arXiv subjects

Joan Elias Miro

Publications and source records attributed to Joan Elias Miro.

14 recordsLinked to original sources

arXiv2026

The Phases of the Scalar S-Matrix Island

The two-to-two four-dimensional scattering amplitude of identical scalars obeys rigorous two-sided non-perturbative bounds derived via the modern numerical S-matrix bootstrap. These bounds carve out an allowed region with a rich boundary structure, featuring edges and vertices. In this work we further tighten this region and uncover the physics of its boundary by analyzing the asymptotic Regge behavior of the amplitude and the spectrum of resonances and virtual states. We find that the S-matrices along a given edge exhibit universal behavior, sharply contrasting with that on other edges. This reveals a classification of the boundary into distinct phases, corresponding to different UV mechanisms by which a gapped scalar arises.

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arXiv2025

Thermodynamics from the S-matrix reloaded: emergent thermal mass

The formalism of Dashen, Ma and Bernstein (DMB) expresses the thermal partition function of a system in terms of the S-matrix operator, roughly $Z(β) \propto \int dE\, e^{-βE}\,\text{Tr}\,\ln S(E),$ where $S$ denotes the full scattering operator on the asymptotic Fock space -- i.e. including all multi-particle sectors -- defined via the Lippmann-Schwinger equation. Recently we have employed this formalism to compute the free energy of flux tubes (essentially a two-dimensional theory of derivatively coupled scalars) and the two-loop $O(α_s)$ QCD thermal free energy. Moving to higher orders, it is well known that at $O(α_s^2)$ in QCD, or e.g. at $O(λ^2)$ in $λϕ^4$ theory, the free energy develops IR divergences. These IR divergences are resolved by the screening Debye mass. However, the DMB formalism expresses the free energy in terms of a trace of the S-matrix operator in the vacuum. How, then, does the Debye mass arise in this framework? In this work we address this question, thereby paving the way for higher-order applications of the DMB formalism in relativistic QFT.

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arXiv2025

A Geometric View on Crossing-Symmetric Dispersion Relations

We introduce a general framework for constructing dispersion relations using crossing-symmetric variables, leading to infinitely many distinct representations of the 2-to-2 scattering amplitude of identical scalars. Classical formulations such as the Auberson-Khuri crossing-symmetric dispersion relations (CSDRs), the Mahoux-Roy-Wanders relations, and the local CSDR, as well as fixed-t dispersion relations emerge as special cases. Within this setting we re-derive the null constraints from a geometric perspective. Finally, we present, for the first time, an explicit extension of Roy-like equations that remain valid at arbitrarily high energies, relying only on the rigorously established analyticity domain of scattering amplitudes.

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arXiv2025

Flowing from the Ising Model on the Fuzzy Sphere to the 3D Lee-Yang CFT

We employ the Fuzzy Sphere regulator to study the 3D Lee-Yang CFT. The model is defined by deforming the Ising model on the Fuzzy Sphere via a purely imaginary longitudinal magnetic field. This model undergoes a quantum phase transition, whose critical point we determine and identify with the 3D Lee-Yang CFT. We show how to tune the model and find that the lowest-lying states of the Hamiltonian align well with the expected CFT spectrum. We discuss the Fuzzy Sphere estimates for the scaling dimension $Δ_ϕ$ of the lowest primary operator. Finally, we interpret small deviations from the CFT expectations in terms of the leading irrelevant operators of the Lee-Yang CFT. We show that the Fuzzy Sphere calculations are compatible with the best five-loop $ε$-expansion estimates.

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arXiv2025

Testing the RG-flow $M(3,10)+ϕ_{1,7}\to M(3,8)$ with Hamiltonian Truncation

Hamiltonian Truncation (HT) methods provide a powerful numerical approach for investigating strongly coupled QFTs. In this work, we develop HT techniques to analyse a specific Renormalization Group (RG) flow recently proposed in Refs. [1, 3]. These studies put forward Ginzburg-Landau descriptions for the conformal minimal models $M(3,10)$ and $M(3,8)$, as well as the RG flow connecting them. Specifically, the RG-flow is defined by deforming the $M(3,10)$ with the relevant primary operator $ϕ_{1,7}$ (whose indices denote its position in the Kac table), yielding $M(3,10)+ ϕ_{1,7}$. From the perspective of HT, realising such an RG-flow presents significant challenges, as the $ϕ_{1,7}$ deformation requires renormalizing the UV theory up to third order in the coupling constant of the deformation. In this study, we carry out the necessary calculations to formulate HT for this theory and numerically investigate the spectrum of $M(3,10)+ ϕ_{1,7}$ in the large coupling regime, finding strong evidence in favour of the proposed flow.

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arXiv2025

Hamiltonian Truncation Crafted for UV-divergent QFTs

We develop the theory of Hamiltonian Truncation (HT) to systematically study RG flows that require the renormalization of coupling constants. This is a necessary step towards making HT a fully general method for QFT calculations. We apply this theory to a number of QFTs defined as relevant deformations of $d=1+1$ CFTs. We investigated three examples of increasing complexity: the deformed Ising, Tricritical-Ising, and non-unitary minimal model $M(3,7)$. The first two examples provide a crosscheck of our methodologies against well established characteristics of these theories. The $M(3,7)$ CFT deformed by its $Z_2$-even operators shows an intricate phase diagram that we clarify. At a boundary of this phase diagram we show that this theory flows, in the IR, to the $M(3,5)$ CFT.

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arXiv2024

Thermodynamics from the S-matrix reloaded, with applications to QCD and the confining Flux Tube

Over the past decade and more, S-matrix-based calculational methods have experienced a resurgence, proving to be both an elegant and powerful tool for extracting physical quantities without the need for an underlying Lagrangian formulation. In this work, we critically review and further develop the formalism introduced by Dashen, Ma, and Bernstein, which connects the thermodynamics of relativistic systems to the information contained in their scattering amplitudes. As a demonstration, we revisit the computation of the QCD equation of state to leading order in the strong coupling, showcasing the advantages of this method over traditional Thermal Field Theory techniques. Additionally, we apply these tools to the effective theory of a long confining Flux Tube in D dimensions, analyzing thermal effects up to and including NNLO contributions. Our results are compared with those obtained using the Thermodynamic Bethe Ansatz method. We also discuss how these techniques enable the inclusion of non-universal effects in the study of Flux Tubes, while relying solely on the S-matrix as input.

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arXiv2023

Extremal Higgs couplings

We critically assess to what extent it makes sense to bound the Wilson coefficients of dimension-six operators. In the context of Higgs physics, we establish that a closely related observable, $c_H$, is well-defined and satisfies a two-sided bound. $c_H$ is derived from the low momentum expansion of the scattering amplitude, or the derivative of the amplitude at the origin with respect to the Mandelstam variable $s$, expressed as $M(H_iH_i\rightarrow H_jH_j)=c_H s +O(g_\text{SM}, s^{-2})$ where $g_\text{SM}$ represents all Standard Model couplings. This observable is non-dispersive and, as a result, not sign-definite. We also determine the conditions under which the bound on $c_H$ is equivalent to a bound on the dimension-six operator $O_H=\partial| H|^2 \partial |H|^2$.

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arXiv2023

Effective Hamiltonians and Counterterms for Hamiltonian Truncation

We outline a procedure for applying Hamiltonian Truncation to Quantum Field Theories (QFTs) that have UV divergences. To do this, we derive a novel representation of an Effective Hamiltonian which makes manifest some of its important properties (e.g. the non-perturbative matching of the spectra between the UV theory and the theory described by the Effective Hamiltonian). We check the consistency of our procedure using Conformal Perturbation Theory. Finally we comment on how the Effective Hamiltonian, which incorporates non-local interactions, describes a local QFT.

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arXiv2023

Bridging Positivity and S-matrix Bootstrap Bounds

The main objective of this work is to isolate Effective Field Theory scattering amplitudes in the space of non-perturbative two-to-two amplitudes, using the S-matrix Bootstrap. We do so by introducing the notion of Effective Field Theory cutoff in the S-matrix Bootstrap approach. We introduce a number of novel numerical techniques and improvements both for the primal and the linearized dual approach. We perform a detailed comparison of the full unitarity bounds with those obtained using positivity and linearized unitarity. Moreover, we discuss the notion of Spin-Zero and UV dominance along the boundary of the allowed amplitude space by introducing suitable observables. Finally, we show that this construction also leads to novel bounds on operators of dimension less than or equal to six.

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arXiv2022

Gearing up for the next generation of LFV experiments, via on-shell methods

Lepton Flavor Violating (LFV) observables such as $μ\to eγ$, $μ\to 3e$ and $μN \to eN$ are among the best probes for new physics at the TeV scale. In the near future the bounds on these observables will improve by many orders of magnitude. In this work we use the SM EFT to understand the impact of these measurements. The precision reach is such that the interpretation of the bounds requires an analysis of the dimension-six operator mixing up to the two-loop level. Using on-shell amplitude techniques, which make transparent many selection rules, we classify and calculate the different operator mixing chains. At the leading order, on-shell techniques allow to calculate anomalous dimensions of SM EFT operators from the product of tree-level amplitudes, even for two-loop renormalization group mixings. We illustrate the importance of our EFT approach in models with extra vector-like fermions.

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arXiv2022

Hamiltonian Truncation with Larger Dimensions

Hamiltonian Truncation (HT) is a numerical approach for calculating observables in a Quantum Field Theory non-perturbatively. This approach can be applied to theories constructed by deforming a conformal field theory with a relevant operator of scaling dimension $Δ$. UV divergences arise when $Δ$ is larger than half of the spacetime dimension $d$. These divergences can be regulated by HT or by using a more conventional local regulator. In this work we show that extra UV divergences appear when using HT rather than a local regulator for $Δ\geq d/2+1/4$, revealing a striking breakdown of locality. Our claim is based on the analysis of conformal perturbation theory up to fourth order. As an example we compute the Casimir energy of $d=2$ Minimal Models perturbed by operators whose dimensions take values on either side of the threshold $d/2+1/4$.

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arXiv2021

Flux Tube S-matrix Bootstrap

We bootstrap the S-matrix of massless particles in unitary, relativistic two dimensional quantum field theories. We find that the low energy expansion of such S-matrices is strongly constrained by the existence of a UV completion. In the context of flux tube physics, this allows us to constrain several terms in the S-matrix low energy expansion or -- equivalently -- on Wilson coefficients of several irrelevant operators showing up in the flux tube effective action. These bounds have direct implications for other physical quantities; for instance, they allow us to further bound the ground state energy as well as the level splitting of degenerate energy levels of large flux tubes. We find that the S-matrices living at the boundary of the allowed space exhibit an intricate pattern of resonances with one sharper resonance whose quantum numbers, mass and width are precisely those of the world-sheet axion proposed in [1,2]. The general method proposed here should be extendable to massless S-matrices in higher dimensions and should lead to new quantitative bounds on irrelevant operators in theories of Goldstones and also in gauge and gravity theories.

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arXiv2020

Exploring Hamiltonian Truncation in $\bf{d=2+1}$

We initiate the application of Hamiltonian Truncation methods to solve strongly coupled QFTs in $d=2+1$. By analysing perturbation theory with a Hamiltonian Truncation regulator, we pinpoint the challenges of such an approach and propose a way that these can be addressed. This enables us to formulate Hamiltonian Truncation theory for $ϕ^4$ in $d=2+1$, and to study its spectrum at weak and strong coupling. The results obtained agree well with the predictions of a weak/strong self-duality possessed by the theory. The $ϕ^4$ interaction is a strongly relevant UV divergent perturbation, and represents a case study of a more general scenario. Thus, the approach developed should be applicable to many other QFTs of interest.

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