scholarly journals 3d mirrors of the circle reduction of twisted A2N theories of class S

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Emanuele Beratto ◽  
Simone Giacomelli ◽  
Noppadol Mekareeya ◽  
Matteo Sacchi
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Strong Support ◽  
Three Dimensions ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Group Flow ◽  
Mirror Theory

Abstract Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the circle reduction of twisted A2N theories of class S in four dimensions. Although these quivers bear a resemblance to the star-shaped quivers previously studied in the literature, they contain unitary, symplectic and special orthogonal gauge groups, along with hypermultiplets in the fundamental representation. The vacuum moduli spaces of these quiver theories are studied in detail. The Coulomb branch Hilbert series of the mirror theory can be matched with that of the Higgs branch of the corresponding four dimensional theory, providing a non-trivial check of our proposal. Moreover various deformations by mass and Fayet-Iliopoulos terms of such quiver theories are investigated. The fact that several of them flow to expected theories also gives another strong support for the proposal. Utilising the mirror quiver description, we discover a new supersymmetry enhancement renormalisation group flow.

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 1-form symmetry, isolated $$ \mathcal{N} $$ = 2 SCFTs, and Calabi-Yau threefolds

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Matthew Buican ◽  
Hongliang Jiang
Keyword(s):  
Flavor Symmetry ◽  
Quantum Field ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Gauge Groups ◽  
Complex Dimension ◽  
Hypersurface Singularities ◽  
Chiral Ring ◽  
Type Iib String Theory ◽  
Scaling Dimension

Abstract We systematically study 4D $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in ℂ4. We show that if a theory in this class has no $$ \mathcal{N} $$ N = 2-preserving exactly marginal deformation (i.e., the theory is isolated as an $$ \mathcal{N} $$ N = 2 SCFT), then it has no 1-form symmetry. This situation is somewhat reminiscent of 1-form symmetry and decomposition in 2D quantum field theory. Moreover, our result suggests that, for theories arising from IHSs, 1-form symmetries originate from gauge groups (with vanishing beta functions). One corollary of our discussion is that there is no 1-form symmetry in IHS theories that have all Coulomb branch chiral ring generators of scaling dimension less than two. In terms of the a and c central charges, this condition implies that IHS theories satisfying $$ a<\frac{1}{24}\left(15r+2f\right) $$ a < 1 24 15 r + 2 f and $$ c<\frac{1}{6}\left(3r+f\right) $$ c < 1 6 3 r + f (where r is the complex dimension of the Coulomb branch, and f is the rank of the continuous 0-form flavor symmetry) have no 1-form symmetry. After reviewing the 1-form symmetries of other classes of theories, we are motivated to conjecture that general interacting 4D $$ \mathcal{N} $$ N = 2 SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry.

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 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 Magnetic lattices for orthosymplectic quivers

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Antoine Bourget ◽  
Julius F. Grimminger ◽  
Amihay Hanany ◽  
Rudolph Kalveks ◽  
Marcus Sperling ◽  
...  
Keyword(s):  
Gauge Group ◽  
Moduli Spaces ◽  
Hilbert Series ◽  
Matter Content ◽  
Coulomb Branch ◽  
Gauge Groups ◽  
Orbit Closures ◽  
Littlewood Polynomials ◽  
Monopole Operators ◽  
Crucial Ingredient

Abstract For any gauge theory, there may be a subgroup of the gauge group which acts trivially on the matter content. While many physical observables are not sensitive to this fact, the choice of the precise gauge group becomes crucial when the magnetic lattice of the theory is considered. This question is addressed in the context of Coulomb branches for 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories, which are moduli spaces of dressed monopole operators. We compute the Coulomb branch Hilbert series of many unitary-orthosymplectic quivers for different choices of gauge groups, including diagonal quotients of the product gauge group of individual factors, where the quotient is by a trivially acting subgroup. Choosing different such diagonal groups results in distinct Coulomb branches, related as orbifolds. Examples include nilpotent orbit closures of the exceptional E-type algebras and magnetic quivers that arise from brane physics. This includes Higgs branches of theories with 8 supercharges in dimensions 4, 5, and 6. A crucial ingredient in the calculation of exact refined Hilbert series is the alternative construction of unframed magnetic quivers from resolved Slodowy slices, whose Hilbert series can be derived from Hall-Littlewood polynomials.

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 𝒩 = 2 dualities and Z-extremization in three dimensions

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Brian Willett ◽  
Itamar Yaakov
Keyword(s):  
Three Dimensions ◽  
Partition Functions ◽  
Recent Proposal ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
Seiberg Duality ◽  
Real Mass ◽  
Supersymmetric Gauge ◽  
Chern Simons

Abstract We use localization techniques to study duality in 𝒩 = 2 supersymmetric gauge theories in three dimensions. Specifically, we consider a duality due to Aharony involving unitary and symplectic gauge groups, which is similar to Seiberg duality in four dimensions, as well as related dualities involving Chern-Simons terms. These theories have the possibility of non trivial anomalous dimensions for the chiral multiplets and were previously difficult to examine. We use a matrix model to compute the partition functions on both sides of the duality, deformed by real mass and FI terms. The results provide strong evidence for the validity of the proposed dualities. We also comment on a recent proposal for recovering the exact IR conformal dimensions in such theories using localization.

scholarly journals The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Benjamin Assel ◽  
Stefano Cremonesi
Keyword(s):  
Fixed Points ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Singular Locus ◽  
Low Energy ◽  
Global Symmetry ◽  
Local Geometry ◽  
Coulomb Branch ◽  
Energy Theory ◽  
Mirror Theory

We derive the algebraic description of the Coulomb branch of 3d \mathcal{N}=4𝒩=4USp(2N)USp(2N) SQCD theories with N_fNf fundamental hypermultiplets and determine their low energy physics in any vacuum from the local geometry of the moduli space, identifying the interacting SCFTs which arise at singularities and possible extra free sectors. The SCFT with the largest moduli space arises at the most singular locus on the Coulomb branch. For N_f > 2NNf>2N (good theories) it sits at the origin of the conical variety as expected. For N_f =2NNf=2N we find two separate most singular points, from which the two isomorphic components of the Higgs branch of the UV theory emanate. The SCFTs sitting at any of these two vacua have only odd dimensional Coulomb branch generators, which transform under an accidental SU(2)SU(2) global symmetry. We provide a direct derivation of their moduli spaces of vacua, and propose a Lagrangian mirror theory for these fixed points. For 2 \leq N_f < 2N2≤Nf<2N the most singular locus has one or two extended components, for N_fNf odd or even, and the low energy theory involves an interacting SCFT of one of the above types, plus free twisted hypermultiplets. For N_f=0,1Nf=0,1 the Coulomb branch is smooth. We complete our analysis by studying the low energy theory at the symmetric vacuum of theories with N < N_f \le 2NN<Nf≤2N, which exhibits a local Seiberg-like duality.

scholarly journals Coulomb branch operators and mirror symmetry in three dimensions

2018 ◽  
Vol 2018 (4) ◽  
Author(s):  
Mykola Dedushenko ◽  
Yale Fan ◽  
Silviu S. Pufu ◽  
Ran Yacoby
Keyword(s):  
Mirror Symmetry ◽  
Three Dimensions ◽  
Coulomb Branch
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