arXiv subjects

Jahmall Bersini

Publications and source records attributed to Jahmall Bersini.

At least 19 recordsLinked to original sources

arXiv2026

Semiclassics at the cusp

We study cusped Wilson line operators in the Abelian Higgs model in $ d = 4 - ε$ at large external charges. Using a double-scaling limit $ Q \to \infty $, $ ε\to 0 $ with $ Qε$ fixed, we develop a semiclassical framework that provides analytic control beyond fixed-order perturbation theory. We compute the cusp anomalous dimension for arbitrary charges up to next-to-next-to-leading order in the gauge coupling, while resumming scalar self-interactions to all orders. Our results interpolate between perturbative and large-charge regimes, accessing domains that are invisible in fixed-order perturbation theory. As an application, we provide new predictions for various defect CFT observables, including the Mandelstam-Schwinger-dressed two-point function characterizing the superconducting phase transition.

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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

Resurgence Analysis of the Nambu-Jona-Lasinio model at large charge

We study the fixed point of the three-dimensional NJL model in a double-scaling limit where both the charge $Q$ and the number of fermion flavors $N$ become large with a fixed ratio $q=Q/(2N)$. While a similar analysis has been performed for the bosonic O(N) model, fermionic models pose new challenges. In this work, we systematically explore the CFT spectrum in both the large and small $q$ limits beyond the first few orders, and perform a resurgence analysis. Through this approach, we identify the exponential corrections that relate the convergent small-$q$ expansion to the asymptotic large-$q$ behavior. Our results are suggestive of a geometric interpretation of these results in terms of the worldline of particles moving along the geodesics on the cylinder.

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arXiv2025

On the $θ$-angle physics of QCD under pressure: The strange and isospin phase diagram

We unveil the impact of the $θ$-angle on the QCD phase diagram at nonzero isospin and strangeness chemical potentials for three light flavors and different quark mass ratios. We establish the phase boundaries as well as the nature of the associated phase transitions. The order parameters and the physical spectrum in the different phases are determined. We further elucidate the physics around $θ=π$ where we discover a novel parity-preserving superfluid phase. Finally, we comment on Dashen's phenomenon in the superfluid phases when varying the number of light flavors.

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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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arXiv2024

Scaling results for charged sectors of near conformal QCD

We provide the leading near conformal corrections on a cylinder to the scaling dimension $Δ_Q^\ast$ of fixed isospin charge $Q$ operators defined at the lower boundary of the Quantum Chromodynamics conformal window: \begin{equation} Δ_Q = Δ_Q^\ast +\left(\frac{m_σ}{4 πν}\right)^2 \, Q^{\fracΔ{3}} B_1 + \left(\frac{m_π(θ)}{4πν} \right)^4\ Q^{\frac{2}{3}(1-γ)} B_2 + \mathcal{O}\left ( m_σ^4 , m_π^8, m_σ^2 m_π^4\right) \ . \nonumber \end{equation} The results are expressed in powers of the dilaton and pion masses in units of the chiral symmetry breaking scale $4πν$ with the theta-angle dependence encoded directly in the pion mass. The characteristic $Q$-scaling is dictated by the quark mass operator anomalous dimension $γ$ and the one characterising the dilaton potential $Δ$. The coefficients $B_i$ with $i=1,2$ depend on the geometry of the cylinder and properties of the nearby conformal field theory.

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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

The Dilatonic Dynamics of Baryonic Crystals, Branes and Spheres

We systematically analyze the impact of dilatonic dynamics on Skyrme spheres, crystals and branes. The effects of the dilatonic model parameters, encompassing different underlying near-conformal dynamics, on the macroscopic properties of Skyrmions such as their mass and radius, are discussed. For spheres and crystals we identify special values of the ratio of the decay constants for which the second order differential equations reduce to a solvable first order system. Additionally, in the case of the crystals, the dilaton presence spatially separates the baryon and isospin charge distributions. For branes, we show how the dilaton smooths out their configurations. Our results are expected to have wide implications from the study of near-conformal dynamics stemming from QCD-like theories to phenomenological investigations of nuclear matter in extreme regimes.

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arXiv2023

Charging the conformal window at nonzero $θ$ angle

We determine the impact of the $θ$-angle and axion physics on the near conformal dynamics of the large-charge baryon sector of $SU(2)$ gauge theories with $N_f$ fermions in the fundamental representation. We employ an effective approach featuring Goldstone and dilaton degrees of freedom augmented by the topological terms in the theory. We investigate how different dilaton potentials, including the ones for which a systematic counting scheme can be established, affect the results. Via state-operator correspondence we compute the corrections to the would-be conformal dimensions of the lowest large-charge operators as a function of the $θ$ term and dilaton potential.

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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

The $θ$-angle and axion physics of two-color QCD at fixed baryon charge. Part I

We analyze the impact of the $θ$-angle and axion dynamics for two-color (in fact any $Sp(2N)$) QCD at nonzero baryon charge and as a function of the number of matter fields on the vacuum properties, the pattern of chiral symmetry breaking as well as the spectrum of the theory. We show that the vacuum acquires a rich structure when the underlying $CP$ violating topological operator is added to the theory. We discover novel phases and analyse the order of their transitions characterizing the dynamics of the odd and even number of flavours. We further determine the critical chemical potential as function of the $θ$ angle separating the normal from the superfluid phase of the theory. Our results will guide numerical simulations and novel tests of the model's dynamics. The results are also expected to better inform phenomenological applications of the model ranging from composite Higgs physics to strongly interacting massive dark matter models featuring number changing interactions. In the companion work \cite{PartII} we repurpose and upgrade the approach to determine the impact of the $θ$-angle and axion physics on non-perturbative near conformal dynamics related to the fixed baryon charge sector.

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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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