Abstract
Six-dimensional conformal field theories with $(2,0)$ supersymmetry are shown to possess a protected sector of operators and observables that are isomorphic to a two-dimensional chiral algebra. We argue that the chiral algebra associated to a $(2,0)$ theory labelled by the simply-laced Lie algebra $\mathfrak{g}$ is precisely the W algebra of type $\mathfrak{g}$, for a specific value of the central charge. Simple examples of observables that are made accessible by this correspondence are the three-point functions of half-BPS operators. For the $A_n$ series, we compare our results at large $n$ to those obtained using the holographic dual description and find perfect agreement. We further find protected chiral algebras that appear on the worldvolumes of codimension two defects in $(2,0)$ SCFTs. This construction has likely implications for understanding the microscopic origin of the AGT correspondence.
Highlights
We argue that the chiral algebra associated to a p2, 0q theory labelled by the -laced Lie algebra g is precisely the W algebra of type g, for a specific value of the central charge
We further find protected chiral algebras that appear on the worldvolumes of codimension two defects in p2, 0q superconformal field theories (SCFTs)
This makes the presence of a solvable subsector all the more interesting, as the structure of the computable correlators may hold some clues about the right language with which to describe p2, 0q SCFTs more generally
Summary
We set up the general algebraic machinery that is responsible for the existence of a protected chiral algebra of six-dimensional p2, 0q theories. The fermionic generators of the Dp2, 2q subalgebra comprise eight Poincare supercharges tQA, QrAu and their special conformal conjugates pSA, SrAq, transforming under a uspp4qsup2q2 R-symmetry The embedding of these supercharges into the six-dimensional superalgebra is given by QA :“ QA4 , QrA :“ QA3 , SA :“ SA4 , SrA :“ SA3. By construction, such an operator is annihilated by Q i, and thanks to the second line of eq (2.7) its zdependence is Q i-exact It follows that the cohomology class of the twistedtranslated operator defines a purely meromorphic operator,. Operators constructed in this manner have correlation functions that are meromorphic functions of the insertion points, and enjoy well-defined meromorphic OPEs at the level of the cohomology These are precisely the ingredients that define a two-dimensional chiral algebra
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