arXiv subjects

Elia de Sabbata

Publications and source records attributed to Elia de Sabbata.

6 recordsLinked to original sources

arXiv2026

Conformal defects and Goldstone bosons in Anti-de Sitter space

We study local quantum field theories in Anti-de Sitter (AdS) space, with boundary conditions that break some of the bulk isometries. Specifically, we focus on conformal defects and we prove that their spectrum supports a displacement operator of protected dimension, despite the non-local nature of the conformal theory living at the boundary of AdS. If the defect breaks a global symmetry, a tilt operator is also present. The existence of a displacement was conjectured in arXiv:2508.08250 for Wilson loops in Yang-Mills theories in AdS. Our proof is valid in general and applies, in particular, to defects in long-range models, as we discuss in various examples. In the bulk, the modes sourced by the protected operators have Compton wavelength of order of the AdS radius: they constitute the AdS analogue of the Goldstone bosons for the spontaneous breaking of the corresponding symmetries.

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arXiv2026

$T\bar T$ Deformations through BRST Symmetry

We study the $T\bar T$ deformation using its formulation as a CFT coupled to two-dimensional dynamical gravity. Working within the BRST formalism, we apply the intertwiner construction of arXiv:2411.08865 to obtain a unitary "dressing" map between undeformed CFT operators and elements of the BRST cohomology of the deformed theory. We identify the resulting "dressed" operators corresponding to CFT primaries as the physical observables of the deformed theory and show that they arise from a field-dependent change of coordinates, in agreement with what is expected for the $T\bar T$ deformation. We then give a non-perturbative definition of deformed correlation functions as BRST-invariant expectation values of dressed operators in the gauge theory. Finally, we verify that our construction reproduces known structural and perturbative results.

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arXiv2025

Transdimensional Defects

This note introduces a novel paradigm for conformal defects with continuously adjustable dimensions. Just as the standard $\varepsilon$ expansion interpolates between integer spacetime dimensions, a new parameter, $δ$, is used to interpolate between different integer-dimensional defects. The ensuing framework is explored in detail for defects of dimension $p=2+δ$ in both free and interacting $O(N)$ bulk conformal field theories (CFTs) in $d=4-\varepsilon$. Comprehensive calculations are performed to first and second order in $\varepsilon$ and to high or all orders in $δ$. Additionally, in the large-$N$ limit, the interpolation between defects of dimensions $p=1$ and $p=2$ is analysed for spacetime dimensions $4\leq d\leq 6$. The new parameter $δ$ provides a natural enrichment of the space of defect CFTs and allows to find new integer dimension or co-dimension defects.

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arXiv2024

Defects in the long-range O(N) model

We initiate the study of extended excitations in the long-range O(N) model. We focus on line and surface defects and we discuss the challenges of a naive generalization of the simplest defects in the short-range model. To face these challenges we propose three alternative realizations of defects in the long-range model. The first consists in introducing an additional parameter in the perturbative RG flow or, equivalently, treating the non-locality of the model as a perturbation of the local four-dimensional theory. The second is based on the introduction of non-local defect degrees of freedom coupled to the bulk and it provides some non-trivial defect CFTs also in the case of a free bulk, i.e. for generalized free field theory. The third approach is based on a semiclassical construction of line defects. After finding a non-trivial classical field configuration we consider the fluctuation Lagrangian to obtain quantum corrections for the defect theory.

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arXiv2024

Analytic bootstrap for magnetic impurities

We study the $O(3)$ critical model and the free theory of a scalar triplet in the presence of a magnetic impurity. We use analytic bootstrap techniques to extract results in the $\varepsilon$-expansion. First, we extend by one order in perturbation theory the computation of the beta function for the defect coupling in the free theory. Then, we analyze in detail the low-lying spectrum of defect operators, focusing on their perturbative realization when the defect is constructed as a path-ordered exponential. After this, we consider two different bulk two-point functions and we compute them using the defect dispersion relation. For a free bulk theory, we are able to fix the form of the correlator at all orders in $\varepsilon$. In particular, taking $\varepsilon\to1$, we can show that in $d=3$ one does not have a consistent and non-trivial defect CFT. For an interacting bulk, we compute the correlator up to second order in $\varepsilon$. Expanding these results in the bulk and defect block expansions, we are able to extract an infinite set of defect CFT data. We discuss low-spin ambiguities that affect every result computed through the dispersion relation and we use a combination of consistency conditions and explicit diagrammatic calculations to fix this ambiguity.

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arXiv2022

Analytic bootstrap for the localized magnetic field

We study the two-point function of local operators in the critical O(N) model in the presence of a magnetic field localized on a line. We use a recently developed conformal dispersion relation to compute the correlator at first order in the $ε$-expansion and we extract the full set of defect and bulk CFT data using the Lorentzian inversion formulae. The only input for the computation of the connected correlator is its discontinuity at first order in perturbation theory, which is determined by the anomalous dimension of a single bulk operator. We discuss possible low-spin ambiguities and perform several diagrammatic checks of our results.

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