683 research outputs found
Integrability from 2d N=(2,2) Dualities
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 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
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
on a punctured sphere. We denote the AD theories as , where
and represent an irregular and a regular singularity respectively.
We restrict to the `minimal' case where 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
, where with being
the dual Coxeter number of . 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 . 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
dualities
We study a class of two-dimensional quiver gauge theories
that flow to superconformal field theories. We find dualities for the
superconformal field theories similar to the 4d theories of class
, labelled by a Riemann surface . The dual descriptions
arise from various pair-of-pants decompositions, that involves an analog of the
theory. Especially, we find the superconformal index of such theories can
be written in terms of a topological field theory on . We interpret
this class of SCFTs as the ones coming from compactifying 6d
theory on Comment: 41 pages, 12 figure
ADE String Chains and Mirror Symmetry
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 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 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
and cases as well.Comment: version 2: typos corrected, 30 pages, 8 figure
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