1,544 research outputs found
Orbifolds of Lattice Vertex Operator Algebras at and
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 and . 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 . This means in particular that unlike the second
Renyi entropy, the third one is no longer universal.Comment: 28 pages + Appendice
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