Ivancevic_Applied-Diff-Geom

42 Applied Differential Geometry: A Modern IntroductionContemporary String TheoriesType Dim DetailsBosonic 26 Only bosons, no fermions means only forces, no matter,with both open and closed strings; major flaw:a particle with imaginary mass, called the tachyon,representing an instability in the theoryI 10 Supersymmetry between forces and matter, with bothopen and closed strings, no tachyon, group symmetryis SO(32)IIA 10 Supersymmetry between forces and matter, withclosed strings and open strings bound to D–branes, notachyon, massless fermions spin both ways (nonchiral)IIB 10 Supersymmetry between forces and matter, withclosed strings and open strings bound to D–branes, notachyon, massless fermions only spin one way (chiral)HO 10 Supersymmetry between forces and matter, withclosed strings only, no tachyon, heterotic, meaningright moving and left moving strings differ, groupsymmetry is SO(32)HE 10 Supersymmetry between forces and matter, withclosed strings only, no tachyon, heterotic, meaningright moving and left moving strings differ, groupsymmetry is E 8 × E 8small, and the uncertainty effect, which keeps it ‘stretched’. Consequently,the minimum size of a string must be related to the string tension.Before the 1990s, string theorists believed that there were five distinctsuperstring theories: type I, types IIA and IIB, and the two heterotic stringtheories (SO(32) and E 8 × E 8 ). The thinking was that out of these fivecandidate theories, only one was the actual correct theory of everything,and that theory was the theory whose low energy limit, with ten dimensionsspacetime compactified down to four, matched the physics observed in ourworld today. But now it is known that this naïve picture was wrong, andthat the five superstring theories are connected to one another as if they areeach a special case of some more fundamental theory, of which there is onlyone. These theories are related by transformations that are called dualities.If two theories are related by a duality transformation, it means that the