arXiv subjects

Luigi Castiglioni

Publications and source records attributed to Luigi Castiglioni.

7 recordsLinked to original sources

arXiv2026

Strong coupling dynamics of defect RG flows in ABJM

Wilson loop operators in ABJM theory provide a rich arena for studying defect conformal field theories (dCFTs) and the renormalization group (RG) flows connecting them. While these are well understood at weak coupling, a complete strong-coupling picture remains an open problem. In this paper, we present a systematic strong-coupling analysis of the fixed points and operator spectrum underlying defect RG flows in ABJM, via holography. By examining fluctuations of fundamental strings in the AdS$_4 \times \mathbb{CP}^3$ background around classical AdS$_2$ solutions, we map worldsheet excitations to the operators in the dual dCFT which are responsible for the flows and determine their scaling dimensions, including subleading corrections from one-loop worldsheet effects. We show how different boundary conditions on string coordinates correspond to distinct operators and provide a geometric realization of the RG flows through interpolating boundary conditions. We apply this framework to fermionic 1/2 BPS, bosonic 1/6 BPS, and non-supersymmetric Wilson loops, establishing a coherent strong-coupling picture in which the 1/2 BPS loop is IR stable, the 1/6 BPS loop acts as a saddle point, and the non-supersymmetric configuration emerges as a natural UV fixed point. We also advance a proposal for the holographic dual of a second non-supersymmetric loop, in terms of averaging over Dirichlet boundary conditions.

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arXiv2026

Framed defects in ABJ(M)

We investigate the role of framing in a family of 1/24 BPS Wilson loops in ABJ(M) theory, which define flows between 1/6 BPS and the 1/2 BPS superconformal fixed points. We analyze in perturbation theory how framing affects both the expectation values of these operators and the correlation functions of local insertions on the defect, as well as its interplay with RG flow and the g-theorem. We obtain a non-trivial identity between the one-point function of the defect stress tensor and a Q-exact correlator, which establishes a direct link between scale invariance, superconformal invariance and framing, and clarifies the deep connection between scale and cohomological anomalies. Finally, we propose a holographic interpretation of framing at strong coupling, identifying it with a coupling to the background B-field in the dual string theory.

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arXiv2025

Conformal defects and RG flows in ABJM

Defects play a central role in many contexts, from condensed matter to quantum gravity. The situations in which the bulk theory is conformal and the defect inherits part of this symmetry -- the so-called defect conformal field theories (dCFTs) -- have recently received a lot of attention, also thanks to new powerful methods to tackle them, like supersymmetric localization, integrability or the bootstrap. A dCFT may be deformed by turning on marginally relevant operators, which trigger RG flows connecting different fixed points. A natural arena where this phenomenon can be explored are 3-dimensional Chern-Simons theories coupled to matter. These are in fact known to display a plethora of Wilson loops that can be used to define 1-dimensional dCFTs living on their contours. Here we discuss a few examples from an intricate web of RG flows connecting the dCFTs defined on the BPS and non-BPS Wilson loops of ABJM theory. We compute the anomalous dimensions of the deforming operators, establish g-theorems along the flows, and also discuss the role played by cohomological anomalies and framing.

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arXiv2024

Framing fermionic Wilson loops in ABJ(M)

Framing plays a central role in the evaluation of Wilson loops in theories with Chern-Simons actions. In pure Chern-Simons theory, it guarantees topological invariance, while in theories with matter like ABJ(M), our theory of interest, it is essential to enforce the cohomological equivalence of different BPS Wilson loops. This is the case for the 1/6 BPS bosonic and the 1/2 BPS fermionic Wilson loops, which have the same expectation value when computed as matrix model averages from localization. This equivalence holds at framing $\mathfrak{f}=1$, which has so far been a challenge to implement in perturbative evaluations. In this paper, we compute the expectation value of the 1/2 BPS fermionic circle of ABJ(M) theory up to two loops in perturbation theory at generic framing. This is achieved by a careful analysis of fermionic Feynman diagrams, isolating their framing dependent contributions and evaluating them in point-splitting regularization using framed contours. Specializing our result to $\mathfrak{f}=1$ we recover exactly the matrix model prediction, thus realizing for the first time a direct perturbative check of localization for this operator. We also generalize our computation to the case of a multiply wound circle, again matching the corresponding matrix model prediction.

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arXiv2024

Interpolating Bremsstrahlung function in ABJM

In ABJM theory, enriched RG flows between circular 1/6 BPS bosonic and 1/2 BPS fermionic Wilson loops have been introduced in arXiv:2211.16501. These flows are triggered by deformations corresponding to parametric 1/6 BPS fermionic loops. In this paper we revisit the study of these operators, but instead of circular contours we consider an interpolating cusped line and a latitude and study their RG flow in perturbation theory. This allows for the definition of a Bremsstrahlung function away from fixed points. We generalize to this case the known cusp/latitude correspondence that relates the Bremsstrahlung function to a latitude Wilson loop. We find that away from the conformal fixed points the ordinary identity is broken by the conformal anomaly in a controlled way. From a defect perspective, the breaking of the correspondence can be traced back to the appearance of an anomalous dimension for fermionic operators localized on the defect. As a by-product, we provide a brand new result for the two-loop cusp anomalous dimension of the 1/6 BPS fermionic and the 1/6 BPS bosonic Wilson lines.

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arXiv2023

Wilson loops and defect RG flows in ABJM

We continue our study of renormalization group (RG) flows on Wilson loop defects in ABJM theory, which we have initiated in arXiv:2211.16501. We generalize that analysis by including non-supersymmetric fixed points and RG trajectories. To this end, we first determine the ``ordinary", non-supersymmetric Wilson loops, which turn out to be two and to include an R-symmetry preserving coupling to the scalar fields of the theory, contrary to their four-dimensional counterpart defined solely in terms of the gauge field holonomy. We then deform these operators by turning on bosonic and/or fermionic couplings, which trigger an elaborate, multi-dimensional network of possible RG trajectories connecting a large spectrum of fixed points classified in terms of the amount (possibly zero) of supersymmetry and R-symmetry preserved. The $β$-functions are computed to leading order in the ABJM coupling but exactly in the deformation parameters, using an auxiliary one-dimensional theory on the defect and a dimensional regularization scheme. A striking result is the different behavior of the two ordinary Wilson loops, of which one turns out to be a UV unstable point while the other is IR stable. The same is true for the two 1/2 BPS Wilson loops. We interpret our results from a defect CFT (dCFT) point of view, computing the anomalous dimensions of the operators associated to the deformations and establishing appropriate g-theorems. In particular, the fermionic unstable fixed point is associated to a dCFT which is not reflection positive.

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arXiv2023

Interpolating Wilson loops and enriched RG flows

We study new $1/24$ BPS circular Wilson loops in ABJ(M) theory, which are defined in terms of several parameters that continuously interpolate between previously known $1/6$ BPS loops (both bosonic and fermionic) and $1/2$ BPS fermionic loops. We compute the expectation value of these operators up to second order in perturbation theory using a one-dimensional effective field theory approach. Within dimensional regularization, we find non-trivial $β$-functions for the parameters, which are marginally relevant deformations triggering RG flows from a UV fixed point represented by the $1/6$ BPS bosonic loop to an IR fixed point represented by a $1/2$ BPS fermionic loop. Generically, along all flows at least one supercharge of the theory is preserved, so that we refer to them as enriched RG flows. In particular, fixed points are connected through $1/6$ BPS fermionic operators. This holds at framing zero, which is a consequence of the regularization scheme employed. We also establish a g-theorem, relating the expectation values of the Wilson loops corresponding to the UV and IR fixed points of the flow, and discuss the one-dimensional defect SCFT living on the Wilson loop contour.

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