3d duality with adjoint matter from 4d duality

Nii, Keita

doi:10.1007/jhep02(2015)024

Cited by 31 publications

(61 citation statements)

References 40 publications

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“…Because of the singlets and the peculiar superpotential, the qualitative behavior of the T IR is quite different from the case of adjoint-SQCD with W = Tr(φ h ) studied in the literature [26][27][28][29][30][31], both in 4d and in 3d.…”

Section: Quiver Diagramsmentioning

confidence: 75%

Abelianization and sequential confinement in 2 + 1 dimensions

Benvenuti

Giacomelli

2017

J. High Energ. Phys.

148

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Abstract:We consider the lagrangian description of Argyres-Douglas theories of type A 2N −1 , which is a SU(N ) gauge theory with an adjoint and one fundamental flavor. An appropriate reformulation allows us to map the moduli space of vacua across the duality, and to dimensionally reduce. Going down to three dimensions, we find that the adjoint SQCD "abelianizes": in the infrared it is equivalent to a N = 4 linear quiver theory. Moreover, we study the mirror dual: using a monopole duality to "sequentially confine" quivers tails with balanced nodes, we show that the mirror RG flow lands on N = 4 SQED with N flavors. These results make the supersymmetry enhancement explicit and provide a physical derivation of previous proposals for the three dimensional mirror of AD theories.

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Section: Quiver Diagramsmentioning

confidence: 75%

Abelianization and sequential confinement in 2 + 1 dimensions

Benvenuti

Giacomelli

2017

J. High Energ. Phys.

148

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“…SU (2) with 1 flavor in 3d is described by a quantum modified moduli space [15] M SU (2) tr(qq) = 1 (where M SU (2) is the basic monopole with GNO charges {+1, −1}), which is inconsistent with the F-terms of α 0 . No monopole superpotential is generated compactifying on S 1 , since the only superpotential term that can soak up the zero modes of the adjoint field φ is β 2 tr(φ 2 ), generating β 2 M SU (2) [19]. But a term β 2 M SU (2) does not satisfy the chiral ring stability criterion.…”

Section: Down To 3d: Abelianizationmentioning

confidence: 99%

Supersymmetric Gauge Theories with Decoupled Operators and Chiral Ring Stability

2017

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We propose a general way to complete supersymmetric theories with operators below the unitarity bound, adding gauge-singlet fields which enforce the decoupling of such operators. This makes it possible to perform all usual computations, and to compactify on a circle. We concentrate on a duality between an N = 1 SU (2) gauge theory and the N = 2 A3 Argyres-Douglas [1,2], mapping the moduli space and chiral ring of the completed N = 1 theory to those of the A3 model. We reduce the completed gauge theory to 3d, finding a 3d duality with N = 4 SQED with two flavors. The naive dimensional reduction is instead N = 2 SQED. Crucial is a concept of chiral ring stability, which modifies the superpotential and allows for a 3d emergent global symmetry.In gauge theories with four supercharges, many nonperturbative properties of the infrared strongly coupled fixed points are known, for instance the scaling dimensions of Sometimes a BPS operator violates the bound imposed by conformal invariance and unitarity, which in 4d (3d) is ∆ > 1 (∆ > 1 2 ). The standard lore is that the operator decouples and becomes free [6]: the infrared fixed point is described by some interacting superconformal theory (SCFT) plus a free chiral field. How to perform computations in such theories is however an open problem: it is known how to perform a/Z-extremizations [3-5] or compute supersymmetric indices/partition functions, but it is not known how to compute, for instance, the chiral ring or the moduli space of vacua.In this note we propose a prescription to re-formulate theories with decoupled operators: introduce a gaugesinglet chiral multiplet β O for each operator O violating the bound, and add the superpotential term β O O. Gauge singlet fields entering the superpotential in this way are usually said to "flip the operator O". The F-term of β O sets O = 0 in the chiral ring, there are no unitarity violations and all usual computations can be performed.This "completion" isolates the interacting sector and also allows to compactify dualities where at least one side has decoupled operators. Unitarity bounds change as we change the dimension of spacetime and what decouples in higher dimension may not decouple in lower dimension, so a compactification of dual theories without introducing the β O fields generically fails to produce a dual pair.We check the validity of our proposal focusing on a class of theories in four dimensions recently discovered in [1,2,7]: certain N = 1 gauge theories exhibit unitarity bound violations, the interacting sector is proposed to be equivalent to a well-known class of N = 2 SCFT's called Argyres-Douglas (AD) theories [8][9][10][11], which cannot have a manifestly N = 2 lagrangian description.We focus on a simple case, the A 3 AD theory, which admits an N = 1 lagrangian description in terms of an SU (2) gauge theory with an adjoint and two doublets [2].First we point out that the superpotential as written in [2,7] are inconsistent: a superpotential term must be discarded, in order to satisfy a chiral ring stability ...

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“…We discuss this issue in detail in section 5. Compactifying our theory to 3d, a monopole superpotential is generated, similarly to [16] (the monopole has four fermion zero modes and thanks to the term β 2 Trφ 2 we can soak two of them, obtaining the superpotential term β 2 M), and the 3d compactified theory is dual to U (1) with 3 flavors N = 4. Upon dropping by hand the monopole superpotential term, the resulting 3d theory is dual to U (1) with 3 flavors N = 2 with a peculiar superpotential.…”

Section: (A 1 D 4 ) In 4 Dimensionsmentioning

confidence: 99%

Lagrangians for generalized Argyres-Douglas theories

Benvenuti

Giacomelli

2017

J. High Energ. Phys.

109

162

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Abstract:We continue the study of Lagrangian descriptions of N = 2 Argyres-Douglas theories. We use our recent interpretation in terms of sequential confinement to guess the Lagrangians of all the Argyres-Douglas models with Abelian three dimensional mirror. We find classes of four dimensional N = 1 quivers that flow in the infrared to generalized Argyres-Douglas theories, such as the (A k , A kN +N −1 ) models. We study in detail how the N = 1 chiral rings map to the Coulomb and Higgs Branches of the N = 2 CFT's. The three dimensional mirror RG flows are shown to land on the N = 4 complete graph quivers. We also compactify to three dimensions the gauge theory dual to (A 1 , D 4 ), and find the expected Abelianization duality with N = 4 SQED with 3 flavors.

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3d duality with adjoint matter from 4d duality

Cited by 31 publications

References 40 publications

Abelianization and sequential confinement in 2 + 1 dimensions

Abelianization and sequential confinement in 2 + 1 dimensions

Supersymmetric Gauge Theories with Decoupled Operators and Chiral Ring Stability

Lagrangians for generalized Argyres-Douglas theories

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