arXiv subjects

Agnese Bissi

Publications and source records attributed to Agnese Bissi.

At least 19 recordsLinked to original sources

arXiv2025

Bubbles in AdS

We investigate loop corrections to the four-point function of identical scalar operators in a four-dimensional large $N$ conformal field theory, holographically dual to AdS with a quartic interaction. We focus on the universal part of the correlator that, at any order in $1/N$, is completely determined by tree-level data. We show how this contribution controls the part of the anomalous dimensions of double-trace operators, that exhibits a characteristic $\log \ell$ dependence at large spin $\ell$. We resum these effects to all orders in $1/N$ and show that they admit a natural effective description in AdS. Finally, by reformulating the problem in Mellin space, we demonstrate that the same contribution corresponds to consecutive unitarity cuts of bubble diagrams in the flat space limit.

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arXiv2024

Composite operators in $\mathcal{N}=4$ Super Yang-Mills

We consider four-point functions of protected, double- and single-trace operators in the large central charge limit. We use superconformal symmetry to disentangle the contribution of protected operators in the partial wave decomposition. With this information, we fix the non protected part of such correlators up to subleading order in the large central charge expansion. We particularly focus on the triple-trace sector of the correlator and comment on the connection to the holographic description of these correlators.

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arXiv2024

On the $1/c$ expansion in $2d$ CFTs with degenerate operators

We analytically determine the large central charge asymptotic expansion of the Virasoro conformal blocks entering in four-point functions with external degenerate operators on a sphere in $2d$ CFTs, and study its resurgence properties as a function of the conformal cross-ratio $z$. We focus on the cases of four heavy $(2,1)$ degenerate operators, and two $(2,1)$ heavy degenerate ones plus two arbitrary light operators. The $1/c$ asymptotic series is Borel summable for generic values of $z$, but it jumps when a Stokes line is crossed. Starting from the $1/c$ series of the identity block, we show how a resurgent analysis allows us to completely determine the other Virasoro block and in fact to reconstruct the full correlator. We also show that forbidden singularities, known to exist in correlators with two heavy and two light operators, appear with four heavy operators as well. In both cases, they are turning points emanating Stokes lines, artefacts of the asymptotic expansion, and we show how they are non perturbatively resolved. More general correlators and implications for gravitational theories in $\text{AdS}_{3}$ are briefly discussed. Our results are based on new asymptotic expansions for large parameters $(a,b,c)$ of certain hypergeometric functions $\,_2 F_1(a,b,c;z)$ which can be useful in general.

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arXiv2024

Logarithmic doublets in CCFT

We investigate the presence of logarithmic CFT doublets in the soft sector of celestial CFT related with supertranslations. We show that the quantum operator associated with a $\log u$ late-time behavior for the asymptotic gravitational shear forms a logarithmic CFT pair of conformal dimension $\Delta=1$ with an IR-regulated supertranslation Goldstone current. We discuss this result in connection with previous encounters of log CFT structures in the IR-finite part of celestial OPEs.

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arXiv2023

A constructive solution to the cosmological bootstrap

In this paper we revisit a generalised crossing equation that follows from harmonic analysis on the conformal group, and is of particular interest for the cosmological bootstrap programme. We present an exact solution to this equation, for dimensions two or higher, in terms of 6j symbols of the Euclidean conformal group, and discuss its relevance. In the process we provide a detailed derivation of the analogue of the Biedenharn-Elliot identity for said 6j symbols.

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arXiv2023

Spinning correlators in $\mathcal{N} = 2$ SCFTs: Superspace and AdS amplitudes

We study four-point functions of spinning operators in the flavor current multiplet in four dimensional $\mathcal{N}=2$ SCFTs, using superspace techniques. In particular we explicitly construct the differential operators relating the different components of the super-correlator. As a byproduct of our analysis, we report the computation of the four-point amplitudes of gluons in bosonic Yang-Mills theories on $\mathrm{AdS}_5$ and we give evidence of an AdS double copy relation between the gluon amplitude and its gravitational counterpart.

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arXiv2022

Positivity, low twist dominance and CSDR for CFTs

We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correlation with identical scalar operators, which is manifestly symmetric under the cross-ratios $u,v$ interchange. This representation has several features in common with the CSDR for quantum field theories. It enables a study of the expansion of the correlation function around $u=v=1/4$, which is used in the numerical conformal bootstrap program. We elucidate several remarkable features of the dispersive representation using the four point correlation function of $Φ_{1,2}$ operators in 2d minimal models as a test-bed. When the dimension of the external scalar operator ($Δ_σ$) is less than $\frac{1}{2}$, the CSDR gets contribution from only a single tower of global primary operators with the second tower being projected out. We find that there is a notion of low twist dominance (LTD) which, as a function of $Δ_σ$, is maximized near the 2d Ising model as well as the non-unitary Yang-Lee model. The CSDR and LTD further explain positivity of the Taylor expansion coefficients of the correlation function around the crossing symmetric point and lead to universal predictions for specific ratios of these coefficients. These results carry over to the epsilon expansion in $4-ε$ dimensions. We also conduct a preliminary investigation of geometric function theory ideas, namely the Bieberbach-Rogosinski bounds.

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arXiv2022

Selected Topics in Analytic Conformal Bootstrap: A Guided Journey

This review aims to offer a pedagogical introduction to the analytic conformal bootstrap program via a journey through selected topics. We review analytic methods which include the large spin perturbation theory, Mellin space methods and the Lorentzian inversion formula. These techniques are applied to a variety of topics ranging from large-N theories, to the epsilon expansion and holographic superconformal correlators, and are demonstrated in a large number of explicit examples.

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arXiv2022

OPE coefficients in Argyres-Douglas theories

The calculation of physical quantities in certain quantum field theories such as those of the Argyres-Douglas type is notoriously hard, due to the lack of a Lagrangian description. Here we tackle this problem following two alternative approaches. On the one hand, we use localization on the four-sphere to compute two-correlators and OPE coefficients in Argyres-Douglas superconformal theories. On the other hand, we use the conformal bootstrap machinery to put stringent bounds on such coefficients, only relying on the knowledge of central charge and conformal dimension of the operators. We compare the results obtained with these two methods and find good agreement for all rank-one cases and for the rank-two Argyres-Douglas theories (A_1,A_4) and (A_1,A_5), in the moduli space of pure SU(5) and SU(6) super Yang-Mills. We also apply our results from localization to obtain bounds on the dimensions of the lightest neutral unprotected operators of the CFTs.

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arXiv2022

Interacting conformal scalar in a wedge

We study a class of two-point functions in a conformal field theory near a wedge. This is a set-up with two boundaries intersecting at an angle $\theta$. We compute it as a solution to the Dyson-Schwinger equation of motion for a quartic interaction in the $d=4-\epsilon$ bulk and in the $d=3-\epsilon$ boundary, up to order $\mathcal{O}(\epsilon)$. We have extracted the anomalous dimensions from such correlators and we have complemented them with Feynman diagrams computations.

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arXiv2022

Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills

We start a systematic study of quarter-BPS operators in four-dimensional $\mathcal{N}=4$ Super Yang-Mills with gauge group $\mathrm{SU}(N)$ making use of recently developed tools in conformal field theory. We adapt the technology of embedding space tensor structures in four dimensions to the problem of computing R-symmetry tensor structures and we use the underlying chiral algebra to obtain the superconformal Ward identities. This allows us to fix the protected part of the four-point correlators, up to few ambiguities. As applications, we use the Lorentzian inversion formula to study the leading order OPE data in the large~$N$ supergravity limit and we make contact with the OPE limit of the five-point function of half-BPS operators.

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arXiv2021

One-loop Gluon Amplitudes in AdS

We initiate the study of one-loop gluon amplitudes in AdS space. These amplitudes were recently computed at tree level for a variety of backgrounds of the form $AdS_{d+1} \times S^3$. For concreteness, we compute the one-loop correction to the massless gluon amplitude on $AdS_5\times S^3$, which corresponds to the four-point correlator of the flavor current multiplet in the dual 4d $\mathcal{N}=2$ SCFT. This requires solving a mixing problem that involves tree-level amplitudes of arbitrarily massive Kaluza-Klein modes. The final answer has the same color structure as in flat space but the dependence on Mandelstam variables is more complicated, with logarithms replaced by polygamma functions.

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arXiv2021

Two applications of the analytic conformal bootstrap: A quick tour guide

We review the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are based solely on symmetries, in particular in the analytic structure and in the associativity of the operator product expansion. We focus on two applications of the analytic conformal bootstrap: the study of the $ε$ expansion of the Wilson Fisher model via the introduction of a dispersion relation and the large $N$ expansion of maximally supersymmetric Super Yang Mills theory in four dimensions.

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arXiv2021

All loop structures in Supergravity Amplitudes on $AdS_5 \times S^5$ from CFT

We computed a set of structures which appear in the four-point function of protected operators of dimension two in $\mathcal{N}=4$ Super Yang Mills with $SU(N)$ gauge group, at any order in a large $N$ expansion. They are determined only by leading order CFT data. By focusing on a specific limit, we made connection with the dual supergravity amplitude in flat space, where such structures correspond to iterated $s$-cuts. We made several checks and we conjecture that the same interpretation holds for supergravity amplitudes on $AdS_5 \times S^5$.

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arXiv2020

Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills

We perform a numerical bootstrap study of the mixed correlator system containing the half-BPS operators of dimension two and three in $\mathcal N = 4$ Super Yang-Mills. This setup improves on previous works in the literature that only considered single correlators of one or the other operator. We obtain upper bounds on the leading twist in a given representation of the R-symmetry by imposing gaps on the twist of all operators rather than the dimension of a single one. As a result we find a tension between the large $N$ supergravity predictions and the numerical finite $N$ results already at $N\sim 100$. A few possible solutions are discussed: the extremal spectrum suggests that at large but finite $N$, in addition to the double trace operators, there exists a second tower of states with smaller dimension. We also obtain new bounds on the dimension of operators which were not accessible with a single correlator setup. Finally we consider bounds on the OPE coefficients of various operators. The results obtained for the OPE coefficient of the lightest scalar singlet show evidences of a two dimensional conformal manifold.

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arXiv2019

Loops in AdS from Conformal Field Theory

We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual $1/N$ expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in $1/N^2$, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of $ϕ^4$ theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving part of the four-point function in $ϕ^3+ϕ^4$ theory in AdS which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an infinite series of poles, and discuss applications to more complicated cases such as the ${\cal N}=4$ super-Yang-Mills theory.

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arXiv2019

Analytic Bootstrap for Boundary CFT

We propose a method to analytically solve the bootstrap equation for two point functions in boundary CFT. We consider the analytic structure of the correlator in Lorentzian signature and in particular the discontinuity of bulk and boundary conformal blocks to extract CFT data. As an application, the correlator $\langle ϕϕ\rangle$ in $ϕ^4$ theory at the Wilson-Fisher fixed point is computed to order $ε^2$ in the $ε$ expansion.

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arXiv2019

Dispersion Relation for CFT Four-Point Functions

We present a dispersion relation in conformal field theory which expresses the four point function as an integral over its single discontinuity. Exploiting the analytic properties of the OPE and crossing symmetry of the correlator, we show that in perturbative settings the correlator depends only on the spectrum of the theory, as well as the OPE coefficients of certain low twist operators, and can be reconstructed unambiguously. In contrast to the Lorentzian inversion formula, the validity of the dispersion relation does not assume Regge behavior and is not restricted to the exchange of spinning operators. As an application, the correlator $\langle ϕϕϕϕ\rangle$ in $ϕ^4$ theory at the Wilson-Fisher fixed point is computed in closed form to order $ε^2$ in the $ε$ expansion.

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