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

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.

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

Journal of High Energy Physics ◽

10.1007/jhep11(2020)124 ◽

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.

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Flavor symmetry of 5d SCFTs. Part I. General setup

Journal of High Energy Physics ◽

10.1007/jhep09(2021)186 ◽

2021 ◽

Vol 2021 (9) ◽

Author(s):

Lakshya Bhardwaj

Keyword(s):

Large Class ◽

Field Theories ◽

Flavor Symmetry ◽

Superconformal Field Theories ◽

Compact Surfaces ◽

M Theory ◽

General Setup ◽

General Method

Abstract A large class of 5d superconformal field theories (SCFTs) can be constructed by integrating out BPS particles from 6d SCFTs compactified on a circle. We describe a general method for extracting the flavor symmetry of any 5d SCFT lying in this class. For this purpose, we utilize the geometric engineering of 5d$$ \mathcal{N} $$ N = 1 theories in M-theory, where the flavor symmetry is encoded in a collection of non-compact surfaces.

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On the compactification of 5d theories to 4d

Journal of High Energy Physics ◽

10.1007/jhep08(2021)017 ◽

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.

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5d and 4d SCFTs: canonical singularities, trinions and S-dualities

Journal of High Energy Physics ◽

10.1007/jhep05(2021)274 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Cyril Closset ◽

Simone Giacomelli ◽

Sakura Schäfer-Nameki ◽

Yi-Nan Wang

Keyword(s):

String Theory ◽

Field Theories ◽

Flavor Symmetry ◽

Crepant Resolution ◽

Superconformal Field Theories ◽

Hypersurface Singularities ◽

Canonical Singularities ◽

Type Iib String Theory ◽

M Theory

Abstract Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain residual terminal singularities and/or 3-cycles. We focus on a certain class of ‘trinion’ singularities which exhibit these properties. In Type IIB, they give rise to 4d $$ \mathcal{N} $$ N = 2 SCFTs that we call $$ {D}_p^b $$ D p b (G)-trinions, which are marginal gaugings of three SCFTs with G flavor symmetry. In order to understand the 5d physics of these trinion singularities in M-theory, we reduce these 4d and 5d SCFTs to 3d $$ \mathcal{N} $$ N = 4 theories, thus determining the electric and magnetic quivers (or, more generally, quiverines). In M-theory, residual terminal singularities give rise to free sectors of massless hypermultiplets, which often are discretely gauged. These free sectors appear as ‘ugly’ components of the magnetic quiver of the 5d SCFT. The 3-cycles in the crepant resolution also give rise to free hypermultiplets, but their physics is more subtle, and their presence renders the magnetic quiver ‘bad’. We propose a way to redeem the badness of these quivers using a class $$ \mathcal{S} $$ S realization. We also discover new S-dualities between different $$ {D}_p^b $$ D p b (G)-trinions. For instance, a certain E8 gauging of the E8 Minahan-Nemeschansky theory is S-dual to an E8-shaped Lagrangian quiver SCFT.

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Fibre-base duality of 5d KK theories

Journal of High Energy Physics ◽

10.1007/jhep05(2021)200 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Andreas P. Braun ◽

Jin Chen ◽

Babak Haghighat ◽

Marcus Sperling ◽

Shuhang Yang

Keyword(s):

Field Theory ◽

Field Theories ◽

Quantum Field ◽

Explicit Dependence ◽

Superconformal Field Theories ◽

Study Circle ◽

Rank 2 ◽

M Theory ◽

Kaluza Klein ◽

Theory Interpretation

Abstract We study circle compactifications of 6d superconformal field theories giving rise to 5d rank 1 and rank 2 Kaluza-Klein theories. We realise the resulting theories as M-theory compactifications on local Calabi-Yau 3-folds and match the prepotentials from geometry and field theory. One novelty in our approach is that we include explicit dependence on bare gauge couplings and mass parameters in the description which in turn leads to an accurate parametrisation of the prepotential including all parameters of the field theory. We find that the resulting geometries admit “fibre-base” duality which relates their six-dimensional origin with the purely five-dimensional quantum field theory interpretation. The fibre-base duality is realised simply by swapping base and fibre curves of compact surfaces in the local Calabi-Yau which can be viewed as the total space of the anti-canonical bundle over such surfaces. Our results show that such swappings precisely occur for surfaces with a zero self-intersection of the base curve and result in an exchange of the 6d and 5d pictures.

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M5-brane sources, holography, and Argyres-Douglas theories

Journal of High Energy Physics ◽

10.1007/jhep11(2021)140 ◽

2021 ◽

Vol 2021 (11) ◽

Author(s):

Ibrahima Bah ◽

Federico Bonetti ◽

Ruben Minasian ◽

Emily Nardoni

Keyword(s):

Warped Product ◽

Central Charge ◽

Field Theories ◽

Internal Space ◽

Flavor Symmetry ◽

Perfect Agreement ◽

Strongly Coupled ◽

Superconformal Field Theories ◽

Holographic Duals ◽

M Theory

Abstract We initiate a study of the holographic duals of a class of four-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories that are engineered by wrapping M5-branes on a sphere with an irregular puncture. These notably include the strongly-coupled field theories of Argyres-Douglas type. Our solutions are obtained in 7d gauged supergravity, where they take the form of a warped product of AdS5 and a “half-spindle.” The irregular puncture is modeled by a localized M5-brane source in the internal space of the gravity duals. Our solutions feature a realization of supersymmetry that is distinct from the usual topological twist, as well as an interesting Stückelberg mechanism involving the gauge field associated to a generator of the isometry algebra of the internal space. We check the proposed duality by computing the holographic central charge, the flavor symmetry central charge, and the dimensions of various supersymmetric probe M2-branes, and matching these with the dual Argyres-Douglas field theories. Furthermore, we compute the large-N ’t Hooft anomalies of the field theories using anomaly inflow methods in M-theory, and find perfect agreement with the proposed duality.

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Non-simply-connected symmetries in 6D SCFTs

Journal of High Energy Physics ◽

10.1007/jhep10(2020)173 ◽

2020 ◽

Vol 2020 (10) ◽

Cited By ~ 1

Author(s):

Markus Dierigl ◽

Paul-Konstantin Oehlmann ◽

Fabian Ruehle

Keyword(s):

Abelian Group ◽

Large Class ◽

Group Structure ◽

Field Theories ◽

Symmetry Groups ◽

Superconformal Field Theories ◽

Weil Group ◽

Superconformal Theories ◽

Simply Connected ◽

M Theory

Abstract Six-dimensional $$ \mathcal{N} $$ N = (1, 0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This allows us to identify the full non-Abelian group structure rather than just the algebra. The presence of torsion also modifies the center of the symmetry groups and the matter representations that can appear. This in turn affects the tensor branch of these theories. We analyze this change for a large class of superconformal theories with torsion and explicitly construct their tensor branches. Finally, we elaborate on the connection to the dual heterotic and M-theory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons.

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THE SUPERCONFORMAL MASTER EQUATION

International Journal of Modern Physics A ◽

10.1142/s0217751x92000429 ◽

1992 ◽

Vol 07 (05) ◽

pp. 947-972 ◽

Cited By ~ 7

Author(s):

A. GIVEON ◽

M. B. HALPERN ◽

E. B. KIRITSIS ◽

N. A. OBERS

Keyword(s):

Master Equation ◽

Large Class ◽

Field Theories ◽

Signed Graphs ◽

Superconformal Field Theories ◽

Superconformal Symmetry ◽

High Level

We obtain the superconformal master equation, which collects the superconformal solutions of the Virasoro master equation on gx × SO (p, q)1. The associated super C-function and super C-theorem are also obtained. A high-level expansion of the superconformal ansatz { SO (n) diag × SO [ dim SO (n)]1}N=1 shows a large class of new, generically irrational superconformal field theories with a three-form living on the signed graphs of order n. The extension to general N = 2 superconformal symmetry is also given.

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Bootstrapping BPS spectra of 5d/6d field theories

Journal of High Energy Physics ◽

10.1007/jhep04(2021)161 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Hee-Cheol Kim ◽

Minsung Kim ◽

Sung-Soo Kim ◽

Ki-Hong Lee

Keyword(s):

Gauge Theory ◽

Systematic Approach ◽

Field Theories ◽

Geometric Description ◽

Superconformal Field Theories ◽

Significant Generalization ◽

Rank 2 ◽

Bps Spectrum ◽

Chern Simons ◽

Kaluza Klein

Abstract We propose a systematic approach to computing the BPS spectrum of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka’s blowup equations. We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup $$ \hat{\mathrm{\mathbb{C}}} $$ ℂ ̂ 2 and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. We employ our method to compute BPS spectra of all rank-1 and rank-2 5d Kaluza-Klein (KK) theories descending from 6d $$ \mathcal{N} $$ N = (1, 0) superconformal field theories (SCFTs) compactified on a circle with/without twist. We also discuss various 5d SCFTs and KK theories of higher ranks, which include a few exotic cases such as new rank-1 and rank-2 5d SCFTs engineered with frozen singularity as well as the 5d SU(3)8 gauge theory currently having neither a brane web nor a smooth shrinkable geometric description. The results serve as non-trivial checks for a large class of non-trivial dualities among 5d theories and also as independent evidences for the existence of certain exotic theories.

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Supersymmetric Janus solutions in $$\omega $$-deformed $$N=8$$ gauged supergravity

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09582-y ◽

2021 ◽

Vol 81 (9) ◽

Author(s):

Parinya Karndumri ◽

Chawakorn Maneerat

Keyword(s):

Large Class ◽

Critical Points ◽

Domain Walls ◽

Field Theories ◽

Two Dimensional ◽

Superconformal Field Theories

AbstractWe give a large class of supersymmetric Janus solutions in $$\omega $$ ω -deformed (dyonic) SO(8) maximal gauged supergravity with $$\omega =\frac{\pi }{8}$$ ω = π 8 . Unlike the purely electric counterpart, the dyonic SO(8) gauged supergravity exhibits a richer structure of $$AdS_4$$ A d S 4 vacua with $$N=8,2,1,1$$ N = 8 , 2 , 1 , 1 supersymmetries and SO(8), U(3), $$G_2$$ G 2 and SU(3) symmetries, respectively. Similarly, domain walls interpolating among these critical points show a very rich structure as well. In this paper, we show that this gauged supergravity also accommodates a number of interesting supersymmetric Janus solutions in the form of $$AdS_3$$ A d S 3 -sliced domain walls asymptotically interpolating between the aforementioned $$AdS_4$$ A d S 4 geometries. These solutions could be holographically interpreted as two-dimensional conformal defects within the superconformal field theories (SCFTs) of ABJM type dual to the $$AdS_4$$ A d S 4 vacua. We also give a class of solutions interpolating among the SO(8), $$G_2$$ G 2 and U(3) $$AdS_4$$ A d S 4 vacua in the case of $$\omega =0$$ ω = 0 which have not previously appeared in the presently known Janus solutions of electric SO(8) gauged supergravity.

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