Simple current extensions beyond semi-simplicity

Let [Formula: see text] be a simple vertex operator algebra (VOA) and consider a representation category of [Formula: see text] that is a vertex tensor category in the sense of Huang–Lepowsky. In particular, this category is a braided tensor category. Let [Formula: see text] be an object in this category that is a simple current of order two of either integer or half-integer conformal dimension. We prove that [Formula: see text] is either a VOA or a super VOA. If the representation category of [Formula: see text] is in addition ribbon, then the categorical dimension of [Formula: see text] decides this parity question. Combining with Carnahan’s work, we extend this result to simple currents of arbitrary order. Our next result is a simple sufficient criterion for lifting indecomposable objects that only depends on conformal dimensions. Several examples of simple current extensions that are [Formula: see text]-cofinite and non-rational are then given and induced modules listed.

Combinatorial bases of modules for affine Lie algebra B 2(1)

We construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B 2(1) consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces W(Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W(kΛ0) for B 2(1) and the integrable highest weight module L(kΛ0) for A 1(1) have the same parametrization of combinatorial bases and the same presentation P/I.

OPEN DESCENDANTS OF U(2N) ORBIFOLDS AT RATIONAL RADII

We construct explicitly the open descendants of some exceptional automorphism invariants of U (2N) orbifolds. We focus on the case N = p1 × p2, p1 and p2 prime, and on the automorphisms of the diagonal and charge conjugation invariants that exist for these values of N. These correspond to orbifolds of the circle with radius R2 = 2p1/p2. For each automorphism invariant we find two consistent Klein bottles, and for each Klein bottle we find a complete (and probably unique) set of boundary states. The two Klein bottles are in each case related to each other by simple currents, but surprisingly for the automorphism of the charge conjugation invariant neither of the Klein bottle choices is the canonical (symmetric) one.

SIMPLE CURRENTS, MODULAR INVARIANTS AND FIXED POINTS

We review the use of simple currents in constructing modular invariant partition functions and the problem of resolving their fixed points. We present some new results, in particular regarding fixed point resolution. Additional empirical evidence is provided in support of our conjecture that fixed points are always related to some conformal field theory. We complete the identification of the fixed point conformal field theories for all simply laced and most non-simply laced Kac-Moody algebras, for which the fixed point CFT’s turn out to be Kac-Moody algebras themselves. For the remaining non-simply laced ones we obtain spectra that appear to correspond to new non-unitary conformal field theories. The fusion rules of the simplest unidentified example are computed.