arXiv subjects

Diego Trancanelli

Publications and source records attributed to Diego Trancanelli.

At least 19 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

Nielsen complexity with multiple cost factors

We investigate Nielsen's geometric approach to quantum complexity in the presence of multiple cost factors, extending the standard framework where a single penalty distinguishes easy from hard directions of the group manifold. By introducing a hierarchy of penalties associated with different degrees of non-locality, we develop a generalized right-invariant complexity geometry and analyze its implications for geodesic evolution. We derive the modified Euler-Arnold and Jacobi equations and study how multiple cost factors reshape the structure and scaling of conjugate points, where geodesic optimality breaks down. The formalism is illustrated in two settings: a single-qubit system with two cost factors, where we derive approximate analytic solutions for the complexity growth and its dependence on penalty hierarchies, and SYK-type models, where we analyze both free and chaotic regimes. In these many-body systems, we show that distinct non-local sectors generate multiple families of conjugate points whose occurrence depends on both the cost hierarchy and the system size. Our results highlight how refining the penalty structure provides a richer and more realistic description of quantum complexity and its dynamical behavior.

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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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arXiv2024

Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories

We compute correlation functions of local operator insertions on the 1/2 BPS Wilson lines of N=4 Chern-Simons-matter theories in 3 dimensions. We study the algebra preserved by the defect CFT supported on the line, identify the superdisplacement multiplet and discuss some of its weak-coupling realizations. By employing a superspace description, we present the 4-point functions of the superdisplacement and show how they are determined by functions of cross-ratios. Within an analytic bootstrap approach, we derive these functions at leading and next-to-leading order at strong coupling, obtaining a result in agreement with appropriate orbifolds of the ABJM case considered in arXiv:2004.07849.

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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

Topological Quantum Computation on Supersymmetric Spin Chains

Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the Ising ($k=2$), Fibonacci ($k=3$) and Jones-Kauffman ($k=4$) anyons. We show that the fusion spaces of these anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains. As a result, we can realize the braid group on the product state zero modes of these supersymmetric systems. These operators kill all the other states in the Hilbert space, thus preventing the occurrence of errors while processing information, making them suitable for quantum computing.

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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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arXiv2022

Classifying BPS bosonic Wilson loops in 3d ${\cal N}=4$ Chern-Simons-matter theories

We study the possible BPS Wilson loops in three-dimensional ${\cal N}=4$ Chern-Simons-matter theory which involve only the gauge field and bilinears of the scalars. Previously known examples are the analogues of the Gaiotto-Yin loops preserving four supercharges and "latitude" loops preserving two. We carry out a careful classification and find, in addition, loops preserving three supercharges, further inequivalent classes of loops preserving two supercharges and loops preserving a single supercharge. For each of the classes of loops, we present a representative example and analyse their full orbit under the broken symmetries.

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arXiv2022

Conformal and non-conformal hyperloop deformations of the 1/2 BPS circle

We construct new large classes of BPS Wilson hyperloops in three-dimensional ${\cal N}=4$ quiver Chern-Simons-matter theory on $S^3$. The main strategy is to start with the 1/2 BPS Wilson loop of this theory, choose any linear combination of the supercharges it preserves, and look for deformations built out of the matter fields that still preserve that supercharge. This is a powerful generalization of a recently developed approach based on deformations of 1/4 and 1/8 BPS bosonic loops, which itself was far more effective at discovering new operators than older methods relying on complicated ansatze. We discover many new moduli spaces of BPS hyperloops preserving varied numbers of supersymmetries and varied subsets of the symmetries of the 1/2 BPS operator. In particular, we find new bosonic operators preserving 2 or 3 supercharges as well as new families of loops that do not share supercharges with any bosonic loops, including subclasses of both 1/8 and 1/4 BPS loops that are conformal.

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arXiv2021

Notes on hyperloops in N=4 Chern-Simons-matter theories

We present new circular Wilson loops in three-dimensional N=4 quiver Chern-Simons-matter theory on S^3. At any given node of the quiver, a two-parameter family of operators can be obtained by opportunely deforming the 1/4 BPS Gaiotto-Yin loop. Including then adjacent nodes, the coupling to the bifundamental matter fields allows to enlarge this family and to construct loop operators based on superconnections. We discuss their classification, which depends on both discrete data and continuous parameters subject to an identification. The resulting moduli spaces are conical manifolds, similar to the conifold of the 1/6 BPS loops of the ABJ(M) theory.

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arXiv2021

Local invariants of braiding quantum gates -- associated link polynomials and entangling power

For a generic $n$-qubit system, local invariants under the action of $SL(2,\mathbb{C})^{\otimes n}$ characterize non-local properties of entanglement. In general, such properties are not immediately apparent and hard to construct. Here we consider certain two-qubit Yang-Baxter operators, which we dub of the `X-type', and show that their eigenvalues completely determine the non-local properties of the system. Moreover, we apply the Turaev procedure to these operators and obtain their associated link/knot polynomials. We also compute their entangling power and compare it with that of a generic two-qubit operator.

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arXiv2020

Generating W states with braiding operators

Braiding operators can be used to create entangled states out of product states, thus establishing a correspondence between topological and quantum entanglement. This is well-known for maximally entangled Bell and GHZ states and their equivalent states under Stochastic Local Operations and Classical Communication, but so far a similar result for W states was missing. Here we use generators of extraspecial 2-groups to obtain the W state in a four-qubit space and partition algebras to generate the W state in a three-qubit space. We also present a unitary generalized Yang-Baxter operator that embeds the W$_n$ state in a $(2n-1)$-qubit space.

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arXiv2020

Braiding quantum gates from partition algebras

Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the $(d,m,l)$-generalized Yang-Baxter equation, for $m/2\leq l \leq m$, which allows to systematically construct such braiding operators. This is achieved by using partition algebras, a generalization of the Temperley-Lieb algebra encountered in statistical mechanics. We obtain families of unitary and non-unitary braiding operators that generate the full braid group. Explicit examples are given for a 2-, 3-, and 4-qubit system, including the classification of the entangled states generated by these operators based on Stochastic Local Operations and Classical Communication.

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arXiv2020

Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation

Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding operators as quantum entanglers, and is part of a larger speculated connection between topological and quantum entanglement. We push the analysis of this connection forward, by showing that supersymmetry algebras can be used to construct large families of solutions of the spectral parameter-dependent generalized Yang-Baxter equation. We present a number of explicit examples and outline a general algorithm for arbitrary numbers of qubits. The operators we obtain produce, in turn, all the entangled states in a multi-qubit system classified by the Stochastic Local Operations and Classical Communication protocol introduced in quantum information theory.

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arXiv2019

Roadmap on Wilson loops in 3d Chern-Simons-matter theories

This is a compact review of recent results on supersymmetric Wilson loops in ABJ(M) and related theories. It aims to be a quick introduction to the state of the art in the field and a discussion of open problems. It is divided into short chapters devoted to different questions and techniques. Some new results, perspectives and speculations are also presented. We hope this might serve as a baseline for further studies of this topic.

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