Interpolation in local theory extensions

In this paper we study interpolation in local extensions of a base theory. We identify situations in which it is possible to obtain interpolants in a hierarchical manner, by using a prover and a procedure for generating interpolants in the base theory as black-boxes. We present several examples of theory extensions in which interpolants can be computed this way, and discuss applications in verification, knowledge representation, and modular reasoning in combinations of local theories.Comment: 31 pages, 1 figur

Non-supersymmetric Tachyon-free Type-II and Type-I Closed Strings from RCFT

We consider non-supersymmetric four-dimensional closed string theories constructed out of tensor products of N=2 minimal models. Generically such theories have closed string tachyons, but these may be removed either by choosing a non-trivial partition function or a suitable Klein bottle projection. We find large numbers of examples of both types.Comment: 9 pages, 1 tabl

Local fields in boundary conformal QFT

Conformal field theory on the half-space x>0 of Minkowski space-time ("boundary CFT") is analyzed from an algebraic point of view, clarifying in particular the algebraic structure of local algebras and the bi-localized charge structure of local fields. The field content and the admissible boundary conditions are characterized in terms of a non-local chiral field algebra.Comment: 58 pages, 5 figures. v2: organization of results improved; version to appear in RM

Local cocycles and central extensions for multi-point algebras of Krichever-Novikov type

Multi-point algebras of Krichever Novikov type for higher genus Riemann surfaces are generalisations of the Virasoro algebra and its related algebras. Complete existence and uniqueness results for local 2-cocycles defining almost-graded central extensions of the functions algebra, the vector field algebra, and the differential operator algebra (of degree \le 1) are shown. This is applied to the higher genus, multi-point affine algebras to obtain uniqueness for almost-graded central extensions of the current algebra of a simple finite-dimensional Lie algebra. An earlier conjecture of the author concerning the central extension of the differential operator algebra induced by the semi-infinite wedge representations is proved.Comment: 38 pages, Amslatex, some minor changes in Section

Permutation orbifolds of heterotic Gepner models

We study orbifolds by permutations of two identical N=2 minimal models within the Gepner construction of four dimensional heterotic strings. This is done using the new N=2 supersymmetric permutation orbifold building blocks we have recently developed. We compare our results with the old method of modding out the full string partition function. The overlap between these two approaches is surprisingly small, but whenever a comparison can be made we find complete agreement. The use of permutation building blocks allows us to use the complete arsenal of simple current techniques that is available for standard Gepner models, vastly extending what could previously be done for permutation orbifolds. In particular, we consider (0,2) models, breaking of SO(10) to subgroups, weight-lifting for the minimal models and B-L lifting. Some previously observed phenomena, for example concerning family number quantization, extend to this new class as well, and in the lifted models three family models occur with abundance comparable to two or four.Comment: 49 pages, 4 figure

Local Hidden Variable Theories for Quantum States

While all bipartite pure entangled states violate some Bell inequality, the relationship between entanglement and non-locality for mixed quantum states is not well understood. We introduce a simple and efficient algorithmic approach for the problem of constructing local hidden variable theories for quantum states. The method is based on constructing a so-called symmetric quasi-extension of the quantum state that gives rise to a local hidden variable model with a certain number of settings for the observers Alice and Bob.Comment: 8 pages Revtex; v2 contains substantial changes, a strengthened main theorem and more reference

Extended massive gravity in three dimensions

Using a first order Chern-Simons-like formulation of gravity we systematically construct higher-derivative extensions of general relativity in three dimensions. The construction ensures that the resulting higher-derivative gravity theories are free of scalar ghosts. We canonically analyze these theories and construct the gauge generators and the boundary central charges. The models we construct are all consistent with a holographic c-theorem which, however, does not imply that they are unitary. We find that Born-Infeld gravity in three dimensions is contained within these models as a subclass.Comment: 35p, v2; minor changes, references adde

The Five Instructions

Five elementary lectures delivered at TASI 2011 on the Standard Model, its extensions to neutrino masses, flavor symmetries, and Grand-Unification