arXiv subjects

Manuel Loparco

Publications and source records attributed to Manuel Loparco.

7 recordsLinked to original sources

arXiv2026

QFT as a set of ODEs: higher dimensions

Correlation functions of local operators in Quantum Field Theory (QFT) in Anti-de Sitter space (AdS) are completely fixed by the QFT data: the set of scaling dimensions $\Delta_i$ and OPE coefficients $C_{ijk}$ of the boundary operators, and the bulk-boundary (BOE) coefficients $b^{\hat\Phi}_i$ encoding how bulk fields decompose into boundary operators. In this work, we generalize the ordinary differential equations (ODEs) that govern the variation of the QFT data under a bulk relevant deformation, originally derived for AdS$_2$ \cite{Loparco:2026fki}, to the cases of AdS$_3$ and AdS$_4$. We demonstrate that these flow equations natively capture the mechanism of merger-annihilation when a boundary operator hits marginality, as well as level repulsion when different $\Delta_i$'s approach each other. Furthermore, we address the practical implementation of the framework: we propose substituting the ODE for the OPE coefficients with the crossing equation for greater efficiency, and we observe that Pad\'e approximants dramatically improve the convergence of the sums over boundary operators, at least in free theories. Altogether, these advances lay the groundwork for the future application of the flow equations to the study of strongly coupled QFTs in AdS and their flat space limits.

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arXiv2026

Locality constraints in AdS$_2$ without parity

We study bulk locality constraints in quantum field theories in AdS$_2$. The known derivation of locality sum rules in AdS$_{d+1}$ does not apply for $d=1$ due to the different singularity structure of the conformal blocks and the inequivalence of operator orderings on the boundary. Assuming unitarity and a mild growth condition, we establish power-law bounds for correlators, derive dispersion relations and an expansion in terms of ``even'' and ``odd'' local blocks that converges in the entire AdS$_2$. These yield two novel families of symmetric and antisymmetric locality sum rules. We test these sum rules explicitly in the free scalar field theory.

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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 $\lbrace \Delta_i,C_{ijk},b^{\hat{\mathcal{O}}}_j\rbrace$. These are the scaling dimensions of boundary operators $\Delta_i$, 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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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

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

RG flows in de Sitter: c-functions and sum rules

We study the renormalization group flow of unitary Quantum Field Theories on two-dimensional de Sitter (dS) spacetime. We prove the existence of two functions of the radius of dS that interpolate between the central charges of the UV and IR fixed points of the flow when tuning the radius $R$ while keeping the mass scales fixed. The first is constructed from certain components of the two-point function of the stress tensor evaluated at antipodal separation. The second is the spectral weight of the stress tensor in the $\Delta=2$ discrete series. This last fact implies that the stress tensor of any unitary QFT in dS$_2$ must interpolate between the vacuum and states in the $\Delta=2$ discrete series irrep. We verify that the c-functions are monotonic for intermediate radii in the free massive boson and free massive fermion theories, but we lack a general proof of said monotonicity. We derive a variety of sum rules that relate the central charges and the c-functions to integrals of the two-point function of the trace of the stress tensor and to integrals of its spectral densities. The positivity of these formulas implies $c^{\text{UV}}\geq c^{\text{IR}}$. In the infinite radius limit the sum rules reduce to the well known formulas in flat space. Throughout the paper, we prove some general properties of the spectral decomposition of the stress tensor in dS$_{d+1}$.

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arXiv2023

A radial variable for de Sitter two-point functions

We introduce a "radial" two-point invariant for quantum field theory in de Sitter (dS) analogous to the radial coordinate used in conformal field theory. We show that the two-point function of a free massive scalar in the Bunch-Davies vacuum has an exponentially convergent series expansion in this variable with positive coefficients only. Assuming a convergent Källén-Lehmann decomposition, this result is then generalized to the two-point function of any scalar operator non-perturbatively. A corollary of this result is that, starting from two-point functions on the sphere, an analytic continuation to an extended complex domain is admissible. dS two-point configurations live inside or on the boundary of this domain, and all the paths traced by Wick rotations between dS and the sphere or between dS and Euclidean Anti-de Sitter are also contained within this domain.

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