Fibrations and Hasse diagrams for 6d 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

The Hasse diagram of the moduli space of instantons

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

Localization Properties of the Chalker-Coddington Model

The Chalker Coddington quantum network percolation model is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We study the model restricted to a cylinder of perimeter 2M. We prove firstly that the Lyapunov exponents are simple and in particular that the localization length is finite; secondly that this implies spectral localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov exponent which is independent of M.Comment: 29 pages, 1 figure. New section added in which simplicity of the Lyapunov spectrum and finiteness of the localization length are proven. To appear in Annales Henri Poincar

Magnetic quivers for rank 2 theories

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

Higgs branches of U/SU quivers via brane locking

We solve a long standing problem on the computation of the Higgs branch 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 H are described as 3d N = 4 Coulomb branches. When the starting quiver is good, there is a single component in 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 provided

Praeorbulina-like specimens" in sediments of the Northern Arabian Sea during the last glacial period

Date du colloque : 06/2009International audienc

Extinction controlled Adaptive Mask Coronagraph Lyot and Phase Mask dual concept for wide extinction area

A dual coronagraph based on the Adaptive Mask concept is presented in this paper. A Lyot coronagraph with a variable diameter occulting disk and a nulling stellar coronagraph based on the Adaptive Phase Mask concept using polarization interferometry are presented in this work. Observations on sky and numerical simulations show the usefulness of the proposed method to optimize the nulling efficiency of the coronagraphs. In the case of the phase mask, the active control system will correct for the detrimental effects of image instabilities on the destructive interference (low-order aberrations such as tip-tilt and focus). The phase mask adaptability both in size, phase and amplitude also compensate for manufacturing errors of the mask itself, and potentially for chromatic effects. Liquid-crystal properties are used to provide variable transmission of an annulus around the phase mask, but also to achieve the achromatic π phase shift in the core of the PSF by rotating the polarization by 180°.A compressed mercury (Hg) drop is used as an occulting disk for the Lyot mask, its size control offers an adaptation to the seeing conditions and provides an optimization of the Tip-tilt correction

Eigenvalue distributions from a star product approach

We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimension $D$ tends to infinity. Our approach is based on the $su(2)$ coherent states which allow for a systematic 1/D expansion of the star product. This produces a trace formula for functions of the matrix sequence elements in the large-$D$ limit which includes higher order (finite-$D$) corrections. From this a variety of analytic results pertaining to the asymptotic properties of the density of states, eigenstates and expectation values associated with the matrix sequence follows. It is shown how new and existing results in the settings of collective spin systems and orthogonal polynomial sequences can be readily obtained as special cases. In particular, this approach allows for the calculation of higher order corrections to the zero distributions of a large class of orthogonal polynomials.Comment: 25 pages, 8 figure

S-fold magnetic quivers

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