String Landscape and the Standard Model of Particle Physics

In this paper we describe ideas about the string landscape, and how to relate it to the physics of the Standard Model of particle physics. First, we give a short status report about heterotic string compactifications. Then we focus on the statistics of D-brane models, on the problem of moduli stabilization, and finally on some attempts to derive a probability wave function in moduli space, which goes beyond the purely statistical count of string vacua.Comment: Contribution to the 11th. Marcel Grossmann Meeting on General Relativity in Berlin, July 2006}, new refs. added, typos correcte

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

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

Interacting Two-Time Physics Field Theory With a BRST Gauge Invariant Action

We construct a field theoretic version of 2T-physics including interactions in an action formalism. The approach is a BRST formulation based on the underlying Sp(2,R)gauge symmetry, and shares some similarities with the approach used to construct string field theory. In our first case of spinless particles, the interaction is uniquely determined by the BRST gauge symmetry, and it is different than the Chern-Simons type theory used in open string field theory. After constructing a BRST gauge invariant action for 2T-physics field theory with interactions in d+2 dimensions, we study its relation to standard 1T-physics field theory in (d-1)+1 dimensions by choosing gauges. In one gauge we show that we obtain the Klein-Gordon field theory in (d-1)+1 dimensions with unique SO(d,2) conformal invariant self interactions at the classical field level. This SO(d,2) is the natural linear Lorentz symmetry of the 2T field theory in d+2 dimensions. As indicated in Fig.1, in other gauges we expect to derive a variety of SO(d,2)invariant 1T-physics field theories as gauge fixed forms of the same 2T field theory, thus obtaining a unification of 1T-dynamics in a field theoretic setting, including interactions. The BRST gauge transformation should play the role of duality transformations among the 1T-physics holographic images of the same parent 2T field theory. The availability of a field theory action opens the way for studying 2T-physics with interactions at the quantum level through the path integral approach.Comment: 22 pages, 1 figure, v3 includes corrections of typos and some comment

Supersymmetric Field Theory in 2T-physics

We construct N=1 supersymmetry in 4+2 dimensions compatible with the theoretical framework of 2T physics field theory and its gauge symmetries. The fields are arranged into 4+2 dimensional chiral and vector supermultiplets, and their interactions are uniquely fixed by SUSY and 2T-physics gauge symmetries. Many 3+1 spacetimes emerge from 4+2 by gauge fixing. Gauge degrees of freedom are eliminated as one comes down from 4+2 to 3+1 dimensions without any remnants of Kaluza-Klein modes. In a special gauge, the remaining physical degrees of freedom, and their interactions, coincide with ordinary N=1 supersymmetric field theory in 3+1 dimensions. In this gauge, SUSY in 4+2 is interpreted as superconformal symmetry SU(2,2|1) in 3+1 dimensions. Furthermore, the underlying 4+2 structure imposes some interesting restrictions on the emergent 3+1 SUSY field theory, which could be considered as part of the predictions of 2T-physics. One of these is the absence of the troublesome renormalizable CP violating F*F terms. This is good for curing the strong CP violation problem of QCD. An additional feature is that the superpotential is required to have no dimensionful parameters. To induce phase transitions, such as SUSY or electro-weak symmetry breaking, a coupling to the dilaton is needed. This suggests a common origin of phase transitions that is driven by the vacuum value of the dilaton, and need to be understood in a cosmological scenario as part of a unified theory that includes the coupling of supergravity to matter. Another interesting aspect is the possibility to utilize the inherent 2T gauge symmetry to explore dual versions of the N=1 theory in 3+1 dimensions. This is expected to reveal non-perturbative aspects of ordinary 1T field theory.Comment: 54 pages, late