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

Liouville/Toda central charges from M5-branes

We show that the central charge of the Liouville and ADE Toda theories can be reproduced by equivariantly integrating the anomaly eight-form of the corresponding six-dimensional N=(0,2) theories, which describe the low-energy dynamics of M5-branes.Comment: 9 page

Partially Balanced Incomplete Block Designs from Weakly Divisible Nearrings

In [[6] Riv. Mat. Univ. Parma 11 (2) (1970) 79–96] Ferrero demonstrates a connection between a restricted class of planar nearrings and balanced incomplete block designs. In this paper, bearing in mind the links between planar nearrings and weakly divisible nearrings (wd-nearrings), first we show the construction of a family of partially balanced incomplete block designs from a special class of wd-nearrings; consequently, we are able to give some formulas for calculating the design parameters

The Cost of Application-Class Processing: Energy and Performance Analysis of a Linux-Ready 1.7-GHz 64-Bit RISC-V Core in 22-nm FDSOI Technology

The open-source RISC-V instruction set architecture (ISA) is gaining traction, both in industry and academia. The ISA is designed to scale from microcontrollers to server-class processors. Furthermore, openness promotes the availability of various open-source and commercial implementations. Our main contribution in this paper is a thorough power, performance, and efficiency analysis of the RISC-V ISA targeting baseline "application class" functionality, i.e., supporting the Linux OS and its application environment based on our open-source single-issue in-order implementation of the 64-bit ISA variant (RV64GC) called Ariane. Our analysis is based on a detailed power and efficiency analysis of the RISC-V ISA extracted from silicon measurements and calibrated simulation of an Ariane instance (RV64IMC) taped-out in GlobalFoundries 22FDX technology. Ariane runs at up to 1.7-GHz, achieves up to 40-Gop/sW energy efficiency, which is superior to similar cores presented in the literature. We provide insight into the interplay between functionality required for the application-class execution (e.g., virtual memory, caches, and multiple modes of privileged operation) and energy cost. We also compare Ariane with RISCY, a simpler and a slower microcontroller-class core. Our analysis confirms that supporting application-class execution implies a nonnegligible energy-efficiency loss and that compute performance is more cost-effectively boosted by instruction extensions (e.g., packed SIMD) rather than the high-frequency operation

Gravity duals of 2d supersymmetric gauge theories

We find new supergravity solutions generated by D5-branes wrapping a four-cycle and preserving four and two supersymmetries. We first consider the configuration in which the fivebranes wrap a four-cycle in a Calabi-Yau threefold, which preserves four supersymmetries and is a gravity dual to the Coulomb branch of two-dimensional gauge theories with N=(2,2) supersymmetry. We also study the case of fivebranes wrapping a co-associative four-cycle in a manifold of G_2-holonomy, which provides a gravity dual of N=(1,1) supersymmetric Yang-Mills theory in two dimensions. We also discuss the addition of unquenched fundamental matter fields to these backgrounds and find the corresponding gravity solutions with flavor brane sources.Comment: 34 pages + appendices; v2: minor improvement

Virtual communities as narrative processes

By facing the problem to describe the history of a virtual community as the sequence of events generated by its participants, a different perception of the meaning of communitywares emerges. This paper describes a proposal for a virtual community system based on the narrative process that supports the social evolution of the community

Superconformal index of low-rank gauge theories via the Bethe Ansatz

We study the Bethe Ansatz formula for the superconformal index, in the case of 4d N = 4 super-Yang-Mills with gauge group SU(N). We observe that not all solutions to the Bethe Ansatz Equations (BAEs) contribute to the index, and thus formulate “reduced BAEs” such that all and only their solutions contribute. We then propose, sharpening a conjecture of Arabi Ardehali et al., that there is a one-to-one correspondence between branches of solutions to the reduced BAEs and vacua of the 4d N = 1* theory. We test the proposal in the case of SU(2) and SU(3). In the case of SU(3), we confirm that there is a continuous family of solutions, whose contribution to the index is non-vanishing

Black Holes in 4D N=4 Super-Yang-Mills Field Theory

Black-hole solutions to general relativity carry a thermodynamic entropy, discovered by Bekenstein and Hawking to be proportional to the area of the event horizon, at leading order in the semiclassical expansion. In a theory of quantum gravity, black holes must constitute ensembles of quantum microstates whose large number accounts for the entropy. We study this issue in the context of gravity with a negative cosmological constant. We exploit the most basic example of the holographic description of gravity (AdS/CFT): type IIB string theory on AdS5 7S5, equivalent to maximally supersymmetric Yang-Mills theory in four dimensions. We thus resolve a long-standing question: Does the four-dimensional N=4 SU(N) Super-Yang-Mills theory on S3 at large N contain enough states to account for the entropy of rotating electrically charged supersymmetric black holes in 5D anti-de Sitter space? Our answer is positive. By reconsidering the large N limit of the superconformal index, using the so-called Bethe-ansatz formulation, we find an exponentially large contribution which exactly reproduces the Bekenstein-Hawking entropy of the black holes. Besides, the large N limit exhibits a complicated structure, with many competing exponential contributions and Stokes lines, hinting at new physics. Our method opens the way toward a quantitative study of quantum properties of black holes in anti-de Sitter space

A Bethe Ansatz Type Formula for the Superconformal Index

Inspired by recent work by Closset, Kim, and Willett, we derive a new formula for the superconformal (or supersymmetric) index of 4D N= 1 theories. Such a formula is a finite sum, over the solution set of certain transcendental equations that we dub Bethe Ansatz Equations, of a function evaluated at those solutions

Linear Two-Dimensional MHD of Accretion Disks: Crystalline structure and Nernst coefficient

We analyse the two-dimensional MHD configurations characterising the steady state of the accretion disk on a highly magnetised neutron star. The model we describe has a local character and represents the extension of the crystalline structure outlined in Coppi (2005), dealing with a local model too, when a specific accretion rate is taken into account. We limit our attention to the linearised MHD formulation of the electromagnetic back-reaction characterising the equilibrium, by fixing the structure of the radial, vertical and azimuthal profiles. Since we deal with toroidal currents only, the consistency of the model is ensured by the presence of a small collisional effect, phenomenologically described by a non-zero constant Nernst coefficient (thermal power of the plasma). Such an effect provides a proper balance of the electron force equation via non zero temperature gradients, related directly to the radial and vertical velocity components. We show that the obtained profile has the typical oscillating feature of the crystalline structure, reconciled with the presence of viscosity, associated to the differential rotation of the disk, and with a net accretion rate. In fact, we provide a direct relation between the electromagnetic reaction of the disk and the (no longer zero) increasing of its mass per unit time. The radial accretion component of the velocity results to be few orders of magnitude below the equatorial sound velocity. Its oscillating-like character does not allow a real matter in-fall to the central object (an effect to be searched into non-linear MHD corrections), but it accounts for the out-coming of steady fluxes, favourable to the ring-like morphology of the disk.Comment: 15 pages, 1 figure, accepted for publication on Modern Physics Letters