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The semispin groups in string theory. (English) Zbl 0969.81051

Summary: In string theory, an important role is played by certain Lie groups which are locally isomorphic to \(\text{SO}(4m)\), \(m\leq 8\). It has long been known that these groups are actually isomorphic not to \(\text{SO}(4m)\) but rather to the groups for which the half-spin representations are faithful, which we propose to call \(\text{Semispin}(4m)\). (They are known in the physics literature by the ambiguous name of “\(\text{Spin}(4m)/Z_2\).”) Recent work on string duality has shown that the distinction between \(\text{SO}(4m)\) and \(\text{Semispin}(4m)\) can have a definite physical significance. This work is a survey of the relevant properties of \(\text{Semispin}(4m)\) and its subgroups.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
22E70 Applications of Lie groups to the sciences; explicit representations
53C27 Spin and Spin\({}^c\) geometry
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References:

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