scholarly journals Folding orthosymplectic quivers

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Antoine Bourget ◽  
Julius F. Grimminger ◽  
Amihay Hanany ◽  
Rudolph Kalveks ◽  
Marcus Sperling ◽  
...  
Keyword(s):  
Phase Diagrams ◽  
Moduli Spaces ◽  
Nilpotent Orbits ◽  
Gauge Groups ◽  
Unitary Gauge ◽  
General Family ◽  
New Family ◽  
New Construction ◽  
Exceptional Algebras

Abstract Folding identical legs of a simply-laced quiver creates a quiver with a non-simply laced edge. So far, this has been explored for quivers containing unitary gauge groups. In this paper, orthosymplectic quivers are folded, giving rise to a new family of quivers. This is realised by intersecting orientifolds in the brane system. The monopole formula for these non-simply laced orthosymplectic quivers is introduced. Some of the folded quivers have Coulomb branches that are closures of minimal nilpotent orbits of exceptional algebras, thus providing a new construction of these fundamental moduli spaces. Moreover, a general family of folded orthosymplectic quivers is shown to be a new magnetic quiver realisation of Higgs branches of 4d $$ \mathcal{N} $$ N = 2 theories. The Hasse (phase) diagrams of certain families are derived via quiver subtraction as well as Kraft-Procesi transitions in the brane system.

scholarly journals A string theory realization of special unitary quivers in 3 dimensions

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Andrés Collinucci ◽  
Roberto Valandro
Keyword(s):  
String Theory ◽  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Holomorphic Curves ◽  
Gauge Groups ◽  
Unitary Gauge

Abstract We propose a string theory realization of three-dimensional $$ \mathcal{N} $$ N = 4 quiver gauge theories with special unitary gauge groups. This is most easily understood in type IIA string theory with D4-branes wrapped on holomorphic curves in local K3’s, by invoking the Stückelberg mechanism. From the type IIB perspective, this is understood as simply compactifying the familiar Hanany-Witten (HW) constructions on a T3. The mirror symmetry duals are easily derived. We illustrate this with various examples of mirror pairs.

scholarly journals A NEW CONSTRUCTION FOR POOLING DESIGNS

2011 ◽  
Vol 85 (1) ◽  
pp. 121-127
Author(s):  
FENGLIANG JIN ◽  
HOUCHUN ZHOU ◽  
JUAN XU
Keyword(s):  
Library Screening ◽  
Pooling Design ◽  
Pooling Designs ◽  
Disjunct Matrix ◽  
Helpful Tool ◽  
Dna Library ◽  
New Family ◽  
New Construction ◽  
Dna Library Screening ◽  
Disjunct Matrices

AbstractPooling designs are a very helpful tool for reducing the number of tests for DNA library screening. A disjunct matrix is usually used to represent the pooling design. In this paper, we construct a new family of disjunct matrices and prove that it has a good row to column ratio and error-tolerant property.

scholarly journals DIMENSION OF THE MODULI SPACE AND HAMILTONIAN ANALYSIS OF BF FIELD THEORIES

2011 ◽  
Vol 26 (18) ◽  
pp. 3013-3034 ◽  
Author(s):  
R. CARTAS-FUENTEVILLA ◽  
A. ESCALANTE-HERNANDEZ ◽  
J. BERRA-MONTIEL
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Canonical Analysis ◽  
Field Theories ◽  
Gauge Groups ◽  
Bf Theory ◽  
Extended Action ◽  
Local Symmetries ◽  
Hamiltonian Analysis

By using the Atiyah–Singer theorem through some similarities with the instanton and the antiinstanton moduli spaces, the dimension of the moduli space for two- and four-dimensional BF theories valued in different background manifolds and gauge groups scenarios is determined. Additionally, we develop Dirac's canonical analysis for a four-dimensional modified BF theory, which reproduces the topological YM theory. This framework will allow us to understand the local symmetries, the constraints, the extended Hamiltonian and the extended action of the theory.

scholarly journals A New Family of Boolean Functions with Good Cryptographic Properties

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 42
Author(s):  
Guillermo Sosa-Gómez ◽  
Octavio Paez-Osuna ◽  
Omar Rojas ◽  
Evaristo José Madarro-Capó
Keyword(s):  
Boolean Functions ◽  
Linear Codes ◽  
Bent Functions ◽  
New Family ◽  
Propagation Criterion ◽  
Daunting Task ◽  
Wide Range ◽  
Algebraic Codes ◽  
New Construction

In 2005, Philippe Guillot presented a new construction of Boolean functions using linear codes as an extension of the Maiorana–McFarland’s (MM) construction of bent functions. In this paper, we study a new family of Boolean functions with cryptographically strong properties, such as non-linearity, propagation criterion, resiliency, and balance. The construction of cryptographically strong Boolean functions is a daunting task, and there is currently a wide range of algebraic techniques and heuristics for constructing such functions; however, these methods can be complex, computationally difficult to implement, and not always produce a sufficient variety of functions. We present in this paper a construction of Boolean functions using algebraic codes following Guillot’s work.

scholarly journals Three dimensional mirror symmetry beyond ADE quivers and Argyres-Douglas theories

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Anindya Dey
Keyword(s):  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Dual Pair ◽  
Global Symmetry ◽  
Gauge Groups ◽  
Superconformal Index ◽  
Unitary Gauge ◽  
Simple Realization ◽  
Systematic Field

Abstract Mirror symmetry, a three dimensional $$ \mathcal{N} $$ N = 4 IR duality, has been studied in detail for quiver gauge theories of the ADE-type (as well as their affine versions) with unitary gauge groups. The A-type quivers (also known as linear quivers) and the associated mirror dualities have a particularly simple realization in terms of a Type IIB system of D3-D5-NS5-branes. In this paper, we present a systematic field theory prescription for constructing 3d mirror pairs beyond the ADE quiver gauge theories, starting from a dual pair of A-type quivers with unitary gauge groups. The construction involves a certain generalization of the S and the T operations, which arise in the context of the SL(2, ℤ) action on a 3d CFT with a U(1) 0-form global symmetry. We implement this construction in terms of two supersymmetric observables — the round sphere partition function and the superconformal index on S2 × S1. We discuss explicit examples of various (non-ADE) infinite families of mirror pairs that can be obtained in this fashion. In addition, we use the above construction to conjecture explicit 3d $$ \mathcal{N} $$ N = 4 Lagrangians for 3d SCFTs, which arise in the deep IR limit of certain Argyres-Douglas theories compactified on a circle.

scholarly journals 3d mirrors of the circle reduction of twisted A2N theories of class S

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Emanuele Beratto ◽  
Simone Giacomelli ◽  
Noppadol Mekareeya ◽  
Matteo Sacchi
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Strong Support ◽  
Three Dimensions ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Group Flow ◽  
Mirror Theory

Abstract Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the circle reduction of twisted A2N theories of class S in four dimensions. Although these quivers bear a resemblance to the star-shaped quivers previously studied in the literature, they contain unitary, symplectic and special orthogonal gauge groups, along with hypermultiplets in the fundamental representation. The vacuum moduli spaces of these quiver theories are studied in detail. The Coulomb branch Hilbert series of the mirror theory can be matched with that of the Higgs branch of the corresponding four dimensional theory, providing a non-trivial check of our proposal. Moreover various deformations by mass and Fayet-Iliopoulos terms of such quiver theories are investigated. The fact that several of them flow to expected theories also gives another strong support for the proposal. Utilising the mirror quiver description, we discover a new supersymmetry enhancement renormalisation group flow.

scholarly journals Magnetic lattices for orthosymplectic quivers

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Antoine Bourget ◽  
Julius F. Grimminger ◽  
Amihay Hanany ◽  
Rudolph Kalveks ◽  
Marcus Sperling ◽  
...  
Keyword(s):  
Gauge Group ◽  
Moduli Spaces ◽  
Hilbert Series ◽  
Matter Content ◽  
Coulomb Branch ◽  
Gauge Groups ◽  
Orbit Closures ◽  
Littlewood Polynomials ◽  
Monopole Operators ◽  
Crucial Ingredient

Abstract For any gauge theory, there may be a subgroup of the gauge group which acts trivially on the matter content. While many physical observables are not sensitive to this fact, the choice of the precise gauge group becomes crucial when the magnetic lattice of the theory is considered. This question is addressed in the context of Coulomb branches for 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories, which are moduli spaces of dressed monopole operators. We compute the Coulomb branch Hilbert series of many unitary-orthosymplectic quivers for different choices of gauge groups, including diagonal quotients of the product gauge group of individual factors, where the quotient is by a trivially acting subgroup. Choosing different such diagonal groups results in distinct Coulomb branches, related as orbifolds. Examples include nilpotent orbit closures of the exceptional E-type algebras and magnetic quivers that arise from brane physics. This includes Higgs branches of theories with 8 supercharges in dimensions 4, 5, and 6. A crucial ingredient in the calculation of exact refined Hilbert series is the alternative construction of unframed magnetic quivers from resolved Slodowy slices, whose Hilbert series can be derived from Hall-Littlewood polynomials.

HOMOTOPY DECOMPOSITIONS OF GAUGE GROUPS OVER RIEMANN SURFACES AND APPLICATIONS TO MODULI SPACES

2011 ◽  
Vol 22 (12) ◽  
pp. 1711-1719 ◽  
Author(s):  
STEPHEN D. THERIAULT
Keyword(s):  
Riemann Surface ◽  
Gauge Group ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Riemann Surfaces ◽  
Vector Bundles ◽  
Homotopy Groups ◽  
Gauge Groups ◽  
Stable Vector Bundles

For a prime p, the gauge group of a principal U(p)-bundle over a compact, orientable Riemann surface is decomposed up to homotopy as a product of spaces, each of which is commonly known. This is used to deduce explicit computations of the homotopy groups of the moduli space of stable vector bundles through a range, answering a question of Daskalopoulos and Uhlenbeck.

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