Related papers: On symmetries of N=(4,4) sigma models on T^4
It is shown that the supersymmetry-preserving automorphisms of any non-linear sigma-model on K3 generate a subgroup of the Conway group Co_1. This is the stringy generalisation of the classical theorem, due to Mukai and Kondo, showing that…
The K3 sigma model based on the Z_2-orbifold of the D_4-torus theory is studied. It is shown that it has an equivalent description in terms of twelve free Majorana fermions, or as a rational conformal field theory based on the affine…
We consider two dimensional $\mathcal{N}=(4,4)$ superconformal field theories in the moduli space of symmetric orbifolds of K3. We complete a classification of the discrete groups of symmetries of these models, conditional to a series of…
We study the moduli space ${\cal M}$ of N=(4,4) superconformal field theories with central charge c=6. After a slight emendation of its global description we find the locations of various known models in the component of ${\cal M}$…
We investigate both geometric and conformal field theoretic aspects of mirror symmetry on N=(4,4) superconformal field theories with central charge c=6. Our approach enables us to determine the action of mirror symmetry on (non-stable)…
Given a $K3$ surface, a supersymmetric non-linear K3 sigma model is the internal superconformal field theory (SCFT) in a six dimensional compactification of type IIA superstring on $\mathbb{R}^{1,5} \times K3$. These models have attracted…
We initiate the study of supersymmetry-preserving topological defect lines (TDLs) in the Conway moonshine module $V^{f \natural}$. We show that the tensor category of such defects, under suitable assumptions, admits a surjective but…
We consider symmetries of K3 manifolds. Holomorphic symplectic automorphisms of K3 surfaces have been classified, and observed to be subgroups of the Mathieu group $M_{23}$. More recently, automorphisms of K3 sigma models commuting with…
We study superconformal interfaces between N=(1,1) supersymmetric sigma models on tori, which preserve a u(1)^{2d} current algebra. Their fusion is non-singular and, using parallel transport on CFT deformation space, it can be reduced to…
We propose a correspondence between vertex operator superalgebras and families of sigma models in which the two structures are related by symmetry properties and a certain reflection procedure. The existence of such a correspondence is…
We consider the topological defect lines commuting with the spectral flow and the $\mathcal{N}=(4,4)$ superconformal symmetry in two dimensional non-linear sigma models on K3. By studying their fusion with boundary states, we derive a…
Using geometric engineering method of 4D $\mathcal{N}=2$ quiver gauge theories and results on the classification of Kac-Moody (KM) algebras, we show on explicit examples that there exist three sectors of $\mathcal{N}=2$ infrared CFT$_{4}$s.…
We discuss geometric aspects of orbifold conformal field theories in the moduli space of N=(4,4) superconformal field theories with central charge c=6. Part of this note consists of a summary of our earlier results on the location of these…
We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N>=1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six…
In this note, we describe a connection between the enumerative geometry of curves in K3 surfaces and the chiral ring of an auxiliary superconformal field theory. We consider the invariants calculated by Yau--Zaslow (capturing the Euler…
We study two-dimensional (4,4) superconformal field theories of central charge c=6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the…
We demonstrate the presence of non-invertible symmetries in an infinite family of superconformal Argyres-Douglas theories. This class of theories arises from diagonal gauging of the flavor symmetry of a collection of multiple copies of…
The symmetric orbifold of $\mathbb{T}^4$ is the CFT dual of string theory on AdS$_3\times {\rm S}^3 \times \mathbb{T}^4$ with minimal NS-NS flux. We study its symmetry algebra and provide evidence that it does not have any deformation…
We examine the large $N$ 1/4-BPS spectrum of the symmetric orbifold CFT Sym$^N(M)$ deformed to the supergravity point in moduli space for $M= K3$ and $T^4$. We consider refinement under both left- and right-moving $SU(2)_R$ symmetries of…
For $\mathbb Z_3$-orbifold limits of K3, we provide a counterpart to the extensive studies by Nikulin and others of the geometry and symmetries of classical Kummer surfaces. In particular, we determine the group of holomorphic symplectic…