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Minimally unbalanced quivers
https://repo.scoap3.org/record/31326
We develop a classification of minimally unbalanced 3 d N = 4 $$ \mathcal{N}=4 $$ quiver gauge theories. These gauge theories are important because the isometry group G of their Coulomb branch contains a single factor, which is either a classical or an exceptional Lie group. Concurrently, this provides a classification of hyperkähler cones with isometry group G which are obtainable by Coulomb branch constructions. HyperKähler cones such as Coulomb branches of 3 d N = 4 $$ \mathcal{N}=4 $$ quivers are indispensable tools for describing Higgs branches of different theories in various dimensions. In particular, they are used to describe Higgs branches of 5 d N = 1 $$ \mathcal{N}=1 $$ SQCD with gauge group SU( N c ) and 6 d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ SQCD with gauge group Sp( N c ) at the respective UV fixed points.Cabrera, SantiagoThu, 28 Feb 2019 11:53:09 GMThttps://repo.scoap3.org/record/31326urn:ISSN:1029-8479Springer/SISSA2019-02-27Tropical geometry and five dimensional Higgs branches at infinite coupling
https://repo.scoap3.org/record/30252
Superconformal five dimensional theories have a rich structure of phases and brane webs play a crucial role in studying their properties. This paper is devoted to the study of a three parameter family of SQCD theories, given by the number of colors N c for an SU N c gauge theory, number of fundamental flavors N f , and the Chern Simons level k . The study of their infinite coupling Higgs branch is a long standing problem and reveals a rich pattern of moduli spaces, depending on the 3 values in a critical way. For a generic choice of the parameters we find a surprising number of 3 different components, with intersections that are closures of height 2 nilpotent orbits of the flavor symmetry. This is in contrast to previous studies where except for one case ( N c = 2 , N f = 2), the parameters were restricted to the cases of Higgs branches that have only one component. The new feature is achieved thanks to a concept in tropical geometry which is called stable intersection and allows for a computation of the Higgs branch to almost all the cases which were previously unknown for this three parameter family apart form certain small number of exceptional theories with low rank gauge group. A crucial feature in the construction of the Higgs branch is the notion of dressed monopole operators .Cabrera, SantiagoSun, 13 Jan 2019 05:45:38 GMThttps://repo.scoap3.org/record/30252urn:ISSN:1029-8479Springer/SISSA2019-01-08Quiver theories and formulae for Slodowy slices of classical algebras
https://repo.scoap3.org/record/30004
We utilise SUSY quiver gauge theories to compute properties of Slodowy slices; these are spaces transverse to the nilpotent orbits of a Lie algebra g . We analyse classes of quiver theories, with Classical gauge and flavour groups, whose Higgs branch Hilbert series are the intersections between Slodowy slices and the nilpotent cone S∩N of g . We calculate refined Hilbert series for Classical algebras up to rank 4 (and A5 ), and find descriptions of their representation matrix generators as algebraic varieties encoding the relations of the chiral ring. We also analyse a class of dual quiver theories, whose Coulomb branches are intersections S∩N ; such dual quiver theories exist for the Slodowy slices of A algebras, but are limited to a subset of the Slodowy slices of BCD algebras. The analysis opens new questions about the extent of 3 d mirror symmetry within the class of SCFTs known as Tσρ(G) theories. We also give simple group theoretic formulae for the Hilbert series of Slodowy slices; these draw directly on the SU(2) embedding into G of the associated nilpotent orbit, and the Hilbert series of the nilpotent cone.Cabrera, SantiagoFri, 21 Dec 2018 13:52:25 GMThttps://repo.scoap3.org/record/30004urn:ISSN:0550-3213Elsevier2019-02Quiver subtractions
https://repo.scoap3.org/record/27817
We study the vacuum structure of gauge theories with eight supercharges. It has been recently discovered that in the Higgs branch of 5 d and 6 d SQCD theories with eight supercharges, the new massless states, arising when the gauge coupling is taken to infinity, can be described in terms of Coulomb branches of 3 d N = 4 $$ \mathcal{N}=4 $$ quiver gauge theories. The description of this new phenomenon draws from the ideas discovered in the analysis of nilpotent orbits as Higgs and Coulomb branches of 3 d theories and promotes the Higgs mechanism known as the Kraft-Procesi transition to the status of a new operation between quivers. This is the quiver subtraction . This paper establishes this operation formally and examines some immediate consequences. One is the extension of the physical realization of Kraft-Procesi transitions from the classical to the exceptional Lie algebras. Another result is the extension from special nilpotent orbits to non-special ones. One further consequence is the analysis of the effect in 5 d N = 1 $$ \mathcal{N}=1 $$ SQCD of integrating out a massive quark while the gauge coupling remains infinite. In general, the subtraction of quivers sheds light on the different types of singularities within the Coulomb branch and the structure of the massless states that arise at those singular points; including the nature of the new Higgs branches that open up. This allows for a systematic analysis of mixed branches of 3 d N = 4 $$ \mathcal{N}=4 $$ quivers that do not necessarily have a simple embedding in string theory. The subtraction of two quivers is an extremely simple resource for the theoretical physicist interested in the vacuum structure of gauge theories, and yet its power is so remarkable that is bound to play a crucial role in the coming discoveries of new and exciting physics in 5 and 6 dimensions.Cabrera, SantiagoWed, 05 Sep 2018 07:12:29 GMThttps://repo.scoap3.org/record/27817urn:ISSN:1029-8479Springer/SISSA2018-09-03Branes and the Kraft-Procesi transition: classical case
https://repo.scoap3.org/record/25128
Moduli spaces of a large set of 3 d N = 4 $$ \mathcal{N}=4 $$ effective gauge theories are known to be closures of nilpotent orbits. This set of theories has recently acquired a special status, due to Namikawa’s theorem. As a consequence of this theorem, closures of nilpotent orbits are the simplest non-trivial moduli spaces that can be found in three dimensional theories with eight supercharges. In the early 80’s mathematicians Hanspeter Kraft and Claudio Procesi characterized an inclusion relation between nilpotent orbit closures of the same classical Lie algebra. We recently [1] showed a physical realization of their work in terms of the motion of D3-branes on the Type IIB superstring embedding of the effective gauge theories. This analysis is restricted to A-type Lie algebras. The present note expands our previous discussion to the remaining classical cases: orthogonal and symplectic algebras. In order to do so we introduce O3-planes in the superstring description. We also find a brane realization for the mathematical map between two partitions of the same integer number known as collapse . Another result is that basic Kraft-Procesi transitions turn out to be described by the moduli space of orthosymplectic quivers with varying boundary conditions.Cabrera, SantiagoWed, 25 Apr 2018 16:57:30 GMThttps://repo.scoap3.org/record/25128urn:ISSN:1029-8479Springer/SISSA2018-04-23Nilpotent orbits and the Coulomb branch of T σ ( G ) theories: special orthogonal vs orthogonal gauge group factors
https://repo.scoap3.org/record/22315
Coulomb branches of a set of 3 d N $$ \mathcal{N} $$ = 4 supersymmetric gauge theories are closures of nilpotent orbits of the algebra so n $$ \mathfrak{so}(n) $$ . From the point of view of string theory, these quantum field theories can be understood as effective gauge theories describing the low energy dynamics of a brane configuration with the presence of orientifold planes [1]. The presence of the orientifold planes raises the question to whether the orthogonal factors of a the gauge group are indeed orthogonal O( N ) or special orthogonal SO( N ). In order to investigate this problem, we compute the Hilbert series for the Coulomb branch of T σ (SO( n ) ∨ ) theories, utilizing the monopole formula . The results for all nilpotent orbits from so 3 $$ \mathfrak{so}(3) $$ to so 10 $$ \mathfrak{so}(10) $$ which are special and normal are presented. A new relationship between the choice of SO/O( N ) factors in the gauge group and the Lusztig’s Canonical Quotient A ¯ O λ $$ \overline{A}\left({\mathcal{O}}_{\lambda}\right) $$ of the corresponding nilpotent orbit is observed. We also provide a new way of projecting several magnetic lattices of different SO( N ) gauge group factors by the diagonal action of a ℤ 2 $$ {\mathbb{Z}}_2 $$ group.Cabrera, SantiagoWed, 15 Nov 2017 11:17:37 GMThttps://repo.scoap3.org/record/22315urn:ISSN:1029-8479Springer/SISSA2017-11-14Branes and the Kraft-Procesi transition
https://repo.scoap3.org/record/18127
The Coulomb and Higgs branches of certain 3 d N = 4 $$ \mathcal{N}=4 $$ gauge theories can be understood as closures of nilpotent orbits. Recently, a new theorem by Namikawa suggests that this is the simplest possible case, thus giving this class a special role. In this note we use branes to reproduce the mathematical work by Kraft and Procesi. It studies the classification of all nilpotent orbits for classical groups and it characterizes an inclusion relation via minimal singularities. We show how these minimal singularities arise naturally in the Type IIB superstring embedding of the 3 d A-type theories. The Higgs mechanism can be used to remove the minimal singularity, corresponding to a transition in the brane configuration that induces a new effective 3 d theory. This reproduces the Kraft-Procesi results, endowing the family of gauge theories with a new underlying structure. We provide an efficient procedure for computing such brane transitions.Cabrera, SantiagoWed, 30 Nov 2016 08:27:13 GMThttps://repo.scoap3.org/record/18127urn:ISSN:1029-8479Springer/SISSA2016-11-29