arXiv subjects

Madalena Lemos

Publications and source records attributed to Madalena Lemos.

18 recordsLinked to original sources

arXiv2026

Graded Unitarity in the SCFT/VOA Correspondence

Vertex algebras that arise from four-dimensional, $\mathcal{N}=2$ superconformal field theories inherit a collection of novel structural properties from their four-dimensional ancestors. Crucially, when the parent SCFT is unitary, the corresponding vertex algebra is not unitary in the conventional sense. In this paper, we motivate and define a generalized notion of unitarity for vertex algebras that we call \emph{graded unitarity}, and which captures the consequences of four-dimensional unitarity under this correspondence. We also take the first steps towards a classification program for graded-unitary vertex algebras whose underlying vertex algebras are Virasoro or affine Kac--Moody vertex algebras. Remarkably, under certain natural assumptions about the $\mathfrak{R}$-filtration for these vertex algebras, we show that only the $(2,p)$ central charges for Virasoro VOAs and boundary admissible levels for $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$ Kac--Moody vertex algebras can possibly be compatible with graded unitarity. These are precisely the cases of these vertex algebras that are known to arise from four dimensions.

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arXiv2022

Superconformal surfaces in four dimensions

We study the constraints of superconformal symmetry on codimension two defects in four-dimensional superconformal field theories. We show that the one-point function of the stress tensor and the two-point function of the displacement operator are related, and we discuss the consequences of this relation for the Weyl anomaly coefficients as well as in a few examples, including the supersymmetric Rényi entropy. Imposing consistency with existing results, we propose a general relation that could hold for sufficiently supersymmetric defects of arbitrary dimension and codimension. Turning to $\mathcal{N}=(2,2)$ surface defects in $\mathcal{N} \geqslant 2$ superconformal field theories, we study the associated chiral algebra. We work out various properties of the modules introduced by the defect in the original chiral algebra. In particular, we find that the one-point function of the stress tensor controls the dimension of the defect identity in chiral algebra, providing a novel way to compute it, once the defect identity is identified. Studying a few examples, we show explicitly how these properties are realized.

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arXiv2021

Regge trajectories for the (2,0) theories

We investigate the structure of conformal Regge trajectories for the maximally supersymmetric (2,0) theories in six dimensions. The different conformal multiplets in a single superconformal multiplet must all have similarly-shaped Regge trajectories. We show that these super-descendant trajectories interact in interesting ways, leading to new constraints on their shape. For the four-point function of the stress tensor multiplet supersymmetry also softens the Regge behavior in some channels, and consequently we observe that 'analyticity in spin' holds for all spins greater than -3. All the physical operators in this correlator therefore lie on Regge trajectories and we describe an iterative scheme where the Lorentzian inversion formula can be used to bootstrap the four-point function. Some numerical experiments yield promising results, with OPE data approaching the numerical bootstrap results for all theories with rank greater than one.

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arXiv2020

Lectures on chiral algebras of $\mathcal{N} \geqslant 2$ superconformal field theories

Any four-dimensional $\mathcal{N} \geqslant 2$ superconformal field theory possess a protected subsector isomorphic to a two-dimensional chiral algebra \cite{Beem:2013sza}. The goal of these lectures is to provide an introduction to the subject, covering the construction of the chiral algebras, the consequences for four-dimensional physics, as well as a brief summary of recent progress. This is the writeup of the lectures given at the Winter School "YRISW 2020" to appear in a special issue of JPhysA.

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arXiv2018

Universality at large transverse spin in defect CFT

We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large $s$, $s$ being the charge of the operators under rotations in the space transverse to the defect. Our tools include a formula that inverts the bulk to defect OPE, analogous to the Caron-Huot formula for the four-point function. Analyticity of the formula in $s$ implies that the scaling dimensions of the defect operators are aligned in Regge trajectories $\widehatΔ(s)$. These results require the correlator of two local operators and the defect to be bounded in a certain region, a condition that we do not prove in general. We check our conclusions against examples in perturbation theory and holography, and we make specific predictions concerning the spectrum of defect operators on Wilson lines. We also give an interpretation of the large $s$ spectrum in the spirit of the work of Alday and Maldacena.

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arXiv2018

Long Multiplet Bootstrap

Applications of the bootstrap program to superconformal field theories promise unique new insights into their landscape and could even lead to the discovery of new models. Most existing results of the superconformal bootstrap were obtained form correlation functions of very special fields in short (BPS) representations of the superconformal algebra. Our main goal is to initiate a superconformal bootstrap for long multiplets, one that exploits all constraints from superprimaries and their descendants. To this end, we work out the Casimir equations for four-point correlators of long multiplets of the two-dimensional global $\mathcal{N}=2$ superconformal algebra. After constructing the full set of conformal blocks we discuss two different applications. The first one concerns two-dimensional (2,0) theories. The numerical bootstrap analysis we perform serves a twofold purpose, as a feasibility study of our long multiplet bootstrap and also as an exploration of (2,0) theories. A second line of applications is directed towards four-dimensional $\mathcal{N}=3$ SCFTs. In this context, our results imply a new bound $c \geqslant \tfrac{13}{24}$ for the central charge of such models, which we argue cannot be saturated by an interacting SCFT.

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arXiv2018

Line defects and radiation in $\mathcal{N}=2$ theories

We study the conformal data of a generic superconformal half-BPS line defect in a four-dimensional $\mathcal{N} = 2$ theory. We prove a theory independent relation between the one-point function of the stress tensor in the presence of the line defect and the two-point function of the displacement operator. When the defect is interpreted as a heavy charged particle in a gauge theory, the result relates the energy emitted through Bremsstrahlung with the coupling of the stress tensor to the particle at rest.

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arXiv2018

Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory

We apply bootstrap techniques in order to constrain the CFT data of the $(A_1,A_2)$ Argyres-Douglas theory, which is arguably the simplest of the Argyres-Douglas models. We study the four-point function of its single Coulomb branch chiral ring generator and put numerical bounds on the low-lying spectrum of the theory. Of particular interest is an infinite family of semi-short multiplets labeled by the spin $\ell$. Although the conformal dimensions of these multiplets are protected, their three-point functions are not. Using the numerical bootstrap we impose rigorous upper and lower bounds on their values for spins up to $\ell=20$. Through a recently obtained inversion formula, we also estimate them for sufficiently large $\ell$, and the comparison of both approaches shows consistent results. We also give a rigorous numerical range for the OPE coefficient of the next operator in the chiral ring, and estimates for the dimension of the first R-symmetry neutral non-protected multiplet for small spin.

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arXiv2017

Bootstrapping $\mathcal{N}=3$ superconformal theories

We initiate the bootstrap program for $\mathcal{N}=3$ superconformal field theories (SCFTs) in four dimensions. The problem is considered from two fronts: the protected subsector described by a $2d$ chiral algebra, and crossing symmetry for half-BPS operators whose superconformal primaries parametrize the Coulomb branch of $\mathcal{N}=3$ theories. With the goal of describing a protected subsector of a family of $\mathcal{N}=3$ SCFTs, we propose a new $2d$ chiral algebra with super Virasoro symmetry that depends on an arbitrary parameter, identified with the central charge of the theory. Turning to the crossing equations, we work out the superconformal block expansion and apply standard numerical bootstrap techniques in order to constrain the CFT data. We obtain bounds valid for any theory but also, thanks to input from the chiral algebra results, we are able to exclude solutions with $\mathcal{N}=4$ supersymmetry, allowing us to zoom in on a specific $\mathcal{N}=3$ SCFT.

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arXiv2015

Bootstrapping ${\mathcal N}=2$ chiral correlators

We apply the numerical bootstrap program to chiral operators in four-dimensional ${\mathcal N}=2$ SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special emphasis to bootstrapping a specific theory: the simplest Argyres-Douglas fixed point with no flavor symmetry. In the second part we generalize our setup and consider correlators of fields with unequal dimension. This is an example of a mixed correlator and allows us to probe new regions in the parameter space of ${\mathcal N}=2$ SCFTs. In particular, our results put constraints on relations in the Coulomb branch chiral ring and on the curvature of the Zamolodchikov metric.

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arXiv2015

The ${\mathcal N}=2$ superconformal bootstrap

In this work we initiate the conformal bootstrap program for ${\mathcal N}=2$ superconformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and non-Lagrangian theories, and formulate various conjectures concerning the landscape of theories. We analyze in detail the four-point functions of flavor symmetry current multiplets and of ${\mathcal N}=2$ chiral operators. For both correlation functions we review the solution of the superconformal Ward identities and describe their superconformal block decompositions. This provides the foundation for an extensive numerical analysis discussed in the second half of the paper. We find a large number of constraints for operator dimensions, OPE coefficients, and central charges that must hold for any ${\mathcal N}=2$ superconformal field theory.

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arXiv2015

$\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras

We study protected correlation functions in $\mathcal{N} = 2$ SCFT whose description is captured by a two-dimensional chiral algebra. Our analysis implies a new analytic bound for the $c$-anomaly as a function of the flavor central charge $k$, valid for any theory with a flavor symmetry $G$. Combining our result with older bounds in the literature puts strong constraints on the parameter space of $\mathcal{N}=2$ theories. In particular, it singles out a special set of models whose value of $c$ is uniquely fixed once $k$ is given. This set includes the canonical rank one $\mathcal{N}=2$ SCFTs given by Kodaira's classification.

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arXiv2015

Infinite Chiral Symmetry in Four Dimensions

We describe a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras. The meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four-dimensional theory. Infinite chiral symmetry has far-reaching consequences for the spectral data, correlation functions, and central charges of any four-dimensional theory with ${\mathcal N}=2$ superconformal symmetry.

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arXiv2015

The $(2,0)$ superconformal bootstrap

We develop the conformal bootstrap program for six-dimensional conformal field theories with $(2,0)$ supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on OPE coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the lightcone expansion of the crossing equation. Our principal result is strong evidence that the $A_1$ theory realizes the minimal allowed central charge $(c=25)$ for any interacting $(2,0)$ theory. This implies that the full stress tensor four-point function of the $A_1$ theory is the unique unitary solution to the crossing symmetry equation at $c=25$. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting $(2,0)$ theory of central charge $c$. For large $c$, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.

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arXiv2015

Chiral Algebras for Trinion Theories

It was recently understood that one can identify a chiral algebra in any four-dimensional N=2 superconformal theory. In this note, we conjecture the full set of generators of the chiral algebras associated with the T_n theories. The conjecture is motivated by making manifest the critical affine module structure in the graded partition function of the chiral algebras, which is computed by the Schur limit of the superconformal index for T_n theories. We also explicitly construct the chiral algebra arising from the T_4 theory. Its null relations give rise to new T_4 Higgs branch chiral ring relations.

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arXiv2014

The Superconformal Index of Class S Theories of Type D

We consider the superconformal index of class S theories of type D, which arise by compactification of the (2,0) D_n theories on a punctured Riemann surface C. We also allow for the presence of twist lines on C associated to the Z_2 outer automorphism of D_n. For a two-parameter slice (p=0, q, t) in the space of superconformal fugacities, we determine the 2d TQFT that computes the index.

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arXiv2010

Semianalytical estimates of scattering thresholds and gravitational radiation in ultrarelativistic black hole encounters

Ultrarelativistic collisions of black holes are ideal gedanken experiments to study the nonlinearities of general relativity. In this paper we use semianalytical tools to better understand the nature of these collisions and the emitted gravitational radiation. We explain many features of the energy spectra extracted from numerical relativity simulations using two complementary semianalytical calculations. In the first calculation we estimate the radiation by a "zero-frequency limit" analysis of the collision of two point particles with finite impact parameter. In the second calculation we replace one of the black holes by a point particle plunging with arbitrary energy and impact parameter into a Schwarzschild black hole, and we explore the multipolar structure of the radiation paying particular attention to the near-critical regime. We also use a geodesic analogy to provide qualitative estimates of the dependence of the scattering threshold on the black hole spin and on the dimensionality of the spacetime.

gr-qc↗

arXiv2009

On the instability of Reissner-Nordstrom black holes in de Sitter backgrounds

Recent numerical investigations have uncovered a surprising result: Reissner-Nordstrom-de Sitter black holes are unstable for spacetime dimensions larger than 6. Here we prove the existence of such instability analytically, and we compute the timescale in the near-extremal limit. We find very good agreement with the previous numerical results. Our results may me helpful in shedding some light on the nature of the instability.

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