scholarly journals Conformal manifolds and 3d mirrors of Argyres-Douglas theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Federico Carta ◽  
Simone Giacomelli ◽  
Noppadol Mekareeya ◽  
Alessandro Mininno
Keyword(s):  
Field Theories ◽  
Lagrangian Description ◽  
Important Class ◽  
Superconformal Field Theories ◽  
Conformal Manifolds

Abstract Argyres-Douglas theories constitute an important class of superconformal field theories in 4d. The main focus of this paper is on two infinite families of such theories, known as $$ {D}_p^b $$ D p b (SO(2N)) and (Am, Dn). We analyze in depth their conformal manifolds. In doing so we encounter several theories of class 𝒮 of twisted Aodd, twisted Aeven and twisted D types associated with a sphere with one twisted irregular puncture and one twisted regular puncture. These models include Dp(G) theories, with G non-simply-laced algebras. A number of new properties of such theories are discussed in detail, along with new SCFTs that arise from partially closing the twisted regular puncture. Moreover, we systematically present the 3d mirror theories, also known as the magnetic quivers, for the $$ {D}_p^b $$ D p b (SO(2N)) theories, with p ≥ b, and the (Am, Dn) theories, with arbitrary m and n. We also discuss the 3d reduction and mirror theories of certain $$ {D}_p^b $$ D p b (SO(2N)) theories, with p < b, where the former arises from gauging topological symmetries of some $$ {T}_p^{\sigma } $$ T p σ [SO(2M)] theories that are not manifest in the Lagrangian description of the latter.

scholarly journals A CFT distance conjecture

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Eric Perlmutter ◽  
Leonardo Rastelli ◽  
Cumrun Vafa ◽  
Irene Valenzuela
Keyword(s):  
Spin Symmetry ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Higher Spin ◽  
Spin Fields ◽  
Local Operators ◽  
Conformal Manifolds

Abstract We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

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.

Modular invariance in N=2 superconformal field theories

1987 ◽  
Vol 195 (2) ◽  
pp. 202-208 ◽  
Author(s):  
Francesco Ravanini ◽  
Sung-Kil Yang
Keyword(s):  
Field Theories ◽  
Modular Invariance ◽  
Superconformal Field Theories

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

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.

scholarly journals Complete prepotential for 5d $$ \mathcal{N} $$ = 1 superconformal field theories

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Sung-Soo Kim ◽  
Kimyeong Lee ◽  
Futoshi Yagi
Keyword(s):  
Field Theories ◽  
Superconformal Field Theories

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 Chiral correlators in $$ \mathcal{N} $$ = 2 superconformal quivers

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Galvagno ◽  
Michelangelo Preti
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Flat Space ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
The Matrix ◽  
Superspace Formalism ◽  
Model Approach

Abstract We consider a family of $$ \mathcal{N} $$ N = 2 superconformal field theories in four dimensions, defined as ℤq orbifolds of $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the $$ \mathcal{N} $$ N = 1 superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of N , exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from $$ \mathcal{N} $$ N = 4 only at high orders in perturbation theory.

scholarly journals Fibre-base duality of 5d KK theories

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.

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.

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