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We analyze the properties of the spectral shift function (SSF) for some dispersive self-adjoint operators under suitable compact perturbations. New mechanisms allowing the SSF to have singularities at the thresholds are exhibited, based on the degeneracy of the spectrum of the unperturbed operator. In particular, we show how any desired type of singularities can be engineered in this situation. These results are completed by Levinson type results., Comment: 35 pages

We present the Wavefront Sensor units of the Gravity Plus Adaptive Optics (GPAO) system, which will equip all 8m class telescopes of the VLTI and is an instrumental part of the GRAVITY+ project. It includes two modules for each Wavefront Sensor unit: a Natural Guide Star sensor with high-order 40x40 Shack-Hartmann and a Laser Guide Star 30x30 sensor. The state-of-the-art AO correction will considerably improve the performance for interferometry, in particular high-contrast observations for NGS observations and all-sky coverage with LGS, which will be implemented for the first time on VLTI instruments. In the following, we give an overview of the Wavefront Sensor units system after completion of their integration and characterization., Comment: Optical and Infrared Interferometry and Imaging IX

Scaling up interferometry to 8m collectors should smooth-out the optical piston perturbations and allow a slow fringe tracker to obtain high precision correction on faint targets. In practice, the GRAVITY fringe tracker still observes high frequency OPD components that limit the exposure time, its precision and limiting magnitude. Perturbations seem to come from mechanical vibrations in the train of mirrors. As part of the GRAVITY+ efforts, accelerometers were added to all the mirrors of the coud\'e train to compensate in real-time the optical path using the main delay lines. We show their effectiveness on vibrations peaks between 40 and 200Hz and outline prospects for the upgrade of the deformable mirrors and the beam-compressor differential delay lines., Comment: 11 pages, 12 figures, Proc. SPIE Astronomical Telescopes + Instrumentation 2024 (Yokohama Japan), Optical and Infrared Interferometry and Imaging VI

Since 2019, GRAVITY has provided direct observations of giant planets and brown dwarfs at separations of down to 95 mas from the host star. Some of these observations have provided the first direct confirmation of companions previously detected by indirect techniques (astrometry and radial velocities). We want to improve the observing strategy and data reduction in order to lower the inner working angle of GRAVITY in dual-field on-axis mode. We also want to determine the current limitations of the instrument when observing faint companions with separations in the 30-150 mas range. To improve the inner working angle, we propose a fiber off-pointing strategy during the observations to maximize the ratio of companion-light-to-star-light coupling in the science fiber. We also tested a lower-order model for speckles to decouple the companion light from the star light. We then evaluated the detection limits of GRAVITY using planet injection and retrieval in representative archival data. We compare our results to theoretical expectations. We validate our observing and data-reduction strategy with on-sky observations; first in the context of brown dwarf follow-up on the auxiliary telescopes with HD 984 B, and second with the first confirmation of a substellar candidate around the star Gaia DR3 2728129004119806464. With synthetic companion injection, we demonstrate that the instrument can detect companions down to a contrast of $8\times 10^{-4}$ ($\Delta \mathrm{K}= 7.7$ mag) at a separation of 35 mas, and a contrast of $3\times 10^{-5}$ ($\Delta \mathrm{K}= 11$ mag) at 100 mas from a bright primary (K<6.5), for 30 min exposure time. With its inner working angle and astrometric precision, GRAVITY has a unique reach in direct observation parameter space. This study demonstrates the promising synergies between GRAVITY and Gaia for the confirmation and characterization of substellar companions., Comment: 16 pages, 14 figures. Submitted to A&A

We establish limiting absorption principles for contractions on a Hilbert space. Our sufficient conditions are based on positive commutator estimates. We discuss the dynamical implications of this principle to the corresponding discrete-time semigroup and provide several applications. Notably to Toeplitz operators and contractive quantum walks.

In this paper, we develop the radial transfer matrix formalism for unitary one-channel operators. This generalizes previous formalisms for CMV matrices and scattering zippers. We establish an analog of Carmona's formula and deduce criteria for absolutely continuous spectrum which we apply to random Hilbert Schmidt perturbations of periodic scattering zippers., Comment: 36 pages, 5 figures

The detection of low-mass planets orbiting the nearest stars is a central stake of exoplanetary science, as they can be directly characterized much more easily than their distant counterparts. Here, we present the results of our long-term astrometric observations of the nearest binary M-dwarf Gliese 65 AB (GJ65), located at a distance of only 2.67 pc. We monitored the relative astrometry of the two components from 2016 to 2023 with the VLTI/GRAVITY interferometric instrument. We derived highly accurate orbital parameters for the stellar system, along with the dynamical masses of the two red dwarfs. The GRAVITY measurements exhibit a mean accuracy per epoch of 50-60 microarcseconds in 1.5h of observing time using the 1.8m Auxiliary Telescopes. The residuals of the two-body orbital fit enable us to search for the presence of companions orbiting one of the two stars (S-type orbit) through the reflex motion they imprint on the differential A-B astrometry. We detected a Neptune-mass candidate companion with an orbital period of p = 156 +/- 1 d and a mass of m = 36 +/- 7 Mearth. The best-fit orbit is within the dynamical stability region of the stellar pair. It has a low eccentricity, e = 0.1 - 0.3, and the planetary orbit plane has a moderate-to-high inclination of i > 30{\deg} with respect to the stellar pair, with further observations required to confirm these values. These observations demonstrate the capability of interferometric astrometry to reach microarcsecond accuracy in the narrow-angle regime for planet detection by reflex motion from the ground. This capability offers new perspectives and potential synergies with Gaia in the pursuit of low-mass exoplanets in the solar neighborhood., Comment: Corresponding authors: G.Bourdarot, P.Kervella, O.Pfuhl. Accepted in A&A Letters

Tight relationships exist in the local universe between the central stellar properties of galaxies and the mass of their supermassive black hole. These suggest galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to probe this relationship is at the peaks of star formation and black hole growth 8-12 billion years ago (redshifts 1-3). Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back time of 11 billion years, by spatially resolving the broad line region. We detect a 40 micro-arcsecond (0.31 pc) spatial offset between the red and blue photocenters of the H$\alpha$ line that traces the velocity gradient of a rotating broad line region. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2x10$^{8}$ solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6x10$^{11}$ solar masses, which indicates an under-massive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the supermassive black hole, indicating a delay between galaxy and black hole formation for some systems., Comment: 5 pages Main text, 8 figures, 2 tables, to be published in Nature, under embargo until 29 January 2024 16:00 (London)

Magnetic quivers have been an instrumental technique for advancing our understanding of Higgs branches of supersymmetric theories with 8 supercharges. In this work, we present the decay and fission algorithm for unitary magnetic quivers. It enables the derivation of the complete phase (Hasse) diagram and is characterised by the following key attributes: First and foremost, the algorithm is inherently simple; just relying on convex linear algebra. Second, any magnetic quiver can only undergo decay or fission processes; these reflect the possible Higgs branch RG-flows (Higgsings), and the quivers thereby generated are the magnetic quivers of the new RG fixed points. Third, the geometry of the decay or fission transition (i.e. the transverse slice) is simply read off. As a consequence, the algorithm does not rely on a complete list of minimal transitions, but rather outputs the transverse slice geometry automatically. As a proof of concept, its efficacy is showcased across various scenarios, encompassing SCFTs from dimensions 3 to 6, instanton moduli spaces, and little string theories., Comment: 55 pages; v.2 added clarifications for sec 3.4

FRIPON is an efficient ground-based network for the detection and characterization of fireballs, which was initiated in France in 2016 with over one hundred cameras and which has been very successfully extended to Europe and Canada with one hundred more stations. After seven successful years of operation in the northern hemisphere, it seems necessary to extend this network towards the southern hemisphere - where the lack of detection is evident - to obtain an exhaustive view of fireball activity. The task of extending the network to any region outside the northern hemisphere presents the challenge of a new installation process, where the recommended and tested version of the several sub-systems that compose a station had to be replaced due to regional availability and compatibility considerations, as well as due to constant software and hardware obsolescence and updates. In Chile, we have a unique geography, with a vast extension in latitude, as well as desert regions, which have generated the need to evaluate the scientific and technical performance of the network under special conditions, prioritizing the optimization of a set of factors related to the deployment process, as well as the feasible and achievable versions of the required components, the geographical location of the stations, and their respective operational, maintenance, safety, and communication conditions. In this talk, we will present the current status of this effort, including a brief report on the obstacles and difficulties encountered and how we have solved them, the current operational status of the network in Northern Chile, as well as the challenges and prospects for the densification of the network over South America., Comment: 4 pages, 2 figures, International Meteor Conference proceedings

In exploring supersymmetric theories with 8 supercharges, the Higgs branches present an intriguing window into strong coupling dynamics. Magnetic quivers serve as crucial tools for understanding these branches. Here, we introduce the decay and fission algorithm for unitary magnetic quivers. It efficiently derives complete phase diagrams (Hasse diagrams) through convex linear algebra. It allows magnetic quivers to undergo decay or fission, reflecting Higgs branch RG-flows in the theory. Importantly, the algorithm generates magnetic quivers for the RG fixed points and simplifies the understanding of transverse slice geometry with no need for a list of minimal transitions. In contrast, the algorithm hints to the existence of a new minimal transition, whose geometry and physics needs to be explored., Comment: 5 pages + references

We study particular families of bad 3d $\mathcal{N}=4$ quiver gauge theories, whose Higgs branches consist of many cones. We show the role of a novel brane configuration in realizing the Higgs moduli for each distinct cone. Through brane constructions, magnetic quivers, Hasse diagrams, and Hilbert series computations we study the intricate structure of the classical Higgs branches. These Higgs branches are both non-normal (since they consist of multiple cones) and non-reduced (due to the presence of nilpotent operators in the chiral ring). Applying the principle of \emph{inversion} to the classical Higgs branch Hasse diagrams, we conjecture the quantum Coulomb branch Hasse diagrams. These Coulomb branches have several most singular loci, corresponding to the the several cones in the Higgs branch. We propose the Hasse diagrams of the full quantum moduli spaces of our theories. The quivers we study can be taken to be 5d effective gauge theories living on brane webs. Their infinite coupling theories have Higgs branches which also consist of multiple cones. Some of these cones have \emph{decorated} magnetic quivers, whose 3d Coulomb branches remain elusive.

We study the 3d $\mathcal{N}=4$ RG-flows triggered by Fayet-Iliopoulos deformations in unitary quiver theories. These deformations can be implemented by a new quiver algorithm which contains at its heart a problem at the intersection of linear algebra and graph theory. When interpreted as magnetic quivers for SQFTs in various dimensions, our results provide a systematic way to explore RG-flows triggered by mass deformations and generalizations thereof. This is illustrated by case studies of SQCD theories and low rank 4d $\mathcal{N}=2$ SCFTs. A delightful by-product of our work is the discovery of an interesting new 3d mirror pair.

The GRAVITY instrument has been revolutionary for near-infrared interferometry by pushing sensitivity and precision to previously unknown limits. With the upgrade of GRAVITY and the Very Large Telescope Interferometer (VLTI) in GRAVITY+, these limits will be pushed even further, with vastly improved sky coverage, as well as faint-science and high-contrast capabilities. This upgrade includes the implementation of wide-field off-axis fringe-tracking, new adaptive optics systems on all Unit Telescopes, and laser guide stars in an upgraded facility. GRAVITY+ will open up the sky to the measurement of black hole masses across cosmic time in hundreds of active galactic nuclei, use the faint stars in the Galactic centre to probe General Relativity, and enable the characterisation of dozens of young exoplanets to study their formation, bearing the promise of another scientific revolution to come at the VLTI., Comment: Published in the ESO Messenger

5d Superconformal Field Theories (SCFTs) are intrinsically strongly-coupled UV fixed points, whose realization hinges on string theoretic methods: they can be constructed by compactifying M-theory on local Calabi-Yau threefold singularities or alternatively from the world-volume of 5-brane-webs in type IIB string theory. There is a correspondence between 5-brane-webs and toric Calabi-Yau threefolds, however this breaks down when multiple 5-branes are allowed to end on a single 7-brane. In this paper, we extend this connection and provide a geometric realization of brane configurations including 7-branes. A web with 7-branes defines a so-called generalized toric polygon (GTP), which corresponds to combinatorial data that is obtained by removing vertices along external edges of a toric polygon. We identify the geometries associated to GTPs as non-toric deformations of toric Calabi-Yau threefolds and provide a precise, algebraic description of the geometry, when 7-branes are introduced along a single edge. The key ingredients in our analysis are T-branes in a type IIA frame, which includes D6-branes. We show that performing Hanany-Witten moves for the 7-branes on the type IIB side corresponds to switching on semisimple vacuum expectation values on the worldvolume of D6-branes, which in turn uplifts to complex structure deformations of the Calabi-Yau geometries. We test the proposal by computing the crepant resolutions of the deformed geometries, thereby checking consistency with the expected properties of the SCFTs.

We study the full moduli space of vacua of 6d worldvolume SCFTs on M5 branes probing an $A$-type singularity, focusing on the geometric incarnation of the discrete gauging mechanism which acts as a discrete quotient on the Higgs branch fibered over the tensor branch. We combine insights from brane constructions and magnetic quiver techniques, in which discrete gauging is implemented through the concept of decoration introduced in [arXiv:2202.01218]. We discover and characterize new transverse slices between phases of 6d SCFTs, identifying some of them with a family of isolated symplectic singularities recently discovered in [arXiv:2112.15494], and conjecturing the existence of two new isolated symplectic singularities.

As part of the GRAVITY$^{+}$ project, the near-infrared beam combiner GRAVITY and the VLTI are currently undergoing a series of significant upgrades to further improve the performance and sky coverage. The instrumental changes will be transformational, and for instance uniquely position GRAVITY to observe the broad line region of hundreds of Active Galactic Nuclei (AGN) at a redshift of two and higher. The increased sky coverage is achieved by enlarging the maximum angular separation between the celestial science object (SC) and the off-axis fringe tracking (FT) star from currently 2 arcseconds (arcsec) up to unprecedented 30 arcsec, limited by the atmospheric conditions. This was successfully demonstrated at the VLTI for the first time., Comment: Proceeding of SPIE Astronomical Telescopes + Instrumentation 2022

We present the current status of the I2C stellar intensity interferometer used towards high angular resolution observations of stars in visible wavelengths. In these proceedings, we present recent technical improvements to the instrument, and share results from ongoing campaigns using arrays of small diameter optical telescopes. A tip-tilt adaptive optics unit was integrated into the optical system to stabilize light injection into an optical fiber. The setup was successfully tested with several facilities on the Calern Plateau site of the Observatoire de la C\^ote d'Azur. These include one of the 1 m diameter telescopes of the C2PU observatory, a portable 1 m diameter telescope, and also the 1.5 m M\'eO telescope. To better constrain on-sky measurements, the spectral transmission of instrument was characterized in the laboratory using a high resolution spectrograph. The system was also tested with two of the auxiliary telescopes of the VLTI resulting in successful temporal and spatial correlation measurements of three stars.

GRAVITY+ is the upgrade of GRAVITY and the Very Large Telescope Interferometer (VLTI) with wide-separation fringe tracking, new adaptive optics, and laser guide stars on all four 8~m Unit Telescopes (UTs), for ever fainter, all-sky, high contrast, milliarcsecond interferometry. Here we present the design and first results of the first phase of GRAVITY+, called GRAVITY Wide. GRAVITY Wide combines the dual-beam capabilities of the VLTI and the GRAVITY instrument to increase the maximum separation between the science target and the reference star from 2 arcseconds with the 8 m UTs up to several 10 arcseconds, limited only by the Earth's turbulent atmosphere. This increases the sky-coverage of GRAVITY by two orders of magnitude, opening up milliarcsecond resolution observations of faint objects, and in particular the extragalactic sky. The first observations in 2019 - 2022 include first infrared interferometry of two redshift $z\sim2$ quasars, interferometric imaging on the binary system HD 105913A, and repeated observations of multiple star systems in the Orion Trapezium Cluster. We find the coherence loss between the science object and fringe-tracking reference star well described by the turbulence of the Earth's atmosphere. We confirm that the larger apertures of the UTs result in higher visibilities for a given separation due to larger overlap of the projected pupils on sky and give predictions for visibility loss as a function of separation to be used for future planning., Comment: 15 pages, 12 figures, 5 tables. Accepted by A&A

We study the distribution of resonances for discrete Hamiltonians of the form $H_0+V$ near the thresholds of the spectrum of $H_0$. Here, the unperturbed operator $H_0$ is a multichannel Laplace type operator on $\ell^2(\mathbb Z; \mathfrak{G}) \cong \ell^2(\mathbb Z)\otimes \mathfrak{G}$ where ${\mathfrak G}$ is an abstract separable Hilbert space, and $V$ is a suitable non-selfadjoint compact perturbation. We distinguish two cases. If ${\mathfrak G}$ is of finite dimension, we prove that resonances exist and do not accumulate at the thresholds in the spectrum of $H_0$. Furthermore, we compute exactly their number and give a precise description on their location in clusters in the complex plane. If ${\mathfrak G}$ is of infinite dimension, an accumulation phenomenon occurs at some thresholds. We describe it by means of an asymptotical analysis of the counting function of resonances. Consequences on the distribution of the complex and the embedded eigenvalues are also given., Comment: 23 pages, 6 figures, 1 table

Hasse diagrams (or phase diagrams) for moduli spaces of supersymmetric field theories have been intensively studied in recent years, and many tools to compute them have been developed. The moduli space of instantons, despite being well studied, has proven difficult to deal with. In this note we explore the Hasse diagram of this moduli space from several perspectives -- using the partial Higgs mechanism, using brane systems and using quiver subtraction -- having to refine previously developed techniques. In particular we introduce the new concept of decorated quiver, which allows to deal with a large class of unitary quivers, including those with adjoint matter.

We propose magnetic quivers for partial implosion spaces. Such partial implosions involve a choice of parabolic subgroup, with the Borel subgroup corresponding to the standard implosion. In the subregular case we test the conjecture by verifying that reduction by the Levi group gives the appropriate nilpotent orbit closure. In the case of a parabolic corresponding to a hook diagram we are also able to carry out this verification provided we work at nonzero Fayet-Iliopoulos parameters.

We solve a long standing problem on the computation of the Higgs branch $\mathcal{H}$ of linear quivers with 8 supercharges and with both unitary and special unitary gauge nodes. The solution uses the concept of magnetic quivers, where components of $\mathcal{H}$ are described as 3d $\mathcal{N}=4$ Coulomb branches. When the starting quiver is good, there is a single component in $\mathcal{H}$ and the magnetic quiver is a 3d mirror. The magnetic quivers are obtained from studying the brane web for an auxiliary 5d theory (with only special unitary gauge groups), constrained by a new notion called brane locking, where some branes are required to move together. We view this as a computational tool rather than an operation in 5d. A detailed algorithm is given, and implemented in a code available for download., Comment: Mathematica code available for download

Context:Optical interferometry is at a key development stage. ESO's VLTI has established a stable, robust infrastructure for long-baseline interferometry for general astronomical observers. The present second-generation instruments offer a wide wavelength coverage and improved performance. Their sensitivity and measurement accuracy lead to data and images of high reliability. Aims:We have developed MATISSE, the Multi AperTure mid-Infrared SpectroScopic Experiment, to access high resolution imaging in a wide spectral domain and explore topics such: stellar activity and mass loss; planet formation and evolution in the gas and dust disks around young stars; accretion processes around super massive black holes in AGN. Methods:The instrument is a spectro-interferometric imager covering three atmospheric bands (L,M,N) from 2.8 to 13.0 mu, combining four optical beams from the VLTI's telscopes. Its concept, related observing procedure, data reduction and calibration approach are the product of 30 years of instrumental research. The instrument utilizes a multi-axial beam combination that delivers spectrally dispersed fringes. The signal provides the following quantities at several spectral resolutions: photometric flux, coherent fluxes, visibilities, closure phases, wavelength differential visibilities and phases, and aperture-synthesis imaging. Results:We provide an overview of the physical principle of the instrument and its functionalities, the characteristics of the delivered signal, a description of the observing modes and of their performance limits. An ensemble of data and reconstructed images are illustrating the first acquired key observations. Conclusion:The instrument has been in operation at Cerro Paranal, ESO, Chile since 2018, and has been open for science use by the international community since April 2019. The first scientific results are being published now., Comment: 24 pages, 26 figures, submitted to Astronomy & Astrophysics

In this note we construct magnetic quivers for the known rank-2 four dimensional $\mathcal{N}=2$ superconformal field theories. For every rank-1 theory one can find a unitary magnetic quiver; we observe that this is no longer possible at rank 2. Our list of magnetic quivers necessarily includes orthosymplectic quivers, in addition to unitary ones, of both the simply and non-simply laced variety. Using quiver subtraction, one can compute Higgs branch Hasse diagrams and compare with the results obtained via other methods finding nearly perfect agreement.

Folding identical legs of a simply-laced quiver creates a quiver with a non-simply laced edge. So far, this has been explored for quivers containing unitary gauge groups. In this paper, orthosymplectic quivers are folded, giving rise to a new family of quivers. This is realised by intersecting orientifolds in the brane system. The monopole formula for these non-simply laced orthosymplectic quivers is introduced. Some of the folded quivers have Coulomb branches that are closures of minimal nilpotent orbits of exceptional algebras, thus providing a new construction of these fundamental moduli spaces. Moreover, a general family of folded orthosymplectic quivers is shown to be a new magnetic quiver realisation of Higgs branches of 4d $\mathcal{N}=2$ theories. The Hasse (phase) diagrams of certain families are derived via quiver subtraction as well as Kraft-Procesi transitions in the brane system.

We analyse the Higgs branch of 4d $\mathcal{N}=2$ SQCD gauge theories with non-connected gauge groups $\widetilde{\mathrm{SU}}(N) = \mathrm{SU}(N) \rtimes_{I,II} \mathbb{Z}_2$ whose study was initiated in arXiv:1804.01108. We derive the Hasse diagrams corresponding to the Higgs mechanism using adapted characters for representations of non-connected groups. We propose 3d $\mathcal{N}=4$ magnetic quivers for the Higgs branches in the type $I$ discrete gauging case, in the form of recently introduced wreathed quivers, and provide extensive checks by means of Coulomb branch Hilbert series computations.

The nature of circumstellar envelopes (CSE) around Cepheids is still a matter of debate. The physical origin of their infrared (IR) excess could be either a shell of ionized gas, or a dust envelope, or both. This study aims at constraining the geometry and the IR excess of the environment of the long-period Cepheid $\ell$ Car (P=35.5 days) at mid-IR wavelengths to understand its physical nature. We first use photometric observations in various bands and Spitzer Space Telescope spectroscopy to constrain the IR excess of $\ell$ Car. Then, we analyze the VLTI/MATISSE measurements at a specific phase of observation, in order to determine the flux contribution, the size and shape of the environment of the star in the L band. We finally test the hypothesis of a shell of ionized gas in order to model the IR excess. We report the first detection in the L band of a centro-symmetric extended emission around l Car, of about 1.7$R_\star$ in FWHM, producing an excess of about 7.0\% in this band. In the N band, there is no clear evidence for dust emission from VLTI/MATISSE correlated flux and Spitzer data. On the other side, the modeled shell of ionized gas implies a more compact CSE ($1.13\pm0.02\,R_\star$) and fainter (IR excess of 1\% in the L band). We provide new evidences for a compact CSE of $\ell$ Car and we demonstrate the capabilities of VLTI/MATISSE for determining common properties of CSEs. While the compact CSE of $\ell$ Car is probably of gaseous nature, the tested model of a shell of ionized gas is not able to simultaneously reproduce the IR excess and the interferometric observations. Further Galactic Cepheids observations with VLTI/MATISSE are necessary for determining the properties of CSEs, which may also depend on both the pulsation period and the evolutionary state of the stars., Comment: 13 pages, 8 figures, accepted in Astronomy and Astrophysics

We propose quivers for Coulomb branch constructions of universal implosions for orthogonal and symplectic groups, extending the work on special unitary groups in arXiv:2004.09620. The quivers are unitary-orthosymplectic as opposed to the purely unitary quivers in the A-type case. Where possible we check our proposals using Hilbert series techniques.

Brane systems provide a large class of gauge theories that arise in string theory. This paper demonstrates how such brane systems fit with a somewhat exotic geometric object, called the affine Grassmannian. This gives a strong motivation to study physical aspects of the affine Grassmannian. Explicit quivers are presented throughout the paper, and a quiver addition algorithm to generate the affine Grassmannian is introduced. An important outcome of this study is a set of quivers for new elementary slices.

Context. The inner few au region of planet-forming disks is a complex environment. High angular resolution observations have a key role in understanding the disk structure and the dynamical processes at work. Aims. In this study we aim to characterize the mid-infrared brightness distribution of the inner disk of the young intermediate-mass star HD 163296, from VLTI/MATISSE observations. Methods. We use geometric models to fit the data. Our models include a smoothed ring, a flat disk with inner cavity, and a 2D Gaussian. The models can account for disk inclination and for azimuthal asymmetries as well. We also perform numerical hydro-dynamical simulations of the inner edge of the disk. Results. Our modeling reveals a significant brightness asymmetry in the L-band disk emission. The brightness maximum of the asymmetry is located at the NW part of the disk image, nearly at the position angle of the semimajor axis. The surface brightness ratio in the azimuthal variation is $3.5 \pm 0.2$. Comparing our result on the location of the asymmetry with other interferometric measurements, we confirm that the morphology of the $r<0.3$ au disk region is time-variable. We propose that this asymmetric structure, located in or near the inner rim of the dusty disk, orbits the star. For the physical origin of the asymmetry, we tested a hypothesis where a vortex is created by Rossby wave instability, and we find that a unique large scale vortex may be compatible with our data. The half-light radius of the L-band emitting region is $0.33\pm 0.01$ au, the inclination is ${52^\circ}^{+5^\circ}_{-7^\circ}$, and the position angle is $143^\circ \pm 3^\circ$. Our models predict that a non-negligible fraction of the L-band disk emission originates inside the dust sublimation radius for $\mu$m-sized grains. Refractory grains or large ($\gtrsim 10\ \mu$m-sized) grains could be the origin for this emission., Comment: accepted for publication in A&A

5d superconformal field theories (SCFTs) can be obtained from 6d SCFTs by circle compactification and mass deformation. Successive decoupling of hypermultiplet matter and RG-flow generates a decoupling tree of descendant 5d SCFTs. In this paper we determine the magnetic quivers and Hasse diagrams, that encode the Higgs branches of 5d SCFTs, for entire decoupling trees. Central to this undertaking is the approach in arXiv:2008.05577, which, starting from the generalized toric polygons (GTPs) dual to 5-brane webs/tropical curves, provides a systematic and succinct derivation of magnetic quivers and their Hasse diagrams. The decoupling in the GTP description is straightforward, and generalizes the standard flop transitions of curves in toric polygons. We apply this approach to a large class of 5d KK-theories, and compute the Higgs branches for their descendants. In particular we determine the decoupling tree for all rank 2 5d SCFTs. For each tree, we also identify the flavor symmetry algebras from the magnetic quivers, including non-simply-laced flavor symmetries., Comment: 82 pages, many figures, 23 tables

Magnetic quivers and Hasse diagrams for Higgs branches of rank $r$ 4d $\mathcal{N}=2$ SCFTs arising from $\mathbb{Z}_{\ell}$ $\mathcal{S}$-fold constructions are discussed. The magnetic quivers are derived using three different methods: 1) Using clues like dimension, global symmetry, and the folding parameter $\ell$ to guess the magnetic quiver. 2) From 6d $\mathcal{N}=(1,0)$ SCFTs as UV completions of 5d marginal theories, and specific FI deformations on their magnetic quiver, which is further folded by $\mathbb{Z}_{\ell}$. 3) From T-duality of Type IIA brane systems of 6d $\mathcal{N}=(1,0)$ SCFTs and explicit mass deformation of the resulting brane web followed by $\mathbb{Z}_{\ell}$ folding. A choice of the ungauging scheme, either on a long node or on a short node, yields two different moduli spaces related by an orbifold action, thus suggesting a larger set of SCFTs in four dimensions than previously expected.

We derive the structure of the Higgs branch of 5d superconformal field theories or gauge theories from their realization as a generalized toric polygon (or dot diagram). This approach is motivated by a dual, tropical curve decomposition of the $(p,q)$ 5-brane-web system. We define an edge coloring, which provides a decomposition of the generalized toric polygon into a refined Minkowski sum of sub-polygons, from which we compute the magnetic quiver. The Coulomb branch of the magnetic quiver is then conjecturally identified with the 5d Higgs branch. Furthermore, from partial resolutions, we identify the symplectic leaves of the Higgs branch and thereby the entire foliation structure. In the case of strictly toric polygons, this approach reduces to the description of deformations of the Calabi-Yau singularities in terms of Minkowski sums., Comment: 68 pages, 1 figure, many Tikz pictures, and 1 ancillary Mathematica notebook

For any gauge theory, there may be a subgroup of the gauge group which acts trivially on the matter content. While many physical observables are not sensitive to this fact, the identification of the precise gauge group becomes crucial when the magnetic spectrum of the theory is considered. This question is addressed in the context of Coulomb branches for $3$d $\mathcal{N}=4$ quiver gauge theories, which are moduli spaces of dressed monopole operators. Since monopole operators are characterized by their magnetic charge, the identification of the gauge group is imperative for the determination of the magnetic lattice. It is well-known that the gauge group of unframed unitary quivers is the product of all unitary nodes in the quiver modded out by the diagonal $\mathrm{U}(1)$ acting trivially on the matter representation. This reasoning generalises to the notion that a choice of gauge group associated to a quiver is given by the product of the individual nodes quotiented by any subgroup that acts trivially on the matter content. For unframed (unitary-) orthosymplectic quivers composed of $\mathrm{SO}(\textrm{even})$, $\mathrm{USp}$, and possibly $\mathrm{U}$ gauge nodes, the maximal subgroup acting trivially is a diagonal $\mathbb{Z}_2$. For unframed unitary quivers with a single $\mathrm{SU}(N)$ node it is $\mathbb{Z}_N$. We use this notion to compute the Coulomb branch Hilbert series of many unitary-orthosymplectic quivers. Examples include nilpotent orbit closures of the exceptional E-type algebras and magnetic quivers that arise from brane physics. This includes Higgs branches of theories with 8 supercharges in dimensions $4$, $5$, and $6$. A crucial ingredient in the calculation of exact refined Hilbert series is the alternative construction of unframed magnetic quivers from resolved Slodowy slices, whose Hilbert series can be derived from Hall-Littlewood polynomials., Comment: v2: 44 pages + appendices, matches JHEP version, added references and fixed typos

Magnetic quivers and Hasse diagrams for Higgs branches of rank 1 $4d$ $\mathcal{N}=2$ SCFTs are provided. These rank 1 theories fit naturally into families of higher rank theories, originating from higher dimensions, which are addressed.