| 总结: | <p>The correspondence between four-dimensional N = 2 superconformal field theories and vertex operator algebras, when applied to theories of class S, leads to a rich family of vertex algebras that have been given the moniker chiral algebras of class S. These vertex algebras are fascinating from both a physical and mathematical point of view since they furnish novel representations of critical level affine Kac–Moody algebras. A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in [Ara18]. The construction takes as input a choice of simple Lie algebra g, and applies equally well regardless of whether g is simply laced or not. In the non-simply laced case, however, the resulting VOAs do not correspond in any clear way to known four-dimensional theories. On the other hand, the standard realisation of class S theories involving non-simply laced symmetry algebras requires the inclusion of punctures that have been twisted by an outer automorphism of the Lie algebra.</p>
<p>In this thesis, we extend the construction of loc. cit. to theories of class S with twisted punctures. The resulting family of vertex algebras are, simultaneously, modules over two different critical level affine Kac–Moody algebras. We show that our proposal passes a number of consistency checks and establish results on gluing isomorphisms, and the action of generalised S-duality.</p>
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