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 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 (Symplectic) leaves and (5d Higgs) branches in the Poly(go)nesian Tropical Rain Forest

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Marieke van Beest ◽  
Antoine Bourget ◽  
Julius Eckhard ◽  
Sakura Schäfer-Nameki
Keyword(s):  
Rain Forest ◽  
Tropical Rain Forest ◽  
Gauge Theories ◽  
Edge Coloring ◽  
Field Theories ◽  
Minkowski Sum ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Minkowski Sums ◽  
Symplectic Leaves

Abstract We derive the structure of the Higgs branch of 5d superconformal field theories or gauge theories from their realization as a generalized toric polygon (or dot diagram). This approach is motivated by a dual, tropical curve decomposition of the (p, q) 5-brane-web system. We define an edge coloring, which provides a decomposition of the generalized toric polygon into a refined Minkowski sum of sub-polygons, from which we compute the magnetic quiver. The Coulomb branch of the magnetic quiver is then conjecturally identified with the 5d Higgs branch. Furthermore, from partial resolutions, we identify the symplectic leaves of the Higgs branch and thereby the entire foliation structure. In the case of strictly toric polygons, this approach reduces to the description of deformations of the Calabi-Yau singularities in terms of Minkowski sums.

scholarly journals Solving q-Virasoro constraints

2019 ◽  
Vol 110 (1) ◽  
pp. 179-210 ◽  
Author(s):  
Rebecca Lodin ◽  
Aleksandr Popolitov ◽  
Shamil Shakirov ◽  
Maxim Zabzine
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Free Field ◽  
Point Of View ◽  
Difference Operators ◽  
Highest Weight ◽  
Virasoro Constraints ◽  
Zero Momentum ◽  
Complete Analogy ◽  
Full Derivative

Abstract We show how q-Virasoro constraints can be derived for a large class of (q, t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators under the integral, in complete analogy with full-derivative insertions for $$\beta $$ β -ensembles. From free field point of view, the models considered have zero momentum of the highest weight, which leads to an extra constraint $$T_{-1} \mathcal {Z} = 0$$ T - 1 Z = 0 . We then show how to solve these q-Virasoro constraints recursively and comment on the possible applications for gauge theories, for instance calculation of (supersymmetric) Wilson loop averages in gauge theories on $$D^2 \times S^1$$ D 2 × S 1 and $$S^3$$ S 3 .

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 Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective

2019 ◽  
Vol 6 (5) ◽  
Author(s):  
Cyril Closset ◽  
Michele Del Zotto ◽  
Vivek Saxena
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Low Energy ◽  
Field Theories ◽  
Isolated Singularity ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Ale Space ◽  
M Theory

We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities \mathbf{X}𝐗 and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to \mathbf{X}𝐗. Focussing on the case of toric CY singularities, we analyze the “gauge-theory phases” of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this setup, the low-energy gauge group simply arises on stacks of coincident D6-branes wrapping 2-cycles in some ALE space of type A_{M-1}AM−1 fibered over a real line, and the map between the Kähler parameters of \mathbf{X}𝐗 and the Coulomb branch parameters of the field theory (masses and VEVs) can be read off systematically. Different type IIA “reductions” give rise to different gauge theory phases, whose existence depends on the particular (partial) resolutions of the isolated singularity \mathbf{X}𝐗. We also comment on the case of non-isolated toric singularities. Incidentally, we propose a slightly modified expression for the Coulomb-branch prepotential of 5d \mathcal{N}=1𝒩=1 gauge theories.

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.

BRANE TILINGS

2007 ◽  
Vol 22 (18) ◽  
pp. 2977-3038 ◽  
Author(s):  
KRISTIAN D. KENNAWAY
Keyword(s):  
Moduli Space ◽  
Mirror Symmetry ◽  
Gauge Theories ◽  
Field Theories ◽  
Einstein Metric ◽  
Dimensional Torus ◽  
Infinite Class ◽  
Superconformal Field Theories ◽  
The Past ◽  
Dimer Models

We review and extend the progress made over the past few years in understanding the structure of toric quiver gauge theories; those which are induced on the worldvolume of a stack of D3-branes placed at the tip of a toric Calabi–Yau cone, at an "orbifold point" in Kähler moduli space. These provide an infinite class of four-dimensional [Formula: see text] superconformal field theories which may be studied in the context of the AdS/CFT correspondence. It is now understood that these gauge theories are completely specified by certain two-dimensional torus graphs, called brane tilings, and the combinatorics of the dimer models on these graphs. In particular, knowledge of the dual Sasaki–Einstein metric is not required to determine the gauge theory, only topological and symplectic properties of the toric Calabi–Yau cone. By analyzing the symmetries of the toric quiver theories we derive the dimer models and use them to construct the moduli space of the theory both classically and semiclassically. Using mirror symmetry the brane tilings are shown to arise in string theory on the worldvolumes of the fractional D6-branes that are mirror to the stack of D3-branes at the tip of the cone.

scholarly journals Instantons and Bows for the Classical Groups

2020 ◽  
Author(s):  
Sergey A Cherkis ◽  
Jacques Hurtubise
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Finite Subgroup ◽  
Structure Group ◽  
Classical Groups ◽  
Coulomb Branch ◽  
Quiver Gauge Theory ◽  
Instanton Bundles ◽  
Similar Classification

Abstract The construction of Atiyah, Drinfeld, Hitchin and Manin provided complete description of all instantons on Euclidean four-space. It was extended by Kronheimer and Nakajima to instantons on ALE spaces, resolutions of orbifolds $\mathbb{R}^4/\Gamma$ by a finite subgroup Γ⊂SU(2). We consider a similar classification, in the holomorphic context, of instantons on some of the next spaces in the hierarchy, the ALF multi-Taub-NUT manifolds, showing how they tie in to the bow solutions to Nahm’s equations via the Nahm correspondence. Recently Nakajima and Takayama constructed the Coulomb branch of the moduli space of vacua of a quiver gauge theory, tying them to the same space of bow solutions. One can view our construction as describing the same manifold as the Higgs branch of the mirror gauge theory as described by Cherkis, O’Hara and Saemann. Our construction also yields the monad construction of holomorphic instanton bundles on the multi-Taub-NUT space for any classical compact Lie structure group.

scholarly journals Connecting 5d Higgs branches via Fayet-Iliopoulos deformations

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Marieke van Beest ◽  
Simone Giacomelli
Keyword(s):  
Mirror Symmetry ◽  
Weak Coupling ◽  
Gauge Theories ◽  
Field Theories ◽  
Local Version ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Mirror Map

Abstract We describe how the geometry of the Higgs branch of 5d superconformal field theories is transformed under movement along the extended Coulomb branch. Working directly with the (unitary) magnetic quiver, we demonstrate a correspondence between Fayet-Iliopoulos deformations in 3d and 5d mass deformations. When the Higgs branch has multiple cones, characterised by a collection of magnetic quivers, the mirror map is not globally well-defined, however we are able to utilize the correspondence to establish a local version of mirror symmetry. We give several detailed examples of deformations, including decouplings and weak-coupling limits, in (Dn, Dn) conformal matter theories, TN theory and its parent PN, for which we find new Lagrangian descriptions given by quiver gauge theories with fundamental and anti-symmetric matter.

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.

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