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 (5d RG-flow) trees in the tropical rain forest

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Marieke van Beest ◽  
Antoine Bourget ◽  
Julius Eckhard ◽  
Sakura Schäfer-Nameki
Keyword(s):  
Large Class ◽  
Rain Forest ◽  
Tropical Rain Forest ◽  
Field Theories ◽  
Flavor Symmetry ◽  
Superconformal Field Theories ◽  
Hasse Diagrams ◽  
Flavor Symmetries ◽  
Rank 2 ◽  
Mass Deformation

Abstract 5d superconformal field theories (SCFTs) can be obtained from 6d SCFTs by circle compactification and mass deformation. Successive decoupling of hypermultiplet matter and RG-flow generates a decoupling tree of descendant 5d SCFTs. In this paper we determine the magnetic quivers and Hasse diagrams, that encode the Higgs branches of 5d SCFTs, for entire decoupling trees. Central to this undertaking is the approach in [1], which, starting from the generalized toric polygons (GTPs) dual to 5-brane webs/tropical curves, provides a systematic and succinct derivation of magnetic quivers and their Hasse diagrams. The decoupling in the GTP description is straightforward, and generalizes the standard flop transitions of curves in toric polygons. We apply this approach to a large class of 5d KK-theories, and compute the Higgs branches for their descendants. In particular we determine the decoupling tree for all rank 2 5d SCFTs. For each tree, we also identify the flavor symmetry algebras from the magnetic quivers, including non-simply-laced flavor symmetries.

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 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.

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 Twisted circle compactifications of 6d SCFTs

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Lakshya Bhardwaj ◽  
Patrick Jefferson ◽  
Hee-Cheol Kim ◽  
Houri-Christina Tarazi ◽  
Cumrun Vafa
Keyword(s):  
Field Theories ◽  
Geometric Description ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Physical Data ◽  
Algebraic Description ◽  
Genus One ◽  
M Theory ◽  
Kaluza Klein

Abstract We study 6d superconformal field theories (SCFTs) compactified on a circle with arbitrary twists. The theories obtained after compactification, often referred to as 5d Kaluza-Klein (KK) theories, can be viewed as starting points for RG flows to 5d SCFTs. According to a conjecture, all 5d SCFTs can be obtained in this fashion. We compute the Coulomb branch prepotential for all 5d KK theories obtainable in this manner and associate to these theories a smooth local genus one fibered Calabi-Yau threefold in which is encoded information about all possible RG flows to 5d SCFTs. These Calabi-Yau threefolds provide hitherto unknown M-theory duals of F-theory configurations compactified on a circle with twists. For certain exceptional KK theories that do not admit a standard geometric description we propose an algebraic description that appears to retain the properties of the local Calabi-Yau threefolds necessary to determine RG flows to 5d SCFTs, along with other relevant physical data.

scholarly journals New $$ \mathcal{N} $$ = 2 superconformal field theories from $$ \mathcal{S} $$-folds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Simone Giacomelli ◽  
Carlo Meneghelli ◽  
Wolfger Peelaers
Keyword(s):  
Moduli Spaces ◽  
Field Theories ◽  
Coulomb Branch ◽  
Infinite Class ◽  
Superconformal Field Theories ◽  
New Class

Abstract We study the four-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories that describe D3-branes probing the recently constructed $$ \mathcal{N} $$ N = 2 $$ \mathcal{S} $$ S -folds in F-theory. We introduce a novel, infinite class of superconformal field theories related to $$ \mathcal{S} $$ S -fold theories via partial Higgsing. We determine several properties of both the $$ \mathcal{S} $$ S -fold models and this new class of theories, including their central charges, Coulomb branch spectrum, and moduli spaces of vacua, by bringing to bear an array of field-theoretical techniques, to wit, torus-compactifications of six-dimensional $$ \mathcal{N} $$ N = (1, 0) theories, class $$ \mathcal{S} $$ S technology, and the SCFT/VOA correspondence.

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 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 Weyl invariant Jacobi forms along Higgsing trees

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Zhihao Duan ◽  
David Jaramillo Duque ◽  
Amir-Kian Kashani-Poor
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Gauge Theories ◽  
Topological String ◽  
Field Theories ◽  
Jacobi Forms ◽  
Superconformal Field Theories ◽  
Counting Functions ◽  
String Techniques

Abstract Using topological string techniques, we compute BPS counting functions of 5d gauge theories which descend from 6d superconformal field theories upon circle compactification. Such theories are naturally organized in terms of nodes of Higgsing trees. We demonstrate that the specialization of the partition function as we move from the crown to the root of a tree is determined by homomorphisms between rings of Weyl invariant Jacobi forms. Our computations are made feasible by the fact that symmetry enhancements of the gauge theory which are manifest on the massless spectrum are inherited by the entire tower of BPS particles. In some cases, these symmetry enhancements have a nice relation to the 1-form symmetry of the associated gauge theory.

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