scholarly journals Hasse diagrams for 3d $$ \mathcal{N} $$ = 4 quiver gauge theories — Inversion and the full moduli space

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Julius F. Grimminger ◽  
Amihay Hanany
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Gauge Theories ◽  
Hasse Diagram ◽  
Coulomb Branch ◽  
Hasse Diagrams

Abstract We study Hasse diagrams of moduli spaces of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories. The goal of this work is twofold: 1) We introduce the notion of inverting a Hasse diagram and conjecture that the Coulomb branch and Higgs branch Hasse diagrams of certain theories are related through this operation. 2) We introduce a Hasse diagram to map out the entire moduli space of the theory, including the Coulomb, Higgs and mixed branches. For theories whose Higgs and Coulomb branch Hasse diagrams are related by inversion it is straight forward to generate the Hasse diagram of the entire moduli space. We apply inversion of the Higgs branch Hasse diagram in order to obtain the Coulomb branch Hasse diagram for bad theories and obtain results consistent with the literature. For theories whose Higgs and Coulomb branch Hasse diagrams are not related by inversion it is nevertheless possible to produce the Hasse diagram of the full moduli space using different methods. We give examples for Hasse diagrams of the entire moduli space of theories with enhanced Coulomb branches.

scholarly journals Discrete gauging and Hasse diagrams

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Guillermo Arias Tamargo ◽  
Antoine Bourget ◽  
Alessandro Pini
Keyword(s):  
Gauge Theories ◽  
Hilbert Series ◽  
Higgs Mechanism ◽  
Coulomb Branch ◽  
Gauge Groups ◽  
Hasse Diagrams

We analyse the Higgs branch of 4d \mathcal{N}=2𝒩=2 SQCD gauge theories with non-connected gauge groups \widetilde{\mathrm{SU}}(N) = \mathrm{SU}(N) \rtimes_{I,II} \mathbb{Z}_2SŨ(N)=SU(N)⋊I,IIℤ2 whose study was initiated in . We derive the Hasse diagrams corresponding to the Higgs mechanism using adapted characters for representations of non-connected groups. We propose 3d \mathcal{N}=4𝒩=4 magnetic quivers for the Higgs branches in the type II discrete gauging case, in the form of recently introduced wreathed quivers, and provide extensive checks by means of Coulomb branch Hilbert series computations.

scholarly journals Decomposition of BPS moduli spaces and asymptotics of supersymmetric partition functions

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Arash Arabi Ardehali ◽  
Junho Hong
Keyword(s):  
Partition Function ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Gauge Theories ◽  
Asymptotic Expression ◽  
Effective Field ◽  
Asymptotic Result ◽  
Partition Functions ◽  
Abelian Gauge ◽  
Scale Hierarchy

Abstract We present a prototype for Wilsonian analysis of asymptotics of supersymmetric partition functions of non-abelian gauge theories. Localization allows expressing such partition functions as an integral over a BPS moduli space. When the limit of interest introduces a scale hierarchy in the problem, asymptotics of the partition function is obtained in the Wilsonian approach by i) decomposing (in some suitable scheme) the BPS moduli space into various patches according to the set of light fields (lighter than the scheme dependent cut-off Λ) they support, ii) localizing the partition function of the effective field theory on each patch (with cut-offs set by the scheme), and iii) summing up the contributions of all patches to obtain the final asymptotic result (which is scheme-independent and accurate as Λ → ∞). Our prototype concerns the Cardy-like asymptotics of the 4d superconformal index, which has been of interest recently for its application to black hole microstate counting in AdS5/CFT4. As a byproduct of our analysis we obtain the most general asymptotic expression for the index of gauge theories in the Cardy-like limit, encompassing and extending all previous results.

scholarly journals Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2

2020 ◽  
Vol 9 (6) ◽  
Author(s):  
Philip Argyres ◽  
Antoine Bourget ◽  
Mario Martone
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Large Majority ◽  
Field Theories ◽  
Coordinate Ring ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Complex Dimension ◽  
Rank 2

We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional \mathcal{N}\geq 3𝒩≥3 superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them. Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an \mathcal{N}=2𝒩=2 Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic \mathcal{N}=3𝒩=3 theories.

scholarly journals The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Benjamin Assel ◽  
Stefano Cremonesi
Keyword(s):  
Fixed Points ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Singular Locus ◽  
Low Energy ◽  
Global Symmetry ◽  
Local Geometry ◽  
Coulomb Branch ◽  
Energy Theory ◽  
Mirror Theory

We derive the algebraic description of the Coulomb branch of 3d \mathcal{N}=4𝒩=4USp(2N)USp(2N) SQCD theories with N_fNf fundamental hypermultiplets and determine their low energy physics in any vacuum from the local geometry of the moduli space, identifying the interacting SCFTs which arise at singularities and possible extra free sectors. The SCFT with the largest moduli space arises at the most singular locus on the Coulomb branch. For N_f > 2NNf>2N (good theories) it sits at the origin of the conical variety as expected. For N_f =2NNf=2N we find two separate most singular points, from which the two isomorphic components of the Higgs branch of the UV theory emanate. The SCFTs sitting at any of these two vacua have only odd dimensional Coulomb branch generators, which transform under an accidental SU(2)SU(2) global symmetry. We provide a direct derivation of their moduli spaces of vacua, and propose a Lagrangian mirror theory for these fixed points. For 2 \leq N_f < 2N2≤Nf<2N the most singular locus has one or two extended components, for N_fNf odd or even, and the low energy theory involves an interacting SCFT of one of the above types, plus free twisted hypermultiplets. For N_f=0,1Nf=0,1 the Coulomb branch is smooth. We complete our analysis by studying the low energy theory at the symmetric vacuum of theories with N < N_f \le 2NN<Nf≤2N, which exhibits a local Seiberg-like duality.

scholarly journals Ungauging schemes and Coulomb branches of non-simply laced quiver theories

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Amihay Hanany ◽  
Anton Zajac
Keyword(s):  
Moduli Spaces ◽  
Gauge Theories ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Coulomb Branch ◽  
Highest Weight ◽  
Monopole Operators ◽  
Supersymmetric Gauge ◽  
The One ◽  
Scheme Analysis

Abstract Three dimensional Coulomb branches have a prominent role in the study of moduli spaces of supersymmetric gauge theories with 8 supercharges in 3, 4, 5, and 6 dimensions. Inspired by simply laced 3d $$ \mathcal{N} $$ N = 4 supersymmetric quiver gauge theories, we consider Coulomb branches constructed from non-simply laced quivers with edge multiplicity k and no flavor nodes. In a computation of the Coulomb branch as the space of dressed monopole operators, a center-of-mass U(1) symmetry needs to be ungauged. Typically, for a simply laced theory, all choices of the ungauged U(1) (i.e. all choices of ungauging schemes ) are equivalent and the Coulomb branch is unique. In this note, we study various ungauging schemes and their effect on the resulting Coulomb branch variety. It is shown that, for a non-simply laced quiver, inequivalent ungauging schemes exist which correspond to inequivalent Coulomb branch varieties. Ungauging on any of the long nodes of a non-simply laced quiver yields the same Coulomb branch $$ \mathcal{C} $$ C . For choices of ungauging the U(1) on a short node of rank higher than 1, the GNO dual magnetic lattice deforms anisotropically such that it no longer corresponds to a Lie group, and therefore, the monopole formula yields a non-valid Coulomb branch. However, if the ungauging is performed on a short node of rank 1, the one-dimensional magnetic lattice is rescaled along its single direction i.e. isotropically and the corresponding Coulomb branch is an orbifold of the form $$ \mathcal{C} $$ C /ℤk . Ungauging schemes of 3d Coulomb branches provide a particularly interesting and intuitive description of a subset of actions on the nilpotent orbits studied by Kostant and Brylinski [1]. The ungauging scheme analysis is carried out for minimally unbalanced Cn, affine F4, affine G2, and twisted affine $$ {D}_4^{(3)} $$ D 4 3 quivers, respectively. The analysis is complemented with computations of the Highest Weight Generating functions.

scholarly journals Factorised 3d $$ \mathcal{N} $$ = 4 orthosymplectic quivers

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Mohammad Akhond ◽  
Federico Carta ◽  
Siddharth Dwivedi ◽  
Hirotaka Hayashi ◽  
Sung-Soo Kim ◽  
...  
Keyword(s):  
Moduli Space ◽  
Gauge Theories ◽  
Hilbert Series ◽  
Point Of View ◽  
Coulomb Branch ◽  
Dual Pairs ◽  
Superconformal Field Theories ◽  
Quiver Gauge Theory ◽  
Highest Weight ◽  
Exceptional Sequences

Abstract We study the moduli space of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d $$ \mathcal{N} $$ N = 1 superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expansion.

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

scholarly journals The Volume of the Quiver Vortex Moduli Space

2021 ◽  
Author(s):  
Kazutoshi Ohta ◽  
Norisuke Sakai
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Target Space ◽  
Contour Integral ◽  
Quiver Gauge Theory ◽  
Volume Formula ◽  
Volume Operator ◽  
Space Volume

Abstract We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with CPN target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and “Abelianization” of the volume formula.

scholarly journals EXTREMAL CASES OF RAPOPORT–ZINK SPACES

2021 ◽  
pp. 1-56
Author(s):  
Ulrich Görtz ◽  
Xuhua He ◽  
Michael Rapoport
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Complete List ◽  
Qualitative Properties ◽  
Model Case ◽  
Divisible Groups

Abstract We investigate qualitative properties of the underlying scheme of Rapoport–Zink formal moduli spaces of p-divisible groups (resp., shtukas). We single out those cases where the dimension of this underlying scheme is zero (resp., those where the dimension is the maximal possible). The model case for the first alternative is the Lubin–Tate moduli space, and the model case for the second alternative is the Drinfeld moduli space. We exhibit a complete list in both cases.

scholarly journals THE HYPERELLIPTIC THETA MAP AND OSCULATING PROJECTIONS

2020 ◽  
pp. 1-23
Author(s):  
MICHELE BOLOGNESI ◽  
NÉSTOR FERNÁNDEZ VARGAS
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Hyperelliptic Curve ◽  
Geometric Description ◽  
Birational Model ◽  
Rank 2 ◽  
Semistable Vector Bundles ◽  
Ramification Locus

Abstract Let C be a hyperelliptic curve of genus $g \geq 3$ . In this paper, we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on C with trivial determinant. In order to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb {P}^1)^{2g}//\text {PGL(2)}$ . Then, we identify the restriction of the theta map to these GIT quotients with some explicit degree 2 osculating projection. As a corollary of this construction, we obtain a birational inclusion of a fibration in Kummer $(g-1)$ -varieties over $\mathbb {P}^g$ inside the ramification locus of the theta map.

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