695 research outputs found

    Integrability from 2d N=(2,2) Dualities

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    We study integrable models in the context of the recently discovered Gauge/YBE correspondence, where the Yang-Baxter equation is promoted to a duality between two supersymmetric gauge theories. We study flavored elliptic genus of 2d N=(2,2)\mathcal{N}=(2,2) quiver gauge theories, which theories are defined from statistical lattices regarded as quiver diagrams. Our R-matrices are written in terms of theta functions, and simplifies considerably when the gauge groups at the quiver nodes are Abelian. We also discuss the modularity properties of the R-matrix, reduction of 2d index to 1d Witten index, and string theory realizations of our theories.Comment: 30 pages, 8 figure

    Vertex operator algebras of Argyres-Douglas theories from M5-branes

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    We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N=(2, 0) theory of type JJ on a punctured sphere. We denote the AD theories as (Jb[k],Y)(J^b[k],Y), where Jb[k]J^b[k] and YY represent an irregular and a regular singularity respectively. We restrict to the `minimal' case where Jb[k]J^b[k] has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the W-algebra Wk2d(J,Y)\mathcal{W}^{k_{2d}}(J,Y), where k2d=βˆ’h+bb+kk_{2d}=-h+ \frac{b}{b+k} with hh being the dual Coxeter number of JJ. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for b=hb=h. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.Comment: 35 pages, 1 figure, v2: minor corrections, referenced adde

    (0,4)(0, 4) dualities

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    We study a class of two-dimensional N=(0,4){\cal N}=(0, 4) quiver gauge theories that flow to superconformal field theories. We find dualities for the superconformal field theories similar to the 4d N=2{\cal N}=2 theories of class S{\cal S}, labelled by a Riemann surface C{\cal C}. The dual descriptions arise from various pair-of-pants decompositions, that involves an analog of the TNT_N theory. Especially, we find the superconformal index of such theories can be written in terms of a topological field theory on C{\cal C}. We interpret this class of SCFTs as the ones coming from compactifying 6d N=(2,0){\cal N}=(2, 0) theory on CP1Γ—C\mathbb{CP}^1 \times {\cal C}Comment: 41 pages, 12 figure

    ADE String Chains and Mirror Symmetry

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    6d superconformal field theories (SCFTs) are the SCFTs in the highest possible dimension. They can be geometrically engineered in F-theory by compactifying on non-compact elliptic Calabi-Yau manifolds. In this paper we focus on the class of SCFTs whose base geometry is determined by βˆ’2-2 curves intersecting according to ADE Dynkin diagrams and derive the corresponding mirror Calabi-Yau manifold. The mirror geometry is uniquely determined in terms of the mirror curve which has also an interpretation in terms of the Seiberg-Witten curve of the four-dimensional theory arising from torus compactification. Adding the affine node of the ADE quiver to the base geometry, we connect to recent results on SYZ mirror symmetry for the AA case and provide a physical interpretation in terms of little string theory. Our results, however, go beyond this case as our construction naturally covers the DD and EE cases as well.Comment: version 2: typos corrected, 30 pages, 8 figure
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