arXiv subjects

Julien Barrat

Publications and source records attributed to Julien Barrat.

14 recordsLinked to original sources

arXiv2026

Analytic thermal bootstrap in momentum space: From thermal OPE to QNMs

We initiate a bootstrap program that relates ultraviolet data, encoded in the thermal OPE, to infrared observables, namely, the low-frequency behavior and quasinormal modes. Starting from KMS-symmetric completions of individual thermal OPE blocks, which play the role of thermal Polyakov blocks, we construct their Fourier transform, yielding an asymptotic expansion of retarded thermal correlators valid at any spatial momentum. We use these results to derive inversion formulae and connect thermal OPE data to the analytic structure of retarded correlators in the complex frequency plane. Under the assumption of meromorphicity, the inversion formulae express OPE coefficients in terms of the quasinormal-mode frequencies, leading to nontrivial sum rules, constraints on the quasinormal spectrum, and its asymptotics at large spatial momentum. We illustrate these results in free theories, two-dimensional CFTs, the large-$N$ limit and $\varepsilon$-expansion of the $\mathrm{O}(N)$ model, and the $R$-current correlator of strongly coupled $\mathcal N = 4$ SYM at zero spatial momentum. As a byproduct, we derive universal asymptotic formulae for thermal OPE coefficients of heavy operators, resolving their dependence on spin and extending previous results at zero spatial separation. We test these formulae in the three-dimensional Ising CFT, finding good agreement between the resulting truncated correlators and Monte Carlo data.

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arXiv2025

Analytic thermal bootstrap meets holography

We compute thermal holographic correlators by combining their analytic structure with the Kubo-Martin-Schwinger (KMS) condition and multi-stress tensor OPE coefficients determined from the dual AdS description. We focus on two-point functions of identical scalar operators with integer conformal dimensions at zero spatial separation. In the black brane background, we show explicitly that holographic two-point functions split into three contributions: a principal one, computed exactly, plus regularized and arcs contributions, both approximated through the use of OPE coefficients asymptotics. For $\Delta_\phi=3$, we show that the principal contribution agree with good approximation with the numerical solution of the bulk wave equation. Moreover, we demonstrate that the expansion in generalized free field correlators proposed in [Barrat,6/2025] admits a natural interpretation in terms of Witten diagrams. Finally, we initiate the study of thermal correlators in the spherically symmetric black hole background, computing their principal contributions.

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arXiv2025

The analytic bootstrap at finite temperature

We propose new universal formulae for thermal two-point functions of scalar operators based on their analytic structure, constructed to manifestly satisfy all the bootstrap conditions. We derive a dispersion relation in the complexified time plane, which fixes the correlator up to an additive constant and theory-dependent dynamical information. At non-zero spatial separation we introduce a formula for the thermal two-point function obtained by summing over images of the dispersion relation result obtained in the OPE regime. This construction satisfies all thermal bootstrap conditions, with the exception of clustering at infinite distance, which must be verified on a case-by-case basis. We test our results both in weakly and strongly-coupled theories. In particular, we show that the asymptotic behavior for the heavy sector proposed in~\cite{Marchetto:2023xap} and its correction can be explicitly derived from the dispersion relation. We combine analytical and numerical results to compute the thermal two-point function of the energy operator in the $3d$ Ising model and find agreement with Monte Carlo simulations.

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arXiv2024

The thermal bootstrap for the critical O(N) model

We propose a numerical method to estimate one-point functions and the free-energy density of conformal field theories at finite temperature by solving the Kubo-Martin-Schwinger condition for the two-point functions of identical scalars. We apply the method for the critical O(N) model for N = 1,2,3 in 3 $\leq$ d $\leq$ 4. We find agreement with known results from Monte Carlo simulations and previous results for the 3d Ising model, and we provide new predictions for N = 2,3.

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arXiv2024

Perturbative bootstrap of the Wilson-line defect CFT: Multipoint correlators

We study the defect CFT associated with the half-BPS Wilson line in $\mathcal{N}=4$ Super Yang-Mills theory in four dimensions. Using a perturbative bootstrap approach, we derive new analytical results for multipoint correlators of protected defect operators at large $N$ and weak coupling. At next-to-next-to-leading order, we demonstrate that the simplest five- and six-point functions are fully determined by non-perturbative constraints -- which include superconformal symmetry, crossing symmetry, and the pinching of operators to lower-point functions -- as well as by a single integral, known as the train track integral. Additionally, we present new analytical results for the four-point functions $\langle 1122 \rangle$ and $\langle 1212 \rangle$.

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arXiv2024

Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators

We study the correlators of bulk and defect half-BPS operators in $\mathcal{N}=4$ Super Yang-Mills theory with a Maldacena-Wilson line defect, focusing on the case involving one bulk and two defect local operators. We analyze the non-perturbative constraints on these correlators, which include a topological sector, pinching and splitting limits, and we compute a variety of bulk-defect-defect correlators up to next-to-leading order at weak coupling, surprisingly observing that transcendental terms cancel. Additionally, we provide results in the strong-coupling regime for the first two leading orders using a mixture of Witten diagrams and non-perturbative constraints.

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arXiv2024

Conformal line defects at finite temperature

We study conformal field theories at finite temperature in the presence of a temporal conformal line defect, wrapping the thermal circle, akin to a Polyakov loop in gauge theories. Although several symmetries of the conformal group are broken, the model can still be highly constrained from its features at zero-temperature. In this work we show that the defect and bulk one and two-point correlators can be written as functions of zero-temperature data and thermal one-point functions (defect and bulk). The defect one-point functions are new data and they are induced by thermal effects of the bulk. For this new set of data we derive novel sum rules and establish a bootstrap problem for the thermal defect one-point functions from the KMS condition. We also comment on the behaviour of operators with large scaling dimensions. Additionally, we relate the free energy and entropy density to the OPE data through the one-point function of the stress-energy tensor. Our formalism is validated through analytical computations in generalized free scalar field theory, and we present new predictions for the O(N) model with a magnetic impurity in the $\varepsilon$-expansion and the large N limit.

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arXiv2024

Line defects in conformal field theory: from weak to strong coupling

Conformal field theory finds applications across diverse fields, from statistical systems at criticality to quantum gravity through the AdS/CFT correspondence. These theories are subject to strong constraints, enabling a systematic non-perturbative analysis. Conformal defects provide a controlled means of breaking the symmetry, introducing new physical phenomena while preserving crucial benefits of the underlying conformal symmetry. This thesis investigates conformal line defects in both the weak- and strong-coupling regimes. Two distinct classes of models are studied. First, we focus on the supersymmetric Wilson line in $\mathcal{N}=4$ Super Yang--Mills, which serves as an ideal testing ground for the development of innovative techniques such as the analytic conformal bootstrap. The second class consists of magnetic lines in Yukawa models, which have fascinating applications in $3d$ condensed-matter systems. These systems have the potential to emulate phenomena observed in the Standard Model in a low-energy setting.

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arXiv2023

Multipoint correlators on the supersymmetric Wilson line defect CFT II: Unprotected operators

We continue our study of multipoint correlators of scalar fields on the $1d$ defect CFT generated by inserting operators along the Maldacena-Wilson line in $\mathcal{N} = 4$ SYM. We present a weak-coupling recursion relation that captures correlators at next-to-leading order involving an arbitrary number of the elementary scalar fields $ϕ^i$ and $ϕ^6$, the latter being unprotected. We can then build correlators of composite operators by pinching the scalar fields together. As a demonstration of our method, we give explicit results for correlators containing up to six points. We also expand some selected correlators using recently obtained conformal blocks in the comb and snowflake channel, and check that the extracted low-lying CFT data is consistent with explicit computations.

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arXiv2023

Line defect correlators in fermionic CFTs

Scalar-fermion models, such as the Gross-Neveu-Yukawa model, admit natural $1d$ defects given by the exponential of a scalar field integrated along a straight line. In $4-\varepsilon$ dimensions the defect coupling is weakly relevant and the setup defines a non-trivial interacting defect CFT. In this work we study correlation functions on these defect CFTs to order $\varepsilon$. We focus on $1d$ correlators constrained to the line, which include canonical operators like the displacement and the one-dimensional analog of the spin field. These results give access to perturbative CFT data that can be used as input in the numerical bootstrap. We also consider local operators outside the line, in particular two-point functions of scalars whose dynamics are non-trivial due to the presence of the defect.

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arXiv2023

Multipoint correlators on the supersymmetric Wilson line defect CFT

We study multipoint correlators of protected scalars on the Maldacena-Wilson line in $\mathcal{N}=4$ SYM. Working at weak coupling in the planar limit, we derive an explicit recursion relation that captures next-to-leading order correlators with an arbitrary number of insertions of the fundamental scalar field. By pinching fundamental scalars together, we can build composite protected operators with higher values of the R-charge. Our result then encompasses arbitrary $n$-point correlators of protected operators with arbitrary weight. As a demonstration of our method, we give explicit formulae for correlators with up to six points. Using these results we observe that all our correlators are annihilated by a special class of differential operators. We conjecture that these differential operators are non-perturbative constraints and can be considered a multipoint extension of the superconformal Ward identities satisfied by four-point functions.

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arXiv2022

Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills

We study two-point functions of single-trace half-BPS operators in the presence of a supersymmetric Wilson line in $\mathcal{N}=4$ SYM. We use inversion formula technology in order to reconstruct the CFT data starting from a single discontinuity of the correlator. In the planar strong coupling limit only a finite number of conformal blocks contributes to the discontinuity, which allows us to obtain elegant closed-form expressions for two-point functions of single-trace operators $\mathcal{O}_J$ of weight $J=2,3,4$. Our final result passes a number of non-trivial consistency checks: it has the correct discontinuity, it satisfies the superconformal Ward identities, it has a sensible expansion in both defect and bulk OPEs, and is consistent with available results coming from localization. The method is completely algorithmic and can be implemented to calculate correlators of arbitrary weight.

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arXiv2022

A dispersion relation for defect CFT

We present a dispersion relation for defect CFT that reconstructs two-point functions in the presence of a defect as an integral of a single discontinuity. The main virtue of this formula is that it streamlines explicit bootstrap calculations, bypassing the resummation of conformal blocks. As applications we reproduce known results for monodromy defects in the epsilon-expansion, and present new results for the supersymmetric Wilson line at strong coupling in $\mathcal{N}=4$ SYM. In particular, we derive a new analytic formula for the highest $R$-symmetry channel of single-trace operators of arbitrary length.

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arXiv2021

Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM

We study the two-point function of the stress-tensor multiplet of $\mathcal{N}=4$ SYM in the presence of a line defect. To be more precise, we focus on the single-trace operator of conformal dimension two that sits in the $20'$ irrep of the $\mathfrak{so}(6)_\text{R}$ R-symmetry, and add a Maldacena-Wilson line to the configuration which makes the two-point function non-trivial. We use a combination of perturbation theory and defect CFT techniques to obtain results up to next-to-leading order in the coupling constant. Being a defect CFT correlator, there exist two (super)conformal block expansions which capture defect and bulk data respectively. We present a closed-form formula for the defect CFT data, which allows to write an efficient Taylor series for the correlator in the limit when one of the operators is close to the line. The bulk channel is technically harder and closed-form formulae are particularly challenging to obtain, nevertheless we use our analysis to check against well-known data of $\mathcal{N}=4$ SYM. In particular, we recover the correct anomalous dimensions of a famous tower of twist-two operators (which includes the Konishi multiplet), and successfully compare the one-point function of the stress-tensor multiplet with results obtained using matrix-model techniques.

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