Orbifolds of Lattice Vertex Operator Algebras at d=48d=48 and d=72d=72

Motivated by the notion of extremal vertex operator algebras, we investigate cyclic orbifolds of vertex operator algebras coming from extremal even self-dual lattices in $d=48$ and $d=72$. In this way we construct about one hundred new examples of holomorphic VOAs with a small number of low weight states.Comment: 18 pages, LaTe

Cauchy conformal fields in dimensions d>2

Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined everywhere once we know their value on a codimension 1 surface. We classify all the unitary Cauchy fields. By analyzing the mode expansion on the unit sphere, we show that all unitary Cauchy fields are free in the sense that their correlation functions factorize on the 2-point function. We also discuss the possibility of non-unitary Cauchy fields and classify them in d=3 and 4.Comment: 45 pages; v2: references adde

Lifting 1/4-BPS States on K3 and Mathieu Moonshine

The elliptic genus of K3 is an index for the 1/4-BPS states of its sigma model. At the torus orbifold point there is an accidental degeneracy of such states. We blow up the orbifold fixed points using conformal perturbation theory, and find that this fully lifts the accidental degeneracy of the 1/4-BPS states with h=1. At a generic point near the Kummer surface the elliptic genus thus measures not just their index, but counts the actual number of these BPS states. We comment on the implication of this for symmetry surfing and Mathieu moonshine.Comment: 29+5 pp, a sign mistake corrected in eqs. (3.14) and (4.20), footnote 6 added to clarify this point, references adde

From SO/Sp instantons to W-algebra blocks

We study instanton partition functions for N=2 superconformal Sp(1) and SO(4) gauge theories. We find that they agree with the corresponding U(2) instanton partitions functions only after a non-trivial mapping of the microscopic gauge couplings, since the instanton counting involves different renormalization schemes. Geometrically, this mapping relates the Gaiotto curves of the different realizations as double coverings. We then formulate an AGT-type correspondence between Sp(1)/SO(4) instanton partition functions and chiral blocks with an underlying W(2,2)-algebra symmetry. This form of the correspondence eliminates the need to divide out extra U(1) factors. Finally, to check this correspondence for linear quivers, we compute expressions for the Sp(1)-SO(4) half-bifundamental.Comment: 83 pages, 29 figures; minor change

Genus Two Partition Functions and Renyi Entropies of Large c CFTs

We compute genus two partition functions in two dimensional conformal field theories at large central charge, focusing on surfaces that give the third Renyi entropy of two intervals. We compute this for generalized free theories and for symmetric orbifolds, and compare it to the result in pure gravity. We find a new phase transition if the theory contains a light operator of dimension $\Delta\leq0.19$. This means in particular that unlike the second Renyi entropy, the third one is no longer universal.Comment: 28 pages + Appendice