scholarly journals Hilbert series for moduli spaces of instantons on ℂ2/ℤ n

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Anindya Dey ◽  
Amihay Hanany ◽  
Noppadol Mekareeya ◽  
Diego Rodríguez-Gómez ◽  
Rak-Kyeong Seong
Keyword(s):  
Moduli Spaces ◽  
Hilbert Series

scholarly journals Hilbert series and moduli spaces of k U(N ) vortices

2015 ◽  
Vol 2015 (2) ◽  
Author(s):  
Amihay Hanany ◽  
Rak-Kyeong Seong
Keyword(s):  
Moduli Spaces ◽  
Hilbert Series

scholarly journals Hilbert series for moduli spaces of two instantons

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Amihay Hanany ◽  
Noppadol Mekareeya ◽  
Shlomo S. Razamat
Keyword(s):  
Moduli Spaces ◽  
Hilbert Series

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.

scholarly journals Chiral rings, Futaki invariants, plethystics, and Gröbner bases

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jiakang Bao ◽  
Yang-Hui He ◽  
Yan Xiao
Keyword(s):  
Moduli Spaces ◽  
Gauge Theories ◽  
Hilbert Series ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Complete Intersections ◽  
Grobner Basis ◽  
Supersymmetric Gauge Theories ◽  
Chiral Rings ◽  
Supersymmetric Gauge

Abstract We study chiral rings of 4d $$ \mathcal{N} $$ N = 1 supersymmetric gauge theories via the notion of K-stability. We show that when using Hilbert series to perform the computations of Futaki invariants, it is not enough to only include the test symmetry information in the former’s denominator. We discuss a way to modify the numerator so that K-stability can be correctly determined, and a rescaling method is also applied to simplify the calculations involving test configurations. All of these are illustrated with a host of examples, by considering vacuum moduli spaces of various theories. Using Gröbner basis and plethystic techniques, many non-complete intersections can also be addressed, thus expanding the list of known theories in the literature.

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

Geometry and Physics: Volume II

2018 ◽  
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Geometric Analysis ◽  
Mathematical Physics ◽  
Poisson Geometry ◽  
Special Holonomy ◽  
Low Dimensional Topology ◽  
Generalized Complex Structures ◽  
Wide Range ◽  
Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

scholarly journals The Hilbert Series of a Linear Symplectic Circle Quotient

2014 ◽  
Vol 23 (1) ◽  
pp. 46-65 ◽  
Author(s):  
Hans-Christian Herbig ◽  
Christopher Seaton
Keyword(s):  
Hilbert Series
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