scholarly journals Coulomb branch ofN=1supersymmetricSU(Nc)×SU(Nc)gauge theories

1998 ◽  
Vol 57 (4) ◽  
pp. 2537-2542 ◽  
Author(s):  
Martin Gremm
Keyword(s):  
Gauge Theories ◽  
Coulomb Branch

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 M and F Theory Instantons, N = 1 Supersymmetry and Fractional Topological Charge

1997 ◽  
Vol 12 (28) ◽  
pp. 5141-5149 ◽  
Author(s):  
César Gómez ◽  
Rafael Hernández
Keyword(s):  
Topological Charge ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Singular Points ◽  
Coulomb Branch ◽  
Supersymmetric Gauge Theories ◽  
Dimensional Theory ◽  
Pure Gauge ◽  
Supersymmetric Gauge

We analyze instanton generated superpotentials for three-dimensional N = 2 supersymmetric gauge theories obtained by compactifying on S1 N = 1 four-dimensional theories. For SU(2) with Nf = 1, we find that the vacua in the decompactification limit is given by the singular points of the Coulomb branch of the N = 2 four-dimensional theory (we also consider the massive case). The decompactification limit of the superpotential for pure gauge theories without chiral matter is interpreted in terms of 't Hooft's fractional instanton amplitudes.

scholarly journals PREPOTENTIALS OF N=2 SUPERSYMMETRIC GAUGE THEORIES AND SOLITON EQUATIONS

1996 ◽  
Vol 11 (02) ◽  
pp. 131-138 ◽  
Author(s):  
TOHRU EGUCHI ◽  
SUNG-KIL YANG
Keyword(s):  
Gauge Theories ◽  
Scalar Fields ◽  
Vector Multiplet ◽  
Coulomb Branch ◽  
Supersymmetric Gauge Theories ◽  
Expectation Values ◽  
Soliton Equations ◽  
Supersymmetric Gauge ◽  
Β Function ◽  
The One

Using recently proposed soliton equations we derive a basic identity for the scaling violation of N=2 supersymmetric gauge theories Σiai∂F/∂ai−2F=8πib1u. Here F is the prepotential, ai’s are the expectation values of the scalar fields in the vector multiplet, u=1/2 Tr<ϕ2> and b1 is the coefficient of the one-loop β-function. This equation holds in the Coulomb branch of all N=2 supersymmetric gauge theories coupled with massless matter.

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.

scholarly journals Revisiting the multi-monopole point of SU(N) $$ \mathcal{N} $$ = 2 gauge theory in four dimensions

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Eric D’Hoker ◽  
Thomas T. Dumitrescu ◽  
Efrat Gerchkovitz ◽  
Emily Nardoni
Keyword(s):  
Gauge Theory ◽  
Supersymmetry Breaking ◽  
Integrable Systems ◽  
Gauge Theories ◽  
Magnetic Monopoles ◽  
Coulomb Branch ◽  
Four Dimensions ◽  
Broad Agreement ◽  
Exact Agreement ◽  
Soft Supersymmetry Breaking

Abstract Motivated by applications to soft supersymmetry breaking, we revisit the expansion of the Seiberg-Witten solution around the multi-monopole point on the Coulomb branch of pure SU(N) $$ \mathcal{N} $$ N = 2 gauge theory in four dimensions. At this point N − 1 mutually local magnetic monopoles become massless simultaneously, and in a suitable duality frame the gauge couplings logarithmically run to zero. We explicitly calculate the leading threshold corrections to this logarithmic running from the Seiberg-Witten solution by adapting a method previously introduced by D’Hoker and Phong. We compare our computation to existing results in the literature; this includes results specific to SU(2) and SU(3) gauge theories, the large-N results of Douglas and Shenker, as well as results obtained by appealing to integrable systems or topological strings. We find broad agreement, while also clarifying some lingering inconsistencies. Finally, we explicitly extend the results of Douglas and Shenker to finite N , finding exact agreement with our first calculation.

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 Localization and duality for ABJM latitude Wilson loops

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Luca Griguolo ◽  
Luigi Guerrini ◽  
Itamar Yaakov
Keyword(s):  
Quantum Mechanics ◽  
Wilson Loop ◽  
Gauge Theories ◽  
Bound State ◽  
Three Dimensions ◽  
Wilson Loops ◽  
Vortex Loop ◽  
Coulomb Branch ◽  
Vortex Loops ◽  
Chern Simons

Abstract We investigate several aspects of BPS latitude Wilson loops in gauge theories in three dimensions with $$ \mathcal{N} $$ N ≥ 4 supersymmetry. We derive a matrix model for the bosonic latitude Wilson loop in ABJM using supersymmetric localization, and show how to extend the computation to more general Chern-Simons-matter theories. We then define latitude type Wilson and vortex loop operators in theories without Chern-Simons terms, and explore a connection to the recently derived superalgebra defining local Higgs and Coulomb branch operators in these theories. Finally, we identify a BPS loop operator dual to the bosonic latitude Wilson loop which is a novel bound state of Wilson and vortex loops, defined using a worldvolume supersymmetric quantum mechanics.

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