arXiv subjects

Stefanos R. Kousvos

Publications and source records attributed to Stefanos R. Kousvos.

13 recordsLinked to original sources

arXiv2026

Cusped Defects: Cusp Operator Expansion, Conformal Properties and Bootstrap Applications

We analyze general properties of cusped defect lines embedded in generic conformal field theories (CFTs). We prove that suitably defined cusp scaling operators transform like primary operators under general conformal transformations. We show that, via the cusp operator expansion (COE), defects of general shape can be expanded in a basis of cusped defects. These findings are checked and exemplified in the case of the localized magnetic field defect. Finally, we derive analytic constraints on dynamical cusp data by making use of a crossing equation, and discuss possible numerical bootstrap applications of our results.

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arXiv2026

Redundancy Channels in the Conformal Bootstrap

A method for obstructing symmetry enhancement in numerical conformal bootstrap calculations is proposed. Symmetry enhancement refers to situations where bootstrap studies initialised with a certain symmetry end up allowing theories with higher symmetry. In such cases, it is shown that redundant operators in the less symmetric theory can descend from primary scaling operators of the more symmetric one, motivating the imposition of spectral gaps that are justified in the former but not the latter. The same mechanism can also be used to differentiate between decoupled and fully coupled theories which otherwise have the same global symmetry. A systematic understanding of this mechanism is developed and applied to distinguish the cubic from the $O(3)$ model in three dimensions, where a strip of disallowed parameter space, referred to as the cubic redundancy channel, emerges once a gap associated with a redundant operator of the cubic theory is imposed. The channel corresponds precisely to the region of parameter space where the assumed cubic symmetry would be enhanced to $O(3)$.

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arXiv2026

EFT meets CFT: Multiloop renormalization of higher-dimensional operators in general $ϕ^4$ theories

The renormalization of composite operators is a fundamental aspect of quantum field theory, relevant for the description of phase transitions and high energy phenomenology. We calculate the anomalous dimensions of a large set of operators in any scalar $ϕ^4$ theory in $d=4-\varepsilon$ dimensions, up to five loops in most cases. The results have applications in both effective field theory (EFT) and conformal field theory (CFT). As an EFT application, we extract the five-loop renormalization group (RG) equations of the Higgs sector of the Standard Model EFT at dimension six, and up to two loops at dimension eight, aligning our operator basis with custodial symmetry violation. Additionally, for CFT, by resumming the $\varepsilon$-expanded results at the fixed-point, we determine the entire low-lying spectrum (i.e. up to dimension six and Lorentz rank two) of the Ising, $O(n)$ and hypercubic scalar CFTs. Our work enables future conformal bootstrap studies for numerous theories of interest. We include introductions to EFT and CFT, and we illustrate our method and the structure in RG mixing matrices in several illuminating examples, which may also be of general interest. All results in the general theory are publicly available and we describe a systematic path towards applying them to more complicated CFTs.

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arXiv2025

A Bootstrap Study of Confinement in AdS

Yang-Mills theory in AdS$_{4}$ with Dirichlet boundary conditions is expected to undergo a transition as the AdS radius varies, since the boundary data is incompatible with confinement in flat space. Various mechanisms have been proposed for the disappearance of the Dirichlet boundary condition. From the boundary viewpoint, the associated $3d$ CFT is a deformation of a generalised free theory of non-Abelian conserved currents, with the deformation governed by the bulk gauge coupling. We test these scenarios by deriving non-perturbative constraints from the numerical conformal bootstrap of the four-point function of non-Abelian conserved currents. We rule out the scenario in which the boundary current decouples. Bounds on the lightest scalar operators disfavour a bulk Higgs mechanism and instead point to a transition driven by a scalar singlet becoming marginal. We also obtain bounds on other scalar operators and on the current central charge, and we refine character-based techniques incorporating parity and charge-conjugation symmetry to determine the operator spectrum of the $3d$ Generalised Free Vector theory. These results may be of independent interest beyond Yang-Mills theory in AdS.

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arXiv2025

Multi-loop spectra in general scalar EFTs and CFTs

We consider the most general effective field theory (EFT) Lagrangian with scalar fields and derivatives, and renormalise it to substantially higher loop order than existing results in the literature. EFT Lagrangians have phenomenological applications, for example by encoding corrections to the Standard Model from unknown new physics. At the same time, scalar EFTs capture the spectrum of Wilson--Fisher conformal field theories (CFTs) in $4-\varepsilon$ dimensions. Our results are enabled by a more efficient version of the $R^*$ method for renormalisation, in which the IR divergences are subtracted via a small-momentum asymptotic expansion. In particular, we renormalise the most general set of composite operators up to engineering dimension six and Lorentz rank two. We exhibit direct applications of our results to Ising ($Z_2$), $O(n)$, and hypercubic ($S_n \ltimes (Z_2)^n$) CFTs, relevant for a plethora of real-world critical phenomena. The computed scaling dimensions agree well with known non-perturbative results, and they lead to new predictions where such results do not yet exist. We thereby expand the understanding of generic EFTs and open new possibilities in diverse fields, such as the numerical conformal bootstrap.

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arXiv2024

Exploring Replica-Potts CFTs in Two Dimensions

We initiate a numerical conformal bootstrap study of CFTs with $S_n \ltimes (S_Q)^n$ global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the special case $S_3 \ltimes (S_3)^3$, which governs the critical behaviour of three coupled critical 3-state Potts models, a multi-scalar realisation of a (potentially) non-integrable CFT in two dimensions. The model has been studied in earlier works using perturbation theory, transfer matrices, and Monte Carlo simulations. This work represents an independent non-perturbative analysis. Our results are in agreement with previous determinations: we obtain an allowed peninsula within parameter space for the scaling dimensions of the three lowest-lying operators in the theory, which contains the earlier predictions for these scaling dimensions. Additionally, we derive numerous bounds on admissible scaling dimensions in the theory, which are compatible with earlier results. Our work sets the necessary groundwork for a future precision study of these theories in the conformal bootstrap.

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arXiv2024

Anomalous Dimensions in Hypercubic Theories

We perform a comprehensive perturbative study of the operator spectrum in multi-scalar theories with hypercubic global symmetry. This includes working out symmetry representations and their corresponding tensor structures. These structures are then used to compute the anomalous dimensions of scalar operators with up to four fields and arbitrary representations to six-loop order. Moreover, we determine one-loop anomalous dimensions for a large number of low-lying operators in the spectrum which include more powers of the fundamental field and/or insertions of derivatives. As an aside we show how projectors used in the conformal bootstrap can be conveniently reused in computations of anomalous dimensions. The results of our study are of use to the conformal bootstrap. They also illuminate features of conformal perturbation theory and the large $n$ expansion. Our results may be of interest for various crossover phenomena in statistical field theory. In total, we compute the scaling dimension of more than 300 operators, of which 16 are computed to six-loops. Our analysis is exhaustive with respect to group theory up to rank 4 for any number of flavours $n$, and also exhaustive with respect to which representations exist for $n \leq 4$.

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arXiv2023

CFTs with $U(m)\times U(n)$ Global Symmetry in 3D and the Chiral Phase Transition of QCD

Conformal field theories (CFTs) with $U(m)\times U(n)$ global symmetry in $d=3$ dimensions have been studied for years due to their potential relevance to the chiral phase transition of quantum chromodynamics (QCD). In this work such CFTs are analyzed in $d=4-\varepsilon$ and $d=3$. This includes perturbative computations in the $\varepsilon$ and large-$n$ expansions as well as non-perturbative ones with the numerical conformal bootstrap. New perturbative results are presented and a variety of non-perturbative bootstrap bounds are obtained in $d=3$. Various features of the bounds obtained for large values of $n$ disappear for low values of $n$ (keeping $m<n$ fixed), a phenomenon which is attributed to a transition of the corresponding fixed points to the non-unitary regime. Numerous bootstrap bounds are found that are saturated by large-$n$ results, even in the absence of any features in the bounds. A double scaling limit is also observed, for $m$ and $n$ large with $m/n$ fixed, both in perturbation theory as well as in the numerical bootstrap. For the case of two-flavor massless QCD existing bootstrap evidence is reproduced that the chiral phase transition may be second order, albeit associated to a universality class unrelated to the one usually discussed in the $\varepsilon$ expansion. Similar evidence is found for the case of three-flavor massless QCD, where we observe a pronounced kink.

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arXiv2023

Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite $\boldsymbol\varepsilon$

Using numerical conformal bootstrap technology we perform a non-perturbative study of the Ising CFT and its spectrum from infinitesimal to finite values of $\varepsilon=4-d$. Exploiting the recent navigator bootstrap method in conjunction with the extremal functional method, we test various qualitative and quantitative features of the $\varepsilon$-expansion. We follow the scaling dimensions of numerous operators from the perturbatively controlled regime to finite coupling. We do this for $\mathbb Z_2$-even operators up to spin 12 and for $\mathbb Z_2$-odd operators up to spin 6 and find a good matching with perturbation theory. In the finite coupling regime we observe two operators whose dimensions approach each other and then repel, a phenomenon known as level repulsion and which can be analyzed via operator mixing. Our work improves on previous studies in both increased precision and the number of operators studied, and is the first to observe level repulsion in the conformal bootstrap.

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arXiv2022

Bootstrapping Mixed MN Correlators in 3D

The recent emergence of the modern conformal bootstrap method for the study of conformal field theories (CFTs) has enabled the revisiting of old problems in classical critical phenomena described by three-dimensional CFTs. The study of such CFTs with $O(m)^n \rtimes S_n$ global symmetry, also known as MN models, is pursued in this work. Systems of mixed correlators involving scalar operators in two different representations of the global symmetry group are considered. Isolated allowed regions are found in parameter space for various values of $m$ and $n$. These "islands" can be separated into two qualitative groups: those close to the unitarity bound and those further away. As a by-product of our analysis generic tensor structures required to bootstrap any $G^n \rtimes S_n$ theory with $G$ arbitrary are worked out.

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arXiv2020

Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D

Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with $O(m)\times O(n)$ global symmetry in $d=3$ spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in $\varepsilon=4-d$ and in $1/n$, with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for $O(2)\times O(n)$ theories for various values of $n$. Some of these islands can be attributed to fixed points predicted by perturbative methods like the $\varepsilon$ and large-$n$ expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.

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arXiv2020

Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories II

Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier work, we used the nonperturbative numerical conformal bootstrap to provide evidence for the existence of a previously unknown 3D CFT with cubic symmetry, dubbed "Platonic CFT". In this work, we make further use of the numerical conformal bootstrap to perform a three-dimensional scan in the space of scaling dimensions of three low-lying operators. We find a three-dimensional isolated allowed region in parameter space, which includes both the 3D (decoupled) Ising model and the Platonic CFT. The essential assumptions on the spectrum of operators used to provide the isolated allowed region include the existence of a stress-energy tensor and the irrelevance of certain operators (in the renormalization group sense).

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arXiv2019

Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories

Three-dimensional theories with cubic symmetry are studied using the machinery of the numerical conformal bootstrap. Crossing symmetry and unitarity are imposed on a set of mixed correlators, and various aspects of the parameter space are probed for consistency. An isolated allowed region in parameter space is found under certain assumptions involving pushing operator dimensions above marginality, indicating the existence of a conformal field theory in this region. The obtained results have possible applications for ferromagnetic phase transitions as well as structural phase transitions in crystals. They are in tension with previous $\varepsilon$ expansion results, as noticed already in earlier work.

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