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\( \mathcal{N}=1 \) deformations and RG flows of \( \mathcal{N}=2 \) SCFTs

We study certain \( \mathcal{N}=1 \) preserving deformations of four-dimensional \( \mathcal{N}=2 \) superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an \( \mathcal{N}=1 \) chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum...

Surface defects as transfer matrices

The supersymmetric index of the 4D N=1N=1 theory realized by a brane tiling coincides with the partition function of an integrable 2D lattice model. We argue that a class of half-BPS surface defects in brane tiling models are represented on the lattice model side by transfer matrices constructed from L-operators. For the simplest surface defects in theories with SU(2)SU(2) flavor...

\( \mathcal{N} \) =1 Deformations and RG flows of \( \mathcal{N} \) =2 SCFTs, part II: non-principal deformations

We continue to investigate the \( \mathcal{N} \) = 1 deformations of four-dimensional \( \mathcal{N} \) = 2 superconformal field theories (SCFTs) labeled by a nilpotent element of the flavor symmetry [1]. This triggers a renormalization group (RG) flow to an \( \mathcal{N} \) = 1 SCFT. We systematically analyze all possible deformations of this type for certain classes of...

Chiral theories of class \( \mathcal{S} \)

We study a class of four-dimensional \( \mathcal{N}=1 \) superconformal field theories obtained from the six-dimensional (1, 0) theory, on M5-branes on \( {\mathrm{\mathbb{C}}}^2/{\mathrm{\mathbb{Z}}}_k \) orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge theories whose matter contents are chiral. We classify the building blocks...

4d \( \mathcal{N}=1 \) from 6d \( \mathcal{N}=\left(1,0\right) \) on a torus with fluxes

Compactifying \( \mathcal{N}=\left(1,0\right) \) theories on a torus, with additional fluxes for global symmetries, we obtain \( \mathcal{N}=1 \) supersymmetric theories in four dimensions. It is shown that for many choices of flux these models are toric quiver gauge theories with singlet fields. In particular we compare the anomalies deduced from the description of the six...

Quiver tails and \( \mathcal{N}=1 \) SCFTs from M5-branes

We study a class of four-dimensional \( \mathcal{N}=1 \) superconformal field theories obtained by wrapping M5-branes on a Riemann surface with punctures. We identify fourdimensional UV descriptions of the SCFTs corresponding to curves with a class of punctures. The quiver tails appearing in these UV descriptions differ significantly from their \( \mathcal{N}=2 \) counterpart. We...

Seiberg-Witten curve via generalized matrix model

Kazunobu Maruyoshi 1 Futoshi Yagi 0 0 Institut des Hautes E 1 Yukawa Institute for Theoretical Physics, Kyoto University , Kyoto 606-8502, Japan We study the generalized matrix model which

The Quiver Matrix Model and 2d-4d Conformal Connection

We review the quiver matrix model (the ITEP model) in the light of the recent progress on 2d-4d connection of conformal field theories, in particular, on the relation between Toda field theories and a class of quiver superconformal gauge theories. On the basis of the CFT representation of the β deformation of the model, a quantum spectral curve is introduced as 《det (χ - igs ∂φ(z...

Generalized matrix models and AGT correspondence at all genera

We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT correspondence, these describe four dimensional \( \mathcal{N} = 2 \) SU(2) n+3g−3 gauge theories with generalized quiver diagrams. We obtain the generalized matrix models from the perturbative evaluation of the Liouville correlation functions...