arXiv subjects

Pedro Liendo

Publications and source records attributed to Pedro Liendo.

At least 19 recordsLinked to original sources

arXiv2025

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 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

Spontaneous breaking of finite group symmetries at all temperatures

We study conformal field theories with finite group symmetries with spontaneous symmetry breaking (SSB) phases that persist at all temperatures. We work with two $λϕ^4$ theories coupled through their mass terms. The two $λϕ^4$ theories are chosen to preserve either the cubic symmetry group or the tetrahedral symmetry group. A one-loop calculation in the $4-ε$ expansion shows that there exist infinitely many fixed points that can host an all temperature SSB phase. An analysis of the renormalization group (RG) stability matrix of these fixed points, reveals that their spectrum contains at least three relevant operators. In other words, these fixed points are tetracritical points.

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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

Bootstrapping line defects with $O(2)$ global symmetry

We use the numerical bootstrap to study conformal line defects with $O(2)$ global symmetry. Our results are very general and capture in particular conformal line defects originating from bulk CFTs with a continuous global symmetry, which can either be preserved or partially broken by the presence of the defect. We begin with an agnostic approach and perform a systematic bootstrap study of correlation functions between two canonical operators on the defect: the displacement and the tilt. We then focus on two interesting theories: a monodromy line defect and a localized magnetic field line defect. To this end, we combine the numerical bootstrap with the $\varepsilon$-expansion, where we complement existing results in the literature with additional calculations. For the monodromy defect our numerical results are consistent with expectations, with known analytic solutions sitting inside our numerical bounds. For the localized magnetic field line defect our plots show a series of intriguing cusps which we explore.

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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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arXiv2022

Bootstrapping Monodromy Defects in the Wess-Zumino Model

We use analytical bootstrap techniques to study supersymmetric monodromy defects in the critical Wess-Zumino model. In preparation for this result we first study two related systems which are interesting on their own: general monodromy defects (no susy), and the $\varepsilon$--expansion bootstrap for the Wess-Zumino model (no defects). For general monodromy defects, we extend previous work on codimension-two conformal blocks and the Lorentzian inversion formula in order to accommodate parity-odd structures. In the Wess-Zumino model, we bootstrap four-point functions of chiral operators in the $\varepsilon$--expansion, with the goal of obtaining spectral information about the bulk theory. We then proceed to bootstrap two-point functions of chiral operators in the presence of a monodromy defect, and obtain explicit expressions in terms of novel special functions which we analyze in detail. Several of the results presented in this paper are quite general and should be applicable to other setups.

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arXiv2021

The old conformal bootstrap revisited

The "old" conformal bootstrap was originally formulated by Migdal and Polyakov (MP) as a method for calculating conformal dimensions self-consistently. In this work we revisit the MP bootstrap and apply efficient multi-loop Feynman integral techniques in order to solve the corresponding equations. We obtain solutions at first order in the skeleton expansion for finite coupling and for integer values of the spacetime dimension. We focus in particular on the $ϕ^3$ theory in seven dimensions and the $O(N)$ vector models in three dimensions.

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arXiv2021

Seeking SUSY fixed points in the $4-ε$ expansion

We use the $4-ε$ expansion to search for fixed points corresponding to $2+1$ dimensional $\mathcal{N}$=1 Wess-Zumino models of $N_Φ$ scalar superfields interacting through a cubic superpotential. In the $N_Φ=3$ case, we classify all SUSY fixed points that are perturbatively unitary. In the $N_Φ=4$ and $N_Φ=5$ cases, we focus on fixed points where the scalar superfields form a single irreducible representation of the symmetry group (irreducible fixed points). For $N_Φ=4$ we show that the S5 invariant super Potts model is the only irreducible fixed point where the four scalar superfields are fully interacting. For $N_Φ=5$, we go through all Lie subgroups of O(5) and then use the GAP system for computational discrete algebra to study finite subgroups of O(5) up to order 800. This analysis gives us three fully interacting irreducible fixed points. Of particular interest is a subgroup of O(5) that exhibits O(3)/Z2 symmetry. It turns out this fixed point can be generalized to a new family of models, with $N_Φ=\frac{\rm N(N-1)}{2}-1$ and O(N)/Z2 symmetry, that exists for arbitrary integer N$\geq3$.

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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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arXiv2021

Superconformal Boundaries in $4-ε$ dimensions

Boundaries in three-dimensional $\mathcal{N}=2$ superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining $2d$ boundary algebra exhibits $\mathcal{N}=(0,2)$ or $\mathcal{N}=(1,1)$ supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $\mathcal{N}=(1,1)$ supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the $ε$-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a supersymmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.

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arXiv2020

Line and surface defects for the free scalar field

For a single free scalar field in $d \geq 2$ dimensions, almost all the unitary conformal defects must be `trivial' in the sense that they cannot hold interesting dynamics. The only possible exceptions are monodromy defects in $d \geq 4$ and co-dimension three defects in $d \geq 5$. As an intermediate result we show that the $n$-point correlation functions of a conformal theory with a generalized free spectrum must be those of the generalized free theory.

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arXiv2020

Bootstrapping Coulomb and Higgs branch operators

We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in $4d$ $\mathcal{N}=2$ superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In particular, we present improved bounds on OPE coefficients for some selected Argyres-Douglas models, and compare them to recent work where the same cofficients were obtained in the limit of large $r$ charge. There is solid agreement between all the approaches. The improved bounds can be used to extract an approximate spectrum of the Argyres-Douglas models, which can then be used as a guide in order to corner these theories to numerical islands in the space of conformal dimensions. When there is a flavor symmetry present, we complement the analysis by including mixed correlators of Coulomb branch operators and the moment map, a Higgs branch operator which sits in the same multiplet as the flavor current. After calculating the relevant superconformal blocks we apply the numerical machinery to the mixed system. We put general constraints on CFT data appearing in the new channels, with particular emphasis on the simplest Argyres-Douglas model with non-trivial flavor symmetry.

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arXiv2020

Bootstrapping line defects in $\mathcal{N}=2$ theories

We study half-BPS line defects in $\mathcal{N}=2$ superconformal theories using the bootstrap approach. We concentrate on local excitations constrained to the defect, which means the system is a $1d$ defect CFT with $\mathfrak{osp}(4^*|2)$ symmetry. In order to study correlation functions we construct a suitable superspace, and then use the Casimir approach to calculate a collection of new superconformal blocks. Special emphasis is given to the displacement operator, which controls deformations orthogonal to the defect and is always present in a defect CFT. After setting up the crossing equations we proceed with a numerical and analytical bootstrap analysis. We obtain numerical bounds on the CFT data and compare them to known solutions. We also present an analytic perturbative solution to the crossing equations, and argue that this solution captures line defects in $\mathcal{N}=2$ gauge theories at strong coupling.

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arXiv2019

A Lorentzian inversion formula for defect CFT

We present a Lorentzian inversion formula valid for any defect CFT that extracts the bulk channel CFT data as an analytic function of the spin variable. This result complements the already obtained inversion formula for the corresponding defect channel, and makes it now possible to implement the analytic bootstrap program for defect CFT, by going back and forth between both channels. A crucial role in our derivation is played by the Calogero-Sutherland description of defect blocks which we review. As first applications we obtain the large-spin limit of bulk CFT data necessary to reproduce the defect identity, and also calculate the bulk data of the twist defect of the $3d$ Ising model to first order in the $ε$-expansion.

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arXiv2018

Calogero-Sutherland Approach to Defect Blocks

Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave functions of an integrable multi-particle Calogero-Sutherland problem. This generalizes a recent observation in 1602.01858 and makes extensive mathematical results from the modern theory of multi-variable hypergeometric functions available for studies of conformal defects. Applications range from several new relations with scalar four-point blocks to a Euclidean inversion formula for defect correlators.

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arXiv2018

Bootstrapping the half-BPS line defect

We use modern bootstrap techniques to study half-BPS line defects in 4d N=4 superconformal theories. Specifically, we consider the 1d CFT with OSP(4*|4) superconformal symmetry living on such a defect. Our analysis is general and based only on symmetries, it includes however important examples like Wilson and 't Hooft lines in N=4 super Yang-Mills. We present several numerical bounds on OPE coefficients and conformal dimensions. Of particular interest is a numerical island obtained from a mixed correlator bootstrap that seems to imply a unique solution to crossing. The island is obtained if some assumptions about the spectrum are made, and is consistent with Wilson lines in planar N=4 super Yang-Mills at strong coupling. We further analyze the vicinity of the strong-coupling point by calculating perturbative corrections using analytic methods. This perturbative solution has the sparsest spectrum and is expected to saturate the numerical bounds, explaining some of the features of our numerical results.

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