3d mirror symmetry as a canonical transformation

We generalize the free Fermi-gas formulation of certain 3d ${\cal N}=3$ supersymmetric Chern-Simons-matter theories by allowing Fayet-Iliopoulos couplings as well as mass terms for bifundamental matter fields. The resulting partition functions are given by simple modifications of the argument of the Airy function found previously. With these extra parameters it is easy to see that mirror-symmetry corresponds to linear canonical transformations on the phase space (or operator algebra) of the 1-dimensional fermions.Comment: 11 pages, 2 figures. v2: figure added - version published in JHE

Negotiating Reality

Our understanding of research through design is demonstrated by a close examination of the methods used in the project lifeClipper2. This design research project investigates the applicability of immersive outdoor Augmented Reality (AR). lifeClipper2 offers an audiovisual walking experience in a virtually extended public space and focuses on audiovisual perception as well as on the development of the appropriate technology. The project involves contributions of partners from different fields of research. Thus, lifeClipper2 is able to test the potential of AR for visualizing architecture and archaeological information and to challenge our understanding of perception and interaction. Using examples from our research, the paper reflects on how scenario design contributes to the production of design knowledge and explores the possibilities and variations of AR. Finally, the paper drafts our approach to design research. The three tenets of our work are: the use of scenarios as a tool of interdisciplinary research, the experimental exploration of media and the intention to make design knowledge explicit. Keywords: augmented reality; locative media; hybrid environment; immersion; perception; experience design; research through design; scenario design</p

Partition functions of 3d D^\hat D-quivers and their mirror duals from 1d free fermions

We study the matrix models calculating the sphere partition functions of 3d gauge theories with $\mathcal{N}=4$ supersymmetry and a quiver structure of a $\hat D$ Dynkin diagram (where each node is a unitary gauge group). As in the case of necklace ($\hat A$) quivers, we can map the problem to that of free fermion quantum mechanics whose complicated Hamiltonian we find explicitly. Many of these theories are conjectured to be dual under mirror symmetry to certain unitary linear quivers with extra Sp nodes or antisymmetric hypermultiplets. We show that the free fermion formulations of such mirror pairs are related by a linear symplectic transformation. We then study the large N expansion of the partition function, which as in the case of the $\hat A$-quivers is given to all orders in 1/N by an Airy function. We simplify the algorithm to calculate the numerical coefficients appearing in the Airy function and evaluate them for a wide class of $\hat D$-quiver theories.Comment: 39 pages, 8 figure

The N=2\mathcal{N}=2 Schur index from free fermions

We study the Schur index of 4-dimensional $\mathcal{N}=2$ circular quiver theories. We show that the index can be expressed as a weighted sum over partition functions describing systems of free Fermions living on a circle. For circular $SU(N)$ quivers of arbitrary length we evaluate the large $N$ limit of the index, up to exponentially suppressed corrections. For the single node theory ($\mathcal{N}=4$ SYM) and the two node quiver we are able to go beyond the large $N$ limit, and obtain the complete, all orders large $N$ expansion of the index, as well as explicit finite $N$ results in terms of elliptic functions.Comment: 36 pages, 1 figure; v2: Minor corrections, version published in JHEP; v3: Minor correction

The exact Schur index of N=4\mathcal{N}=4 SYM

The Witten index counts the difference in the number of bosonic and fermionic states of a quantum mechanical system. The Schur index, which can be defined for theories with at least $\mathcal{N}=2$ supersymmetry in four dimensions is a particular refinement of the index, dependent on one parameter $q$ serving as the fugacity for a particular set of charges which commute with the hamiltonian and some supersymmetry generators. This index has a known expression for all Lagrangian and some non-Lagrangian theories as a finite dimensional integral or a complicated infinite sum. In the case of $\mathcal{N}=4$ SYM with gauge group $U(N)$ we rewrite this as the partition function of a gas of $N$ non interacting and translationally invariant fermions on a circle. This allows us to perform the integrals and write down explicit expressions for fixed $N$ as well as the exact all orders large $N$ expansion.Comment: 11 pages; v2: typos correcte

The Nonequilibrium Thermodynamics of Small Systems

The interactions of tiny objects with their environment are dominated by thermal fluctuations. Guided by theory and assisted by micromanipulation tools, scientists have begun to study such interactions in detail.Comment: PDF file, 13 pages. Long version of the paper published in Physics Toda

Quantum melting of magnetic long-range order near orbital degeneracy. Classical phases and Gaussian fluctuations

We study the effective spin-orbital model derived for the d9 ions in a three-dimensional perovskite lattice, as in KCuF_3, where at each site the doubly degenerate eg orbitals contain a single hole. The model describes the superexchange interactions that depend on the pattern of orbitals occupied. We present the ground state properties of this model, depending on the splitting between the eg orbitals E_z, and the Hund's rule coupling in the excited d8 states, J_H. The classical phase diagram consists of six magnetic phases which all have different orbital ordering: two antiferromagnetic (AF) phases with G-AF order and either x2-y2 or 3z2-r2 orbitals occupied, two phases with mixed orbital (MO) patterns and A-AF order, and two other MO phases with either C-AF or G-AF order. All of them become degenerate at the multicritical point M=(E_z,J_H)=(0,0). Using a generalization of linear spin-wave theory we study both the transverse excitations which are spin-waves and spin-and-orbital-waves, as well as the longitudinal (orbital) excitations. The transverse modes couple to each other, and the spin-and-orbital-wave turns into a soft mode near the M point. Therefore, quantum corrections to the long-range-order parameter are drastically increased near the orbital degeneracy, and classical order is suppressed in a crossover regime between the G-AF and A-AF phases in the (E_z,J_H) plane. This behavior is reminiscent of that found in frustrated spin models, and we conclude that orbital degeneracy provides a new and physically realizable mechanism which stabilizes a spin liquid ground state due to inherent frustration of magnetic interactions. We also point out that such a disordered magnetic phase is likely to be realized in LiNiO_2.Comment: 33 pages, 19 figure

Quantitative CT analysis in patients with pulmonary emphysema: is lung function influenced by concomitant unspecific pulmonary fibrosis?

Purpose: Quantitative analysis of CT scans has proven to be a reproducible technique, which might help to understand the pathophysiology of chronic obstructive pulmonary disease (COPD) and combined pulmonary fibrosis and emphysema. The aim of this retrospective study was to find out if the lung function of patients with COPD with Global Initiative for Chronic Obstructive Lung Disease (GOLD) stages III or IV and pulmonary emphysema is measurably influenced by high attenuation areas as a correlate of concomitant unspecific fibrotic changes of lung parenchyma. Patients and methods: Eighty-eight patients with COPD GOLD stage III or IV underwent CT and pulmonary function tests. Quantitative CT analysis was performed to determine low attenuation volume (LAV) and high attenuation volume (HAV), which are considered to be equivalents of fibrotic (HAV) and emphysematous (LAV) changes of lung parenchyma. Both parameters were determined for the whole lung, as well as peripheral and central lung areas only. Multivariate regression analysis was used to correlate HAV with different parameters of lung function. Results: Unlike LAV, HAV did not show significant correlation with parameters of lung function. Even in patients with a relatively high HAVof more than 10%, in contrast to HAV (p=0.786) only LAV showed a significantly negative correlation with forced expiratory volume in 1 second (r=−0.309, R2=0.096, p=0.003). A severe decrease of DLCO% was associated with both larger HAV (p=0.045) and larger LAV (p=0.001). Residual volume and FVC were not influenced by LAV or HAV. Conclusion: In patients with COPD GOLD stage III-IV, emphysematous changes of lung parenchyma seem to have such a strong influence on lung function, which is a possible effect of concomitant unspecific fibrosis is overwhelmed