N=4 Characters in Gepner Models, Orbits and Elliptic Genera

We review the properties of characters of the N=4 SCA in the context of a non-linear sigma model on $K3$, how they are used to span the orbits, and how the orbits produce topological invariants like the elliptic genus. We derive the same expression for the $K3$ elliptic genus using three different Gepner models ($1^6$, $2^4$ and $4^3$ theories), detailing the orbits and verifying that their coefficients $F_i$ are given by elementary modular functions. We also reveal the orbits for the $1^3 2^2$, $1^4 4$ and $1^2 4^2$ theories. We derive relations for cubes of theta functions and study the function ${1\over\eta} \sum_{n\in \Z} (-1)^n (6n+1)^k q^{(6n+1)^2 /24}$ for $k=1,2,3,4$.Comment: 39 pages; errors corrected in section 6, section 7 added (mixed Gepner models), ref adde

KK-theoretic obstructions to bounded tt-structures

Schlichting conjectured that the negative K-groups of small abelian categories vanish and proved this for noetherian abelian categories and for all abelian categories in degree $-1$. The main results of this paper are that $K_{-1}(E)$ vanishes when $E$ is a small stable $\infty$-category with a bounded t-structure and that $K_{-n}(E)$ vanishes for all $n\geq 1$ when additionally the heart of $E$ is noetherian. It follows that Barwick's theorem of the heart holds for nonconnective K-theory spectra when the heart is noetherian. We give several applications, to non-existence results for bounded t-structures and stability conditions, to possible K-theoretic obstructions to the existence of the motivic t-structure, and to vanishing results for the negative K-groups of a large class of dg algebras and ring spectra

KK-theoretic obstructions to bounded tt-structures

Schlichting conjectured that the negative K-groups of small abelian categories vanish and proved this for noetherian abelian categories and for all abelian categories in degree $-1$. The main results of this paper are that $K_{-1}(E)$ vanishes when $E$ is a small stable $\infty$-category with a bounded t-structure and that $K_{-n}(E)$ vanishes for all $n\geq 1$ when additionally the heart of $E$ is noetherian. It follows that Barwick's theorem of the heart holds for nonconnective K-theory spectra when the heart is noetherian. We give several applications, to non-existence results for bounded t-structures and stability conditions, to possible K-theoretic obstructions to the existence of the motivic t-structure, and to vanishing results for the negative K-groups of a large class of dg algebras and ring spectra

Asymmetric Gepner Models II. Heterotic Weight Lifting

A systematic study of "lifted" Gepner models is presented. Lifted Gepner models are obtained from standard Gepner models by replacing one of the N=2 building blocks and the $E_8$ factor by a modular isomorphic $N=0$ model on the bosonic side of the heterotic string. The main result is that after this change three family models occur abundantly, in sharp contrast to ordinary Gepner models. In particular, more than 250 new and unrelated moduli spaces of three family models are identified. We discuss the occurrence of fractionally charged particles in these spectra.Comment: 46 pages, 17 figure

Supersymmetries in Free Fermionic Strings

Consistent heterotic free fermionic string models are classified in terms of their number of spacetime supersymmetries, N. For each of the six distinct choices of gravitino sector, we determine what number of supersymmetries can survive additional GSO projections. We prove by exhaustive search that only three of the six can yield N = 1, in addition to the N = 4, 2, or 0 that five of the six can yield. One choice of gravitino sector can only produce N = 4 or 0. Relatedly, we find that only Z_2, Z_4, and Z_8 twists of the internal fermions with worldsheet supersymmetry are consistent with N=1 in free fermionic models. Any other twists obviate N=1.Comment: changes to match journal version; tex, 53 page

Towards A Topological G_2 String

We define new topological theories related to sigma models whose target space is a 7 dimensional manifold of G_2 holonomy. We show how to define the topological twist and identify the BRST operator and the physical states. Correlation functions at genus zero are computed and related to Hitchin's topological action for three-forms. We conjecture that one can extend this definition to all genus and construct a seven-dimensional topological string theory. In contrast to the four-dimensional case, it does not seem to compute terms in the low-energy effective action in three dimensions.Comment: 15 pages, To appear in the proceedings of Cargese 2004 summer schoo

Kaluza-Klein Black Holes in String Theory

Exact solutions of heterotic string theory corresponding to four-dimensional magnetic black holes in $N=4$ supergravity are described. The solutions describe the black holes in the throat limit, and consist of a tensor product of an $SU(2)$ WZW orbifold with the linear dilaton vacuum, supersymmetrized to $(1,0)$ world sheet SUSY. One dimension of the $SU(2)$ model is interpreted as a compactified fifth dimension, leading to a four dimensional solution with a Kaluza-Klein gauge field having a magnetic monopole background; this corresponds to a solution in $N=4$ supergravity, since that theory is obtained by dimensional reduction of string theory.Comment: 13p. uses Harvma

Heterotic Weight Lifting

We describe a method for constructing genuinely asymmetric (2,0) heterotic strings out of N=2 minimal models in the fermionic sector, whereas the bosonic sector is only partly build out of N=2 minimal models. This is achieved by replacing one minimal model plus the superfluous E_8 factor by a non-supersymmetric CFT with identical modular properties. This CFT generically lifts the weights in the bosonic sector, giving rise to a spectrum with fewer massless states. We identify more than 30 such lifts, and we expect many more to exist. This yields more than 450 different combinations. Remarkably, despite the lifting of all Ramond states, it is still possible to get chiral spectra. Even more surprisingly, these chiral spectra include examples with a certain number of chiral families of SO(10), SU(5) or other subgroups, including just SU(3) x SU(2) x U(1). The number of families and mirror families is typically smaller than in standard Gepner models. Furthermore, in a large number of different cases, spectra with three chiral families can be obtained. Based on a first scan of about 10% of the lifted Gepner models we can construct, we have collected more than 10.000 distinct spectra with three families, including examples without mirror fermions. We present an example where the GUT group is completely broken to the standard model, but the resulting and inevitable fractionally charged particles are confined by an additional gauge group factor.Comment: 19 pages, 1 figur

Fractional Superstrings with Space-Time Critical Dimensions Four and Six

We propose possible new string theories based on local world-sheet symmetries corresponding to extensions of the Virasoro algebra by fractional spin currents. They have critical central charges $c=6(K+8)/(K+2)$ and Minkowski space-time dimensions $D=2+16/K$ for $K\geq2$ an integer. We present evidence for their existence by constructing modular invariant partition functions and the massless particle spectra. The dimension $4$ and $6$ strings have space-time supersymmetry.Comment: 9 page

Non-Abelian Bosonization and Haldane's Conjecture

We study the long wavelength limit of a spin S Heisenberg antiferromagnetic chain. The fermionic Lagrangian obtained corresponds to a perturbed level 2S SU(2) Wess-Zumino-Witten model. This effective theory is then mapped into a compact U(1) boson interacting with Z_{2S} parafermions. The analysis of this effective theory allows us to show that when S is an integer there is a mass gap to all excitations, whereas this gap vanishes in the half-odd-integer spin case. This gives a field theory treatment of the so-called Haldane's conjecture for arbitrary values of the spin S.Comment: 9 pages REVTeX, no figure