scholarly journals S-fold magnetic quivers

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Antoine Bourget ◽  
Simone Giacomelli ◽  
Julius F. Grimminger ◽  
Amihay Hanany ◽  
Marcus Sperling ◽  
...  
Keyword(s):  
Moduli Spaces ◽  
Global Symmetry ◽  
Four Dimensions ◽  
Hasse Diagrams ◽  
Mass Deformation

Abstract Magnetic quivers and Hasse diagrams for Higgs branches of rank r 4d $$ \mathcal{N} $$ N = 2 SCFTs arising from ℤℓ$$ \mathcal{S} $$ S -fold constructions are discussed. The magnetic quivers are derived using three different methods: 1) Using clues like dimension, global symmetry, and the folding parameter ℓ to guess the magnetic quiver. 2) From 6d $$ \mathcal{N} $$ N = (1, 0) SCFTs as UV completions of 5d marginal theories, and specific FI deformations on their magnetic quiver, which is further folded by ℤℓ. 3) From T-duality of Type IIA brane systems of 6d $$ \mathcal{N} $$ N = (1, 0) SCFTs and explicit mass deformation of the resulting brane web followed by ℤℓ folding. A choice of the ungauging scheme, either on a long node or on a short node, yields two different moduli spaces related by an orbifold action, thus suggesting a larger set of SCFTs in four dimensions than previously expected.

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 Superconformal multi-black hole moduli spaces in four dimensions

2002 ◽  
Vol 2002 (04) ◽  
pp. 003-003 ◽  
Author(s):  
Alexander Maloney ◽  
Marcus Spradlin ◽  
Andrew Strominger
Keyword(s):  
Black Hole ◽  
Moduli Spaces ◽  
Four Dimensions

scholarly journals Moduli spaces of non-geometric type II/heterotic dual pairs

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Yoan Gautier ◽  
Dan Israël
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Type Ii ◽  
Duality Group ◽  
Dual Pairs ◽  
Perturbative Correction ◽  
Singularity Structure ◽  
Four Dimensions ◽  
Geometric Type ◽  
Perturbative Corrections

Abstract We study the moduli spaces of heterotic/type II dual pairs in four dimensions with $$ \mathcal{N} $$ N = 2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector multiplets moduli space receives perturbative corrections in the heterotic description only, and non- perturbative correction in both descriptions. We derive explicitely the perturbative corrections to the heterotic four-dimensional prepotential, using the knowledge of its singularity structure and of the heterotic perturbative duality group. We also derive the exact hypermultiplets moduli space, that receives corrections neither in the string coupling nor in α′.

scholarly journals Non-invertible global symmetries and completeness of the spectrum

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Ben Heidenreich ◽  
Jacob McNamara ◽  
Miguel Montero ◽  
Matthew Reece ◽  
Tom Rudelius ◽  
...  
Keyword(s):  
Gauge Theories ◽  
Cosmic Strings ◽  
Global Symmetry ◽  
Complete Spectrum ◽  
Abelian Gauge ◽  
Analogous Statement ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Chern Simons ◽  
General Gauge

Abstract It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings.

scholarly journals N = 2* Yang-Mills on the Lattice

2018 ◽  
Vol 175 ◽  
pp. 08019
Author(s):  
Anosh Joseph
Keyword(s):  
Nonzero Temperature ◽  
Gauge Invariant ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Theory ◽  
Hypercubic Lattice ◽  
Thermal Phase Transition ◽  
Thermal Phase ◽  
Lattice Construction ◽  
Mass Deformation

The N = 2* Yang-Mills theory in four dimensions is a non-conformal theory that appears as a mass deformation of maximally supersymmetric N = 4 Yang-Mills theory. This theory also takes part in the AdS/CFT correspondence and its gravity dual is type IIB supergravity on the Pilch-Warner background. The finite temperature properties of this theory have been studied recently in the literature. It has been argued that at large N and strong coupling this theory exhibits no thermal phase transition at any nonzero temperature. The low temperature N = 2* plasma can be compared to the QCD plasma. We provide a lattice construction of N = 2* Yang-Mills on a hypercubic lattice starting from the N = 4 gauge theory. The lattice construction is local, gauge-invariant, free from fermion doubling problem and preserves a part of the supersymmetry. This nonperturbative formulation of the theory can be used to provide a highly nontrivial check of the AdS/CFT correspondence in a non-conformal theory.

scholarly journals Refined large N duality for knots

2020 ◽  
pp. 2041001
Author(s):  
Masaya Kameyama ◽  
Satoshi Nawata
Keyword(s):  
Moduli Spaces ◽  
Bound States ◽  
Simons Theory ◽  
Global Symmetry ◽  
Torus Knots ◽  
Torus Knot ◽  
Large N ◽  
Bps Invariants ◽  
Bps States ◽  
Chern Simons

We formulate large [Formula: see text] duality of [Formula: see text] refined Chern–Simons theory with a torus knot/link in [Formula: see text]. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the [Formula: see text]-background. This form enables us to relate refined Chern–Simons invariants of a torus knot/link in [Formula: see text] to refined BPS invariants in the resolved conifold. Assuming that the extra [Formula: see text] global symmetry acts on BPS states trivially, the duality predicts graded dimensions of cohomology groups of moduli spaces of M2–M5 bound states associated to a torus knot/link in the resolved conifold. Thus, this formulation can be also interpreted as a positivity conjecture of refined Chern–Simons invariants of torus knots/links. We also discuss about an extension to non-torus knots.

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 On the compactification of 5d theories to 4d

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Mario Martone ◽  
Gabi Zafrir
Keyword(s):  
Strong Coupling ◽  
Moduli Spaces ◽  
Integrable Systems ◽  
Strong Coupling Limit ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
General Properties ◽  
Rank 2 ◽  
Mass Deformation

Abstract We study general properties of the mapping between 5d and 4d superconformal field theories (SCFTs) under both twisted circle compactification and tuning of local relevant deformation and CB moduli. After elucidating in generality when a 5d SCFT reduces to a 4d one, we identify nearly all $$ \mathcal{N} $$ N = 1 5d SCFT parents of rank-2 4d$$ \mathcal{N} $$ N = 2 SCFTs. We then use this result to map out the mass deformation trajectories among the rank-2 theories in 4d. This can be done by first understanding the mass deformations of the 5d$$ \mathcal{N} $$ N = 1 SCFTs and then map them to 4d. The former task can be easily achieved by exploiting the fact that the 5d parent theories can be obtained as the strong coupling limit of Lagrangian theories, and the latter by understanding the behavior under compactification. Finally we identify a set of general criteria that 4d moduli spaces of vacua have to satisfy when the corresponding SCFTs are related by mass deformations and check that all our RG-flows satisfy them. Many of the mass deformations we find are not visible from the corresponding complex integrable systems.

scholarly journals Compactifying 5d superconformal field theories to 3d

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Matteo Sacchi ◽  
Orr Sela ◽  
Gabi Zafrir
Keyword(s):  
Riemann Surfaces ◽  
Recent Progress ◽  
Three Dimensions ◽  
Field Theories ◽  
Global Symmetry ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
The One ◽  
Conformal Manifolds ◽  
Chern Simons

Abstract Building on recent progress in the study of compactifications of 6d (1, 0) superconformal field theories (SCFTs) on Riemann surfaces to 4d$$ \mathcal{N} $$ N = 1 theories, we initiate a systematic study of compactifications of 5d$$ \mathcal{N} $$ N = 1 SCFTs on Riemann surfaces to 3d$$ \mathcal{N} $$ N = 2 theories. Specifically, we consider the compactification of the so-called rank 1 Seiberg $$ {E}_{N_f+1} $$ E N f + 1 SCFTs on tori and tubes with flux in their global symmetry, and put the resulting 3d theories to various consistency checks. These include matching the (usually enhanced) IR symmetry of the 3d theories with the one expected from the compactification, given by the commutant of the flux in the global symmetry of the corresponding 5d SCFT, and identifying the spectrum of operators and conformal manifolds predicted by the 5d picture. As the models we examine are in three dimensions, we encounter novel elements that are not present in compactifications to four dimensions, notably Chern-Simons terms and monopole superpotentials, that play an important role in our construction. The methods used in this paper can also be used for the compactification of any other 5d SCFT that has a deformation leading to a 5d gauge theory.

scholarly journals Supersymmetry breaking deformations and phase transitions in five dimensions

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Matteo Bertolini ◽  
Francesco Mignosa
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Phase Transitions ◽  
Supersymmetry Breaking ◽  
Gauge Coupling ◽  
Global Symmetry ◽  
Five Dimensions ◽  
Yang Mills ◽  
New Phase ◽  
Mass Deformation

Abstract We analyze a recently proposed supersymmetry breaking mass deformation of the E1 superconformal fixed point in five dimensions which, at weak gauge coupling, leads to pure SU(2) Yang-Mills and which was conjectured to lead to an interacting CFT at strong coupling. We provide an explicit geometric construction of the deformation using brane-web techniques and show that for large enough gauge coupling a global symmetry is spontaneously broken and the theory enters a new phase which, at infinite coupling, displays an instability. The Yang-Mills and the symmetry broken phases are separated by a phase transition. Depending on the structure of the potential, this can be first or second order.

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