Exceptional Indices

Recently a prescription to compute the superconformal index for all theories of class S was proposed. In this paper we discuss some of the physical information which can be extracted from this index. We derive a simple criterion for the given theory of class S to have a decoupled free component and for it to have enhanced flavor symmetry. Furthermore, we establish a criterion for the "good", the "bad", and the "ugly" trichotomy of the theories. After interpreting the prescription to compute the index with non-maximal flavor symmetry as a residue calculus we address the computation of the index of the bad theories. In particular we suggest explicit expressions for the superconformal index of higher rank theories with E_n flavor symmetry, i.e. for the Hilbert series of the multi-instanton moduli space of E_n.Comment: 33 pages, 11 figures, v2: minor correction

On a modular property of N=2 superconformal theories in four dimensions

In this note we discuss several properties of the Schur index of N=2 superconformal theories in four dimensions. In particular, we study modular properties of this index under SL(2,Z) transformations of its parameters.Comment: 23 page, 2 figure

Gauge Theories and Macdonald Polynomials

We study the N=2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian description, we conjecture explicit formulae for all A-type quivers of class S, which in general do not have one. We test our proposals against several expected dualities. The index can always be interpreted as a correlator in a two-dimensional topological theory, which we identify in each limit as a certain deformation of two-dimensional Yang-Mills theory. The structure constants of the topological algebra are diagonal in the basis of Macdonald polynomials of the holonomies.Comment: 57 pages, 6 figures; v2: references added and minor improvements; v3: typos correcte

Towards structured sharing of raw and derived neuroimaging data across existing resources

Data sharing efforts increasingly contribute to the acceleration of scientific discovery. Neuroimaging data is accumulating in distributed domain-specific databases and there is currently no integrated access mechanism nor an accepted format for the critically important meta-data that is necessary for making use of the combined, available neuroimaging data. In this manuscript, we present work from the Derived Data Working Group, an open-access group sponsored by the Biomedical Informatics Research Network (BIRN) and the International Neuroimaging Coordinating Facility (INCF) focused on practical tools for distributed access to neuroimaging data. The working group develops models and tools facilitating the structured interchange of neuroimaging meta-data and is making progress towards a unified set of tools for such data and meta-data exchange. We report on the key components required for integrated access to raw and derived neuroimaging data as well as associated meta-data and provenance across neuroimaging resources. The components include (1) a structured terminology that provides semantic context to data, (2) a formal data model for neuroimaging with robust tracking of data provenance, (3) a web service-based application programming interface (API) that provides a consistent mechanism to access and query the data model, and (4) a provenance library that can be used for the extraction of provenance data by image analysts and imaging software developers. We believe that the framework and set of tools outlined in this manuscript have great potential for solving many of the issues the neuroimaging community faces when sharing raw and derived neuroimaging data across the various existing database systems for the purpose of accelerating scientific discovery

Superconformal indices of three-dimensional theories related by mirror symmetry

Recently, Kim and Imamura and Yokoyama derived an exact formula for superconformal indices in three-dimensional field theories. Using their results, we prove analytically the equality of superconformal indices in some U(1)-gauge group theories related by the mirror symmetry. The proofs are based on the well known identities of the theory of $q$-special functions. We also suggest the general index formula taking into account the $U(1)_J$ global symmetry present for abelian theories.Comment: 17 pages; minor change