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Modern applications increasingly demand flexible computer vision models that adapt to novel concepts not encountered during training. This necessity is pivotal in emerging domains like extended reality, robotics, and autonomous driving, which require the ability to respond to open-world stimuli. A key ingredient is the ability to identify objects based on free-form textual queries defined at inference time - a task known as open-vocabulary object detection. Multimodal backbones like CLIP are the main enabling technology for current open-world perception solutions. Despite performing well on generic queries, recent studies highlighted limitations on the fine-grained recognition capabilities in open-vocabulary settings - i.e., for distinguishing subtle object features like color, shape, and material. In this paper, we perform a detailed examination of these open-vocabulary object recognition limitations to find the root cause. We evaluate the performance of CLIP, the most commonly used vision-language backbone, against a fine-grained object-matching benchmark, revealing interesting analogies between the limitations of open-vocabulary object detectors and their backbones. Experiments suggest that the lack of fine-grained understanding is caused by the poor separability of object characteristics in the CLIP latent space. Therefore, we try to understand whether fine-grained knowledge is present in CLIP embeddings but not exploited at inference time due, for example, to the unsuitability of the cosine similarity matching function, which may discard important object characteristics. Our preliminary experiments show that simple CLIP latent-space re-projections help separate fine-grained concepts, paving the way towards the development of backbones inherently able to process fine-grained details. The code for reproducing these experiments is available at https://github.com/lorebianchi98/FG-CLIP.

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., Comment: 58 pages, 2 figures, 2 tables

Recent advancements in large vision-language models enabled visual object detection in open-vocabulary scenarios, where object classes are defined in free-text formats during inference. In this paper, we aim to probe the state-of-the-art methods for open-vocabulary object detection to determine to what extent they understand fine-grained properties of objects and their parts. To this end, we introduce an evaluation protocol based on dynamic vocabulary generation to test whether models detect, discern, and assign the correct fine-grained description to objects in the presence of hard-negative classes. We contribute with a benchmark suite of increasing difficulty and probing different properties like color, pattern, and material. We further enhance our investigation by evaluating several state-of-the-art open-vocabulary object detectors using the proposed protocol and find that most existing solutions, which shine in standard open-vocabulary benchmarks, struggle to accurately capture and distinguish finer object details. We conclude the paper by highlighting the limitations of current methodologies and exploring promising research directions to overcome the discovered drawbacks. Data and code are available at https://lorebianchi98.github.io/FG-OVD/., Comment: Accepted as Highlight at CVPR2024

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 $\epsilon$-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., Comment: 41 pages

We derive a dispersion relation for two-point correlation functions in defect conformal field theories. The correlator is expressed as an integral over a (single) discontinuity that is controlled by the bulk channel operator product expansion (OPE). This very simple relation is particularly useful in perturbative settings where the discontinuity is determined by a subset of bulk operators. In particular, we apply it to holographic correlators of two chiral primary operators in $\mathcal{N}= 4$ Super Yang-Mills theory in the presence of a supersymmetric Wilson line. With a very simple computation, we are able to reproduce and extend existing results. We also propose a second relation, which reconstructs the correlator from a double discontinuity, and is controlled by the defect channel OPE. Finally, for the case of codimension-one defects (boundaries and interfaces) we derive a dispersion relation which receives contributions from both OPE channels and we apply it to the boundary correlator in the $O(N)$ critical model. We reproduce the order $\epsilon^2$ result in the $\epsilon$-expansion using as input a finite number of boundary CFT data., Comment: 36 pages, 3 figures

Charged and symmetry-resolved R\'enyi entropies are entanglement measures quantifying the degree of entanglement within different charge sectors of a theory with a conserved global charge. We use holography to determine the dependence of charged R\'enyi entropies on small shape deformations away from a spherical or planar entangling surface in general dimensions. This dependence is completely characterized by a single coefficient appearing in the two point function of the displacement operator associated with the R\'enyi defect. We extract this coefficient using its relation to the one point function of the stress tensor in the presence of a deformed entangling surface. This is mapped to a holographic calculation in the background of a deformed charged black hole with hyperbolic horizon. We obtain numerical solutions for different values of the chemical potential and replica number $n$ in various spacetime dimensions, as well as analytic expressions for small chemical potential near $n=1$. When the R\'enyi defect becomes supersymmetric, we demonstrate a conjectured relation between the two point function of the displacement operator and the conformal weight of the twist operator., Comment: 35+16 pages, 9 figures; v2: references added

We study the entanglement and the energy density of the radiation emitted after a local quench in a boundary conformal field theory. We use the operator product expansion (OPE) to predict the early- and late-time behavior of the entanglement entropy and we find, under mild assumptions, a universal form for the leading term, which we test on some treatable two-dimensional examples. We also derive a general upper bound on the entanglement, valid along the full time evolution. In two dimensions, the bound is computed analytically, while in higher dimensions it is evaluated at early and late time via the OPE. These CFT predictions are then compared with a doubly-holographic setup where the CFT is interpreted as a reservoir for the radiation produced on an end-of-the-world brane. After finding the gravitational dual of a boundary local quench, we compute the time evolution of the holographic entanglement entropy, whose late-time behavior is in perfect agreement with the CFT predictions. In the brane+bath picture, unitarity of the time evolution is preserved thanks to the formation of an island. The holographic results can be recovered explicitly from the island formula, in the limit where the tension of the brane is close to the maximal value., Comment: 44 pages, 16 figures; v2: extended discussion on the relative entropy bound, typos fixed, references added

We define a Mellin amplitude for CFT$_1$ four-point functions. Its analytical properties are inferred from physical requirements on the correlator. We discuss the analytic continuation that is necessary for a fully nonperturbative definition of the Mellin transform. The resulting bounded, meromorphic function of a single complex variable is used to derive an infinite set of nonperturbative sum rules for CFT data of exchanged operators, which we test on known examples. We then consider the perturbative setup produced by quartic interactions with an arbitrary number of derivatives in a bulk AdS$_2$ field theory. With our formalism, we obtain a closed-form expression for the Mellin transform of tree-level contact interactions and for the first correction to the scaling dimension of "two-particle" operators exchanged in the generalized free field theory correlator., Comment: 48 pages, 2 figures, 1 Mathematica notebook attached; v2: enlarged text in Sections 1,3,5, matches published version in JHEP

We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary $d$ dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of $d=4$, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum R\'enyi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a $d=4$ theory of free $\mathcal{N}=2$ hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free $d=4$ Maxwell theory and show that their central charges vanish., Comment: 1+61 pages, 3 figures; v2: references added, minor typos corrected

We study local operator insertions on 1/2-BPS line defects in ABJM theory. Specifically, we consider a class of four-point correlators in the CFT$_1$ with SU$(1, 1|3)$ superconformal symmetry defined on the 1/2-BPS Wilson line. The relevant insertions belong to the short supermultiplet containing the displacement operator and correspond to fluctuations of the dual fundamental string in AdS$_4 \times \mathbb{C}\textrm{P}^3$ ending on the line at the boundary. We use superspace techniques to represent the displacement supermultiplet and we show that superconformal symmetry determines the four-point correlators of its components in terms of a single function of the one-dimensional cross-ratio. Such function is highly constrained by crossing and internal consistency, allowing us to use an analytical bootstrap approach to find the first subleading correction at strong coupling. Finally, we use AdS/CFT to compute the same four-point functions through tree-level AdS$_2$ Witten diagrams, producing a result that is perfectly consistent with the bootstrap solution., Comment: 50 pages, 2 figures. v2: one footnote and one reference added, it matches the published version v3: further references added

We study the constraints of superconformal symmetry on codimension two defects in four-dimensional superconformal field theories. We show that the one-point function of the stress tensor and the two-point function of the displacement operator are related, and we discuss the consequences of this relation for the Weyl anomaly coefficients as well as in a few examples, including the supersymmetric R\'enyi entropy. Imposing consistency with existing results, we propose a general relation that could hold for sufficiently supersymmetric defects of arbitrary dimension and codimension. Turning to $\mathcal{N}=(2,2)$ surface defects in $\mathcal{N} \geqslant 2$ superconformal field theories, we study the associated chiral algebra. We work out various properties of the modules introduced by the defect in the original chiral algebra. In particular, we find that the one-point function of the stress tensor controls the dimension of the defect identity in chiral algebra, providing a novel way to compute it, once the defect identity is identified. Studying a few examples, we show explicitly how these properties are realized., Comment: 60 pages; v3: matches published version

We study the discretized worldsheet of Type IIB strings in the Gubser-Klebanov-Polyakov background in a new setup, which eliminates a complex phase previously detected in the fermionic determinant. A sign ambiguity remains, which a study of the fermionic spectrum shows to be related to Yukawa-like terms, including those present in the original Lagrangian before the linearization standard in a lattice QFT approach. Monte Carlo simulations are performed in a large region of the parameter space, where the sign problem starts becoming severe and instabilities appear due to the zero eigenvalues of the fermionic operator. To face these problems, simulations are conducted using the absolute value of a fermionic Pfaffian obtained introducing a small twisted-mass term, acting as an infrared regulator, into the action. The sign of the Pfaffian and the low modes of the quadratic fermionic operator are then taken into account by a reweighting procedure of which we discuss the impact on the measurement of the observables. In this setup we study bosonic and fermionic correlators and observe a divergence in the latter, which we argue - also via a one-loop analysis in lattice perturbation theory - to originate from the U(1)-breaking of our Wilson-like discretization for the fermionic sector., Comment: v1: 9 figures, 27 pages of which the first 9 overlap with Proceedings in arxiv:1702.02005; v2: cosmetic modification of one plot; v3: it matches the version published in JHEP (modified introduction and abstract)

In conformal $\mathcal{N}=2$ Super Yang-Mills theory, the energy emitted by an accelerated heavy particle is computed by the one-point function of the stress tensor operator in the presence of a Wilson line. In this paper, we consider the theory on the ellipsoid and we prove a conjectured relation between the stress tensor one-point function and the first order expansion of the Wilson loop expectation value in the squashing parameter. To do this, we analyze the behavior of the Wilson loop for a small deformation of the background geometry and, at first order in the deformation, we fix the kinematics using defect CFT constraints. In the final part of the paper, we analyze the consequences of our results for the weak coupling perturbative expansion. In particular, comparing the weakly coupled matrix model with the ordinary Feynman diagram expansion, we find a natural transcendentality driven organization for the latter., Comment: 39 pages, 5 figures, 1 table

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., Comment: 41 pages, 4 figures, prepared for submission to J. Phys. A; v2: minor changes, published version

We deform a defect conformal field theory by an exactly marginal bulk operator and we consider the dependence on the marginal coupling of flat and spherical defect expectation values. For even dimensional spherical defects we find a logarithmic divergence which can be related to a $a$-type defect anomaly coefficient. This coefficient, for defect theories, is not invariant on the conformal manifold and its dependence on the coupling is controlled to all orders by the one-point function of the associated exactly marginal operator. For odd-dimensional defects, the flat and spherical case exhibit different qualitative behaviors, generalizing to arbitrary dimensions the line-circle anomaly of superconformal Wilson loops. Our results also imply a non-trivial coupling dependence for the recently proposed defect $C$-function. We finally apply our general result to a few specific examples, including superconformal Wilson loops and R\'enyi entropy., Comment: 8 pages, v2: derivation on coupling independence for superconformal surface defects added

Form factors of the stress-tensor multiplet operator in $\mathcal{N}=4$ supersymmetric Yang-Mills reveal surprisingly simple structures similar to those appearing in scattering amplitudes. In this paper we show that, as for the case of amplitudes, they also enjoy dual conformal symmetry. We compute the dual conformal anomaly at one loop for an arbitrary number of particles and generic helicities, which matches the expression of the dual conformal anomaly of amplitudes, and perform explicit checks for MHV and NMHV one-loop form factors. In the NMHV case the realisation of dual conformal symmetry requires a delicate cancellation of offending terms arising from three-mass triangles, which we explicitly check in the case of the four-point NMHV form factor., Comment: 38 pages; v2: typos corrected, references added

We introduce a prescription to define form factor integrands at loop level in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory. This relies on a periodic kinematic configuration that has been instrumental to describe form factors at strong coupling in terms of periodic Wilson loops. With this prescription, we are able to formulate loop-level recursion relations for planar form factor integrands, using a two-line (BCFW) and an all-line shift. We also point out important differences with the known recursion relations of integrands of planar loop amplitudes. We present a number of concrete one-loop examples to illustrate and validate our prescription for form factor integrands., Comment: 35 pages

We study the conformal data of a generic superconformal half-BPS line defect in a four-dimensional $\mathcal{N} = 2$ theory. We prove a theory independent relation between the one-point function of the stress tensor in the presence of the line defect and the two-point function of the displacement operator. When the defect is interpreted as a heavy charged particle in a gauge theory, the result relates the energy emitted through Bremsstrahlung with the coupling of the stress tensor to the particle at rest.

In this paper we study the Bremsstrahlung functions for the 1/6 BPS and the 1/2 BPS Wilson lines in ABJM theory. First we use a superconformal defect approach to prove a conjectured relation between the Bremsstrahlung functions associated to the geometric ($B^{\varphi}_{1/6}$) and R-symmetry ($B^{\theta}_{1/6}$) deformations of the 1/6 BPS Wilson line. This result, non-trivially following from a defect supersymmetric Ward identity, provides an exact expression for $B^{\theta}_{1/6}$ based on a known result for $B^{\varphi}_{1/6}$. Subsequently, we explore the consequences of this relation for the 1/2 BPS Wilson line and, using the localization result for the multiply wound Wilson loop, we provide an exact closed form for the corresponding Bremsstrahlung function. Interestingly, for the comparison with integrability, this expression appears particularly natural in terms of the conjectured interpolating function $h(\lambda)$. During the derivation of these results we analyze the protected defect supermultiplets associated to the broken symmetries, including their two- and three-point correlators., Comment: 43 pages, 3 figures. Minor changes. Published version