Effective action of three-dimensional extended supersymmetric matter on gauge superfield background

We study the low-energy effective actions for gauge superfields induced by quantum N=2 and N=4 supersymmetric matter fields in three-dimensional Minkowski space. Analyzing the superconformal invariants in the N=2 superspace we propose a general form of the N=2 gauge invariant and superconformal effective action. The leading terms in this action are fixed by the symmetry up to the coefficients while the higher order terms with respect to the Maxwell field strength are found up to one arbitrary function of quasi-primary N=2 superfields constructed from the superfield strength and its covariant spinor derivatives. Then we find this function and the coefficients by direct quantum computations in the N=2 superspace. The effective action of N=4 gauge multiplet is obtained by generalizing the N=2 effective action.Comment: 1+27 pages; v2: minor corrections, references adde

Tinkertoys for Gaiotto Duality

We describe a procedure for classifying N=2 superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D A_{N-1} SCFT is compactified, can be decomposed into 3-punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. The classification is carried out explicitly, up through N=5, and for several families of SCFTs for arbitrary N. These lead to a wealth of new S-dualities between Lagrangian and non-Lagrangian N=2 SCFTs.Comment: 61 pages, 136 figures (a veritable comic book). V2: Grotty bitmapped figures replaced with PDF versions; a couple of references fixe

Effects of Contact Network Models on Stochastic Epidemic Simulations

The importance of modeling the spread of epidemics through a population has led to the development of mathematical models for infectious disease propagation. A number of empirical studies have collected and analyzed data on contacts between individuals using a variety of sensors. Typically one uses such data to fit a probabilistic model of network contacts over which a disease may propagate. In this paper, we investigate the effects of different contact network models with varying levels of complexity on the outcomes of simulated epidemics using a stochastic Susceptible-Infectious-Recovered (SIR) model. We evaluate these network models on six datasets of contacts between people in a variety of settings. Our results demonstrate that the choice of network model can have a significant effect on how closely the outcomes of an epidemic simulation on a simulated network match the outcomes on the actual network constructed from the sensor data. In particular, preserving degrees of nodes appears to be much more important than preserving cluster structure for accurate epidemic simulations.Comment: To appear at International Conference on Social Informatics (SocInfo) 201

Off-shell superconformal nonlinear sigma-models in three dimensions

We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral superfields. Several superspace proofs of the folklore statement that N=3 supersymmetry implies N=4 are presented both in the on-shell and off-shell settings. We also elaborate on (super)twistor realisations for (super)manifolds on which the three-dimensional N-extended superconformal groups act transitively and which include Minkowski space as a subspace.Comment: 67 pages; V2: typos corrected, one reference added, version to appear on JHE

General Argyres-Douglas Theory

We construct a large class of Argyres-Douglas type theories by compactifying six dimensional (2,0) A_N theory on a Riemann surface with irregular singularities. We give a complete classification for the choices of Riemann surface and the singularities. The Seiberg-Witten curve and scaling dimensions of the operator spectrum are worked out. Three dimensional mirror theory and the central charges a and c are also calculated for some subsets, etc. Our results greatly enlarge the landscape of N=2 superconformal field theory and in fact also include previous theories constructed using regular singularity on the sphere.Comment: 55 pages, 20 figures, minor revision and typos correcte

Spin-2 spectrum of defect theories

We study spin-2 excitations in the background of the recently-discovered type-IIB solutions of D'Hoker et al. These are holographically-dual to defect conformal field theories, and they are also of interest in the context of the Karch-Randall proposal for a string-theory embedding of localized gravity. We first generalize an argument by Csaki et al to show that for any solution with four-dimensional anti-de Sitter, Poincare or de Sitter invariance the spin-2 excitations obey the massless scalar wave equation in ten dimensions. For the interface solutions at hand this reduces to a Laplace-Beltrami equation on a Riemann surface with disk topology, and in the simplest case of the supersymmetric Janus solution it further reduces to an ordinary differential equation known as Heun's equation. We solve this equation numerically, and exhibit the spectrum as a function of the dilaton-jump parameter $\Delta\phi$. In the limit of large $\Delta\phi$ a nearly-flat linear-dilaton dimension grows large, and the Janus geometry becomes effectively five-dimensional. We also discuss the difficulties of localizing four-dimensional gravity in the more general backgrounds with NS5-brane or D5-brane charge, which will be analyzed in detail in a companion paper.Comment: 41 pages, 6 figure

N = 1 dualities in 2+1 dimensions

We consider minimally supersymmetric QCD in 2+1 dimensions, with Chern-Simons and superpotential interactions. We propose an infrared $SU(N) \leftrightarrow U(k)$ duality involving gauge-singlet fields on one of the two sides. It shares qualitative features both with 3d bosonization and with 4d Seiberg duality. We provide a few consistency checks of the proposal, mapping the structure of vacua and performing perturbative computations in the $\varepsilon$-expansion

Phase structure of black branes in grand canonical ensemble

This is a companion paper of our previous work [1] where we studied the thermodynamics and phase structure of asymptotically flat black $p$-branes in a cavity in arbitrary dimensions $D$ in a canonical ensemble. In this work we study the thermodynamics and phase structure of the same in a grand canonical ensemble. Since the boundary data in two cases are different (for the grand canonical ensemble boundary potential is fixed instead of the charge as in canonical ensemble) the stability analysis and the phase structure in the two cases are quite different. In particular, we find that there exists an analog of one-variable analysis as in canonical ensemble, which gives the same stability condition as the rather complicated known (but generalized from black holes to the present case) two-variable analysis. When certain condition for the fixed potential is satisfied, the phase structure of charged black $p$-branes is in some sense similar to that of the zero charge black $p$-branes in canonical ensemble up to a certain temperature. The new feature in the present case is that above this temperature, unlike the zero-charge case, the stable brane phase no longer exists and `hot flat space' is the stable phase here. In the grand canonical ensemble there is an analog of Hawking-Page transition, even for the charged black $p$-brane, as opposed to the canonical ensemble. Our study applies to non-dilatonic as well as dilatonic black $p$-branes in $D$ space-time dimensions.Comment: 32 pages, 2 figures, various points refined, discussion expanded, references updated, typos corrected, published in JHEP 1105:091,201

Cartan-Weyl 3-algebras and the BLG Theory I: Classification of Cartan-Weyl 3-algebras

As Lie algebras of compact connected Lie groups, semisimple Lie algebras have wide applications in the description of continuous symmetries of physical systems. Mathematically, semisimple Lie algebra admits a Cartan-Weyl basis of generators which consists of a Cartan subalgebra of mutually commuting generators H_I and a number of step generators E^\alpha that are characterized by a root space of non-degenerate one-forms \alpha. This simple decomposition in terms of the root space allows for a complete classification of semisimple Lie algebras. In this paper, we introduce the analogous concept of a Cartan-Weyl Lie 3-algebra. We analyze their structure and obtain a complete classification of them. Many known examples of metric Lie 3-algebras (e.g. the Lorentzian 3-algebras) are special cases of the Cartan-Weyl 3-algebras. Due to their elegant and simple structure, we speculate that Cartan-Weyl 3-algebras may be useful for describing some kinds of generalized symmetries. As an application, we consider their use in the Bagger-Lambert-Gustavsson (BLG) theory.Comment: LaTeX. 34 pages.v2. deleted some distracting paragraphs in the introduction to bring more out the main results of the paper. typos corrected and references adde