13th December, 2010.
E-infinity communication No. 55
Crystallographic groups and Heterotic strings in E-infinity.
The following is a notice on a very short paper published in CS&F, 42 (2008), pp. 2282-2284. Although very short and at first glance may appear unassuming, it is extremely important to grasp the idea behind it. It is well known that there are 17 different ‘tiling’ groups in two dimensions corresponding to 17 two and three Stein spaces with total dimensions of 685. In three dimensions there are 230 groups and 219 from that correspond exactly to the 17 groups in two dimensions. The question now is how many dimensions belong to these 219? In this paper El Naschie answers this question. The answer is 8872 which is exactly the number of states of the first massless level of particle-like states of the Heterotic string theory. It is extremely interesting to see that these seemingly abstract 8872 states have such a strong and deep connection with something as real as 3D crystals.
E-infinity group.
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