing to compute correlators via a semiclassical expansion in the inverse powers of the conserved charges. A generalization of the approach to gauge symmetries has faced the problem of defining gauge-independent observables and, therefore, has not been developed so far. We employ the large-charge expansion to calculate the scaling dimension of the lowest-lying operators carrying $U(1)$ charge $Q$ in the critical Abelian Higgs model in $D=4-ε$ dimensions to leading and next-to-leading orders in the charge and all orders in the $ε$ expansion. Remarkably, the results match our independent diagrammatic computation of the three-loop scaling dimension of the operator $ϕ^Q(x)$ in the Landau gauge. We argue that this matching is a consequence of the equivalence between the gauge-independent dressed two-point function of Dirac type with the gauge-dependent two-point function of $ϕ^Q(x)$ in the Landau gauge. We, therefore, shed new light on the problem of defining gauge-independent exponents which has been controversial in the literature on critical superconductors as well as lay the foundation for large-charge methods in gauge theories.

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arXiv2022

Yukawa interactions at Large Charge

We extend the fixed-charge semiclassical method by computing anomalous dimensions of fixed-charge scalar operators in models with Yukawa interactions. In particular, we discuss the Nambu-Jona-Lasinio-Yukawa theory as well as an asymptotically safe gauge-Yukawa model in four dimensions. In the weakly coupled regime, we cross-check our results to the respective maximum known orders of perturbation theory in these models and predict higher order terms for future comparisons with other computational methods. In the strongly coupled regime, we match our results to the predictions of the large-charge effective field theory which can be compared to future Monte Carlo and lattice studies.

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arXiv2022

The analytic structure of the fixed charge expansion

We investigate the analytic properties of the fixed charge expansion for a number of conformal field theories in different space-time dimensions. The models investigated here are $O(N)$ and $QED_3$. We show that in $d=3-ε$ dimensions the contribution to the $O(N)$ fixed charge $Q$ conformal dimensions obtained in the double scaling limit of large charge and vanishing $ε$ is non-Borel summable, doubly factorial divergent, and with order $\sqrt{Q}$ optimal truncation order. By using resurgence techniques we show that the singularities in the Borel plane are related to worldline instantons that were discovered in the other double scaling limit of large $Q$ and $N$ of Ref. [1]. In $d=4-ε$ dimensions the story changes since in the same large $Q$ and small $ε$ regime the next order corrections to the scaling dimensions lead to a convergent series. The resummed series displays a new branch cut singularity which is relevant for the stability of the $O(N)$ large charge sector for negative $ε$. Although the $QED_3$ model shares the same large charge behaviour of the $O(N)$ model, we discover that at leading order in the large number of matter field expansion the large charge scaling dimensions are Borel summable, single factorial divergent, and with order $Q$ optimal truncation order.

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arXiv2021

More on the Weak Gravity Conjecture via Convexity of Charged Operators

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 $Δ(Q)$ 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 different 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 $U(N)\times U(M)$ 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.

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arXiv2021

More on the cubic versus quartic interaction equivalence in the $O(N)$ model

We compute the scaling dimensions of a family of fixed-charge operators at the infrared fixed point of the $O(N)$ model featuring cubic interactions in $d=6-ε$ for arbitrary $N$ to leading and subleading order in the charge but to all orders in the couplings. The results are used to analyze the conjectured equivalence with the $O(N)$ model displaying quartic interactions at its ultraviolet fixed point. This is performed by comparing the cubic model scaling dimensions against the known large $N$ results for the quartic model and demonstrating that they match. Our results reinforce the conjectured equivalence and further provide novel information on the finite $N$ physics stemming from the computations in the cubic model just below 6 dimensions.

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arXiv2021

Charging the $O(N)$ model

We determine, for the first time, the scaling dimensions of a family of fixed-charge operators stemming from the critical $O(N)$ model in 4-$ε$ dimensions to the leading and next to leading order terms in the charge expansion but to all-orders in the coupling. We test our results to the maximum known order in perturbation theory while determining higher order terms.

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arXiv2021

Untangling scaling dimensions of fixed charge operators in Higgs Theories

We go beyond a systematic review of the semiclassical approaches for determining the scaling dimensions of fixed-charge operators in $U(1)$ and $O(N)$ models by introducing a general strategy apt at determining the relation between a given charge configuration and the associated operators for more involved symmetry groups such as the $U(N) \times U(M)$. We show how, varying the charge configuration, it is possible to access anomalous dimensions of different operators transforming according to a variety of irreducible representations of the non-abelian symmetry group without the aid of diagrammatical computations. We illustrate our computational strategy by determining the anomalous dimensions of several composite operators to the next-to-leading order in the semiclassical expansion for the $U(N) \times U(M)$ conformal field theory (CFT) in $4-ε$ dimensions. Thanks to the powerful interplay between semiclassical methods and group theory we can, for the first time, extract scaling dimensions for a wide range of operators.

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arXiv2020

Charging the Walking U(N)$\times$U(N) Higgs Theory as a Complex CFT

We apply a semi-classical method to compute the conformal field theory (CFT) data for the U(N)xU(N) non-abelian Higgs theory in four minus epsilon dimensions at its complex fixed point. The theory features more than one coupling and walking dynamics. Given our charge configuration, we identify a family of corresponding operators and compute their scaling dimensions which remarkably agree with available results from conventional perturbation theory validating the use of the state-operator correspondence for a complex CFT.

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arXiv2019

Spectrum of anomalous dimensions in hypercubic theories

We compute the spectrum of anomalous dimensions of non-derivative composite operators with an arbitrary number of fields $n$ in the $O(N)$ vector model with cubic anisotropy at the one-loop order in the $ε$-expansion. The complete closed-form expression for the anomalous dimensions of the operators which do not undergo mixing effects is derived and the structure of the general solution to the mixing problem is outlined. As examples, the full explicit solution for operators with up to $n=6$ fields is presented and a sample of the OPE coefficients is calculated. The main features of the spectrum are described, including an interesting pattern pointing to the deeper structure.

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arXiv2018

$a$-theorem at large $N_f$

We determine the Jack and Osborn a-function and related metric for gauge-fermion theories to leading order in the large number of fermions and to all orders in the gauge coupling, demonstrating that the strong a-theorem is violated for the minimal choice of the a-function.

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arXiv2018

Resummation in QFT with Meijer G-functions

We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using this technique, we consider in detail the $ϕ^4$ model where we estimate the non-perturbative $β-$function and prove that its asymptotic behavior correctly reproduces instantonic effects calculated using semiclassical methods. After reviewing the emergence of the renormalons in this theory, we also speculate on how one can resum them. Finally, we resum the non-perturbative $β-$function of abelian and non-abelian gauge-fermion theories and analyze the behavior of these theories as a function of the number of fermion flavors. While in the former no fixed points are found, in the latter, a richer phase diagram is uncovered and illustrated by the regions of confinement, large-distance conformality, and asymptotic safety.

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arXiv2018

Gauge-Yukawa theories: Beta functions at large $N_f$

We consider the dynamics of gauge-Yukawa theories in the presence of a large number of matter constituents. We first review the current status for the renormalization group equations of gauge-fermion theories featuring also semi-simple groups. In this regime these theories develop an interacting ultraviolet fixed point that for the semi-simple case leads to a rich phase diagram. The latter contains a complete asymptotically safe fixed point repulsive in all couplings. We then add two gauged Weyl fermions belonging to arbitrary representations of the gauge group and a complex, gauged scalar to the original gauge-fermion theory allowing for new Yukawa interactions and quartic scalar self-coupling. Consequently, we determine the leading $1/N_f$ Yukawa and quartic beta functions. Our work elucidates, consolidates and extends results obtained earlier in the literature. We also acquire relevant knowledge about the dynamics of gauge-Yukawa theories beyond perturbation theory. Our findings are applicable to any extension of the standard model featuring a large number of fermions such as asymptotic safety.

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arXiv2018

The Half-composite Two Higgs Doublet Model and the Relaxion

We study a new confining gauge theory with fermions in a vectorial representation under the SM gauge group that allows for Yukawa interactions with the Higgs. If the fermion masses are smaller than the confinement scale this realizes a type I two Higgs doublet model where a composite Higgs mixes with the elementary Higgs. This class of models interpolates between an elementary and a composite Higgs and has interesting phenomenology with potentially observables effects in collider physics, EDMs and SM couplings but very weak bounds from indirect searches. The very same framework can be used to realize the cosmological relaxation of the electro-weak scale recently discussed in the literature.

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