arXiv subjects

Joao Penedones

Publications and source records attributed to Joao Penedones.

At least 19 recordsLinked to original sources

arXiv2026

QFT as a set of ODEs

Correlation functions of local operators in Quantum Field Theory (QFT) on hyperbolic space can be fully characterized by the set of QFT data $\lbrace Δ_i,C_{ijk},b^{\hat{\mathcal{O}}}_j\rbrace$. These are the scaling dimensions of boundary operators $Δ_i$, the boundary Operator Product Expansion (OPE) coefficients $C_{ijk}$ and the Boundary Operator Expansion (BOE) coefficients $b^{\hat{\mathcal{O}}}_j$ that characterize how each bulk operator $\hat{\mathcal{O}}$ can be expanded in terms of boundary operators $\mathcal{O}_j$.For simplicity, we focus on two dimensional QFTs and derive a universal set of first order Ordinary Differential Equations (ODEs) that encode the variation of the QFT data under an infinitesimal change of a bulk relevant coupling. In principle, our ODEs can be used to follow a Renormalization Group (RG) flow starting from a solvable QFT into a strongly coupled phase and to the flat space limit.

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arXiv2026

Effective strings and particles interacting in 3D: the Ising model

We study how a fluctuating domain wall in three dimensions modifies bulk observables in a gapped phase. We introduce an effective interaction between the wall and the lightest bulk massive mode, and identify the regime in which this description is controlled: nearly on-shell bulk exchange with small momentum along the wall. In this regime, several observables are controlled by a renormalized dimensionless coupling $λ$, including the large-$L_z$ correction to the wall free energy and the large-$|x_\perp|$ tail of two-point functions in the presence of the wall. Other observables, such as one-point functions and two-point functions in the nearby-regime, retain non-universal dependence on operator data and on the bulk spectral density. We test the universal kinematic consequences of wall fluctuations, and find good agreement with the predicted rough-wall broadening and nearby Gaussian behavior in Monte Carlo simulations of the 3D Ising model with anti-periodic boundary conditions.

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arXiv2025

What is a photon in de Sitter spacetime?

The states of a single photon in four-dimensional de Sitter (dS) spacetime form a Unitary Irreducible Representation (UIR) of SO(1,4), which we call the photon UIR. While in flat spacetime photons are intimately tied to gauge symmetry, we demonstrate that in de Sitter, photon states emerge generically in any quantum field theory, even without an underlying U(1) gauge field. We derive a Källén-Lehmann representation for antisymmetric tensor two-point functions and show that numerous composite operators constructed from massive free fields can create states in the photon UIR. Remarkably, we find that some of these operators exhibit two-point functions with slower late-time and large-distance decay than the electromagnetic field strength itself, challenging the conventional notion that photons dominate the infrared regime. Using our spectral representation, we establish non-perturbative bounds on the late-time behavior of electric and magnetic fields in de Sitter, with potential implications for primordial magnetogenesis. Through one-loop calculations, we demonstrate that both the creation of photon states and the enhanced late-time large-distance behavior persist in weakly interacting theories.

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arXiv2025

Effective string theory on a torus: the 3d Ising domain wall

We use effective string theory (EST) to describe a toroidal 2d domain wall embedded in a 3d torus. In particular, we compute the free energy of the domain wall in an expansion in inverse powers of the area, up to the second non-universal order that involves the Wilson coefficient $γ_3$. In order to test our predictions, we simulate the 3d Ising model with anti-periodic boundary conditions, using a two-step flat-histogram Monte Carlo method in an ensemble over the boundary coupling $J$ that delivers high-precision free energy data. The predictions from EST reproduce the lattice results with only two adjustable parameters: the string tension, $1/\ell_s^2$, and $γ_3$. We find $γ_3 /|γ_3^{\text{min}}|= -0.82(15)$, which is compatible with previous estimates.

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arXiv2025

Einstein gravity from a matrix integral -- Part II

Using supersymmetric localization, we compute the partition function and some protected correlators of the polarized IKKT matrix model. Surprisingly, we find that the original IKKT model is different from polarized IKKT in the limit of vanishing mass deformation. We study different regimes of the localization results and recover the electrostatic problem which defines the gravity dual.

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arXiv2025

The Källén-Lehmann representation in de Sitter spacetime

We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the Källén-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are nonnegative. In addition, we recover the Källén-Lehmann decomposition in Minkowski space by taking the flat space limit. Using harmonic analysis and the Wick rotation to Euclidean Anti de Sitter, we derive an inversion formula to compute the spectral densities. Using the inversion formula, we relate the analytic structure of the spectral densities to the late-time boundary operator content. We apply our technical tools to study two-point functions of composite operators in free and weakly coupled theories. In the weakly coupled case, we show how the Källén-Lehmann decomposition is useful to find the anomalous dimensions of the late-time boundary operators. We also derive the Källén-Lehmann representation of two-point functions of spinning primary operators of a Conformal Field Theory on de Sitter.

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arXiv2024

Renormalization group flows in AdS and the bootstrap program

We study correlation functions of the bulk stress tensor and boundary operators in Quantum Field Theories (QFT) in Anti-de Sitter (AdS) space. In particular, we derive new sum rules from the two-point function of the stress tensor and its three-point function with two boundary operators. In AdS2, this leads to a bootstrap setup that involves the central charge of the UV limit of the bulk QFT and may allow us to follow a Renormalization Group (RG) flow non-perturbatively by continuously varying the AdS radius. Along the way, we establish the convergence properties of the newly discovered local block decomposition of the three-point function.

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arXiv2023

Numerical tests of the large charge expansion

We perform Monte-Carlo measurements of two and three point functions of charged operators in the critical O(2) model in 3 dimensions. Our results are compatible with the predictions of the large charge superfluid effective field theory. To obtain reliable measurements for large values of the charge, we improved the Worm algorithm and devised a measurement scheme which mitigates the uncertainties due to lattice and finite size effects.

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arXiv2023

Hilbert space of Quantum Field Theory in de Sitter spacetime

We study the decomposition of the Hilbert space of quantum field theory in $(d+1)$ dimensional de Sitter spacetime into Unitary Irreducible Representations (UIRs) of its isometry group \SO$(1,d+1)$. Firstly, we consider multi-particle states in free theories starting from the tensor product of single-particle UIRs. Secondly, we study conformal multiplets of a bulk Conformal Field Theory with symmetry group \SO$(2,d+1)$. Our main tools are the Harish-Chandra characters and the numerical diagonalization of the (truncated) quadratic Casimir of \SO$(1,d+1)$. We introduce a continuous density that encodes the spectrum of irreducible representations contained in a reducible one of $\SO(1,d+1)$. Our results are complete for $d=1$ and $d=2$. In higher dimensions, we rederive and extend several results previously known in the literature. Our work provides the foundation for future nonperturbative bootstrap studies of Quantum Field Theory in de Sitter spacetime.

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arXiv2022

Injecting the UV into the Bootstrap: Ising Field Theory

We merge together recent developments in the S-matrix bootstrap program to develop a dual setup in 2 space-time dimensions incorporating scattering amplitudes of massive particles and matrix elements of local operators. In particular, the stress energy tensor allows us to input UV constraints on IR observables in terms of the central charge $c_{UV}$ of the UV Conformal Field Theory. We consider two applications: (1) We establish a rigorous lower bound on $c_{UV}$ of a class of $\mathbb{Z}_2$ symmetric scalar theories in the IR (including $ϕ^4$); (2) We target Ising Field Theory by, first, minimizing $c_{UV}$ for different values of the magnetic field and, secondly, by determining the allowed range of cubic coupling and one-particle form-factor for fixed $c_{UV} = 1/2$ and magnetic field.

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arXiv2022

Where is M-theory in the space of scattering amplitudes?

We use the S-matrix bootstrap to carve out the space of unitary, analytic, crossing symmetric and supersymmetric graviton scattering amplitudes in nine, ten and eleven dimensions. We extend and improve the numerical methods of our previous work in ten dimensions. A key new tool employed here is unitarity in the celestial sphere. In all dimensions, we find that the minimal allowed value of the Wilson coefficient $α$, controlling the leading correction to maximal supergravity, is very close but not equal to the minimal value realized in Superstring theory or M-theory. This small difference may be related to inelastic effects that are not well described by our numerical extremal amplitudes. Although $α$ has a unique value in M-theory, we found no evidence of an upper bound on $α$ in 11D.

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arXiv2022

Snowmass White Paper: S-matrix Bootstrap

The S-matrix Bootstrap originated on the idea that the S-matrix might be fully constrained by global symmetries, crossing, unitarity, and analyticity without relying on an underlying dynamical theory that may or may not be a quantum field theory. Recently this approach was revived from a somewhat different point of view. Using the same constraints, one numerically maps out the (infinite-dimensional) space of allowed S-matrices that should contain all consistent quantum field theories (and quantum theories of gravity). Moreover, in the best case scenario one finds special points in the space that can be identified with a certain quantum field theory of interest. In that case, the approach allows the numerical computation of the S-matrix without relying on the particular Lagrangian of the theory. In this white paper we summarize the state of the art and discuss the future of the topic.

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arXiv2022

Spinning S-matrix Bootstrap in 4d

We review unitarity and crossing constraints on scattering amplitudes for particles with spin in four dimensional quantum field theories. As an application we study two to two scattering of neutral spin 1/2 fermions in detail. Assuming Mandelstam analyticity of its scattering amplitude, we use the numerical S-matrix bootstrap method to estimate various non-perturbative bounds on quartic and cubic (Yukawa) couplings.

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arXiv2021

Bootstrapping Massive Quantum Field Theories

We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of the matrix of inner products between asymptotic states (in and out) and states created by the action of local operators on the vacuum. The corresponding matrix elements involve scattering amplitudes, form factors and spectral densities of local operators. We test this method in two-dimensional QFTs by setting up a linear optimization problem that gives a lower bound on the central charge of the UV CFT associated to a QFT with a given mass spectrum of stable particles (and couplings between them). Some of our numerical bounds are saturated by known form factors in integrable theories like the sine-Gordon, E8 and O(N) models.

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arXiv2021

Hamiltonian truncation in Anti-de Sitter spacetime

Quantum Field Theories (QFTs) in Anti-de Sitter (AdS) spacetime are often strongly coupled when the radius of AdS is large, and few methods are available to study them. In this work, we develop a Hamiltonian truncation method to compute the energy spectrum of QFTs in two-dimensional AdS. The infinite volume of constant timeslices of AdS leads to divergences in the energy levels. We propose a simple prescription to obtain finite physical energies and test it with numerical diagonalization in several models: the free massive scalar field, $ϕ^4$ theory, Lee-Yang and Ising field theory. Along the way, we discuss spontaneous symmetry breaking in AdS and derive a compact formula for perturbation theory in quantum mechanics at arbitrary order. Our results suggest that all conformal boundary conditions for a given theory are connected via bulk renormalization group flows in AdS.

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arXiv2021

Where is String Theory?

We use the S-matrix bootstrap to carve out the space of unitary, crossing symmetric and supersymmetric graviton scattering amplitudes in ten dimensions. We focus on the leading Wilson coefficient $α$ controlling the leading correction to maximal supergravity. The negative region $α<0$ is excluded by a simple dual argument based on linearized unitarity (the desert). A whole semi-infinite region $α\gtrsim 0.14$ is allowed by the primal bootstrap (the garden). A finite intermediate region is excluded by non-perturbative unitarity (the swamp). Remarkably, string theory seems to cover all (or at least almost all) the garden from very large positive $α$ -- at weak coupling -- to the swamp boundary -- at strong coupling.

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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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arXiv2021

Applications of dispersive sum rules: $ε$-expansion and holography

We use Mellin space dispersion relations together with Polyakov conditions to derive a family of sum rules for Conformal Field Theories (CFTs). The defining property of these sum rules is suppression of the contribution of the double twist operators. Firstly, we apply these sum rules to the Wilson-Fisher model in $d=4-ε$ dimensions. We re-derive many of the known results to order $ε^4$ and we make new predictions. No assumption of analyticity down to spin $0$ was made. Secondly, we study holographic CFTs. We use dispersive sum rules to obtain tree-level and one-loop anomalous dimensions. Finally, we briefly discuss the contribution of heavy operators to the sum rules in UV complete holographic theories.

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