The structure of a Standard Model family is derived in a class of brane models with a U(M) x U(N) factor, from two mildly anthropic requirements: a massless photon and a universe that does not turn into a plasma of massless charged particles. If we c
hoose M=3 and N=2, the only option is shown to be the Standard Model with an undetermined number of families. We do not assume the U(1) embedding, charge quantization, family repetition, nor the fermion representations; all of these features are derived, assuming a doublet Higgs. With a slightly stronger assumption even the Higgs representation is determined. We also consider a more general class, requiring an asymptotically free strong SU(M) (with M geq 3) interaction from the first factor and an electromagnetic U(1) embedded in both factors. We allow Higgs symmetry breaking of the U(N)x U(1) flavor group by at most one Higgs boson in any representation, combined with any allowed chiral symmetry breaking by SU(M). For M=3 there is a large number of solutions with an unbroken U(1). In all of these, quarks have third-integral charges and color singlets have integer charges in comparison to leptons. Hence Standard Model charge quantization holds for any N. Only for N=2 these models allow an SU(5) GUT extension, but this extension offers no advantages whatsoever for understanding the Standard Model; it only causes complications, such as the doublet-triplet splitting problem. Although all these models have a massless photon, all except the Standard Model are ruled out by the second anthropic requirement. In this class of brane models the Standard Model is realized as a GUT with its intestines removed, to keep only the good parts: a GUT without guts.
If the results of the first LHC run are not betraying us, many decades of particle physics are culminating in a complete and consistent theory for all non-gravitational physics: the Standard Model. But despite this monumental achievement there is a c
lear sense of disappointment: many questions remain unanswered. Remarkably, most unanswered questions could just be environmental, and disturbingly (to some) the existence of life may depend on that environment. Meanwhile there has been increasing evidence that the seemingly ideal candidate for answering these questions, String Theory, gives an answer few people initially expected: a huge landscape of possibilities, that can be realized in a multiverse and populated by eternal inflation. At the interface of bottom-up and top-down physics, a discussion of anthropic arguments becomes unavoidable. We review developments in this area, focusing especially on the last decade.
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.
In the same spirit as heterotic weight lifting, B-L lifting is a way of replacing the superfluous and ubiquitous U(1)_{B-L} with something else with the same modular properties, but different conformal weights and ground state dimensions. This method
works in principle for all variants of (2,2) constructions, such as orbifolds, Calabi-Yau manifolds, free bosons and fermions and Gepner models, since it only modifies the universal SO(10) x E_8 part of the CFT. However, it can only yield chiral spectra if the ``internal sector of the theory provides a simple current of order 5. Here we apply this new method to Gepner models. Including exceptional invariants, 86 of them have the required order 5 simple current, and 69 of these yield chiral spectra. Three family spectra occur abundantly.
In this paper we apply the previously derived formalism of permutation orbifold conformal field theories to N=2 supersymmetric minimal models. By interchanging extensions and permutations of the factors we find a very interesting structure relating v
arious conformal field theories that seems not to be known in literature. Moreover, unexpected exceptional simple currents arise in the extended permuted models, coming from off-diagonal fields. In a few situations they admit fixed points that must be resolved. We determine the complete CFT data with all fixed point resolution matrices for all simple currents of all Z_2-permutations orbifolds of all minimal N=2 models with k eq 2 mod 4.
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 het
erotic 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.
We are in the middle of a remarkable paradigm shift in particle physics, a shift of opinion that occurred so slowly that some even try to deny that they changed their minds at all. It concerns a very basic question: can we expect to derive the laws o
f particle physics from a fundamental theory? The Standard Model of particle physics as well as the 1984 string theory revolution provided ample food for thought about this. The reason this was ignored for so long can be traced back to an old fallacy: a misguided idea about our own importance.
We reconsider a class of heterotic string theories studied in 1989, based on tensor products of N=2 minimal models with asymmetric simple current invariants. We extend this analysis from (2,2) and (1,2) spectra to (0,2) spectra with SO(10) broken to
the Standard Model. In the latter case the spectrum must contain fractionally charged particles. We find that in nearly all cases at least some of them are massless. However, we identify a large subclass where the fractional charges are at worst half-integer, and often vector-like. The number of families is very often reduced in comparison to the 1989 results, but there are no new tensor combinations yielding three families. All tensor combinations turn out to fall into two classes: those where the number of families is always divisible by three, and those where it is never divisible by three. We find an empirical rule to determine the class, which appears to extend beyond minimal N=2 tensor products. We observe that distributions of physical quantities such as the number of families, singlets and mirrors have an interesting tendency towards smaller values as the gauge groups approaches the Standard Model. We compare our results with an analogous class of free fermionic models. This displays similar features, but with less resolution.Finally we present a complete scan of the three family models based on the triply-exceptional combination (1,16*,16*,16*) identified originally by Gepner. We find 1220 distinct three family spectra in this case, forming 610 mirror pairs. About half of them have the gauge group SU(3) x SU(2)_L x SU(2)_R x U(1)^5, the theoretical minimum, and many others are trinification models.
