Vertex algebras at the corner

@article{Gaiotto2019VertexAA,
  title={Vertex algebras at the corner},
  author={Davide Gaiotto and Miroslav Rap{\vc}{\'a}k},
  journal={Journal of High Energy Physics},
  year={2019},
  volume={2019},
  pages={1-88}
}
A bstractWe introduce a class of Vertex Operator Algebras which arise at junctions of supersymmetric interfaces in N$$ \mathcal{N} $$ = 4 Super Yang Mills gauge theory. These vertex algebras satisfy non-trivial duality relations inherited from S-duality of the four-dimensional gauge theory. The gauge theory construction equips the vertex algebras with collections of modules labelled by supersymmetric interface line defects. We discuss in detail the simplest class of algebras YL,M,N, which… 

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Logarithmic W-algebras and Argyres-Douglas theories at higher rank

  • T. Creutzig
  • Mathematics
    Journal of High Energy Physics
  • 2018
A bstractFamilies of vertex algebras associated to nilpotent elements of simply-laced Lie algebras are constructed. These algebras are close cousins of logarithmic W-algebras of Feigin and Tipunin
...

References

SHOWING 1-10 OF 56 REFERENCES

Consistency conditions for orientifolds and D-manifolds.

It is argued that the {ital K}3 orbifold with spin connection embedded in gauge connection corresponds to an interacting conformal field theory in the type I theory.

On S-duality for Non-Simply-Laced Gauge Groups

We point out that for Script N = 4 gauge theories with exceptional gauge groups G_2 and F_4 the S-duality transformation acts on the moduli space by a nontrivial involution. We note that the duality

Symplectic Fermions

Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A2

We construct a representation of the affine W-algebra of ${\mathfrak{g}}{\mathfrak{l}}_{r}$ on the equivariant homology space of the moduli space of Ur-instantons, and we identify the corresponding

Fivebranes and Knots

We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is a

Quantum Calabi-Yau and Classical Crystals

We propose a new duality involving topological strings in the limit of the large string coupling constant. The dual is described in terms of a classical statistical mechanical model of crystal
...