TL;DR
This paper explores the global properties of Spin(32)/Z_2 and its subgroups, revealing that the commonly assumed 'common' SO(16) x SO(16) subgroup does not actually exist, impacting the understanding of string dualities.
Contribution
It provides a comprehensive survey of the global structure of Spin(32)/Z_2 and clarifies misconceptions about the existence of a 'common' SO(16) x SO(16) subgroup in string theory dualities.
Findings
No 'common' SO(16) x SO(16) subgroup exists in Spin(32)/Z_2
Global properties of Spin(32)/Z_2 are clarified
Implications for heterotic string dualities are discussed
Abstract
In discussions of the T-duality between the two heterotic string theories, the duality is actually implemented through the "common" SO(16) x SO(16) subgroup of "SO(32)" and E_8 x E_8. In fact, however, a global investigation shows that no such "common" subgroup exists. This paper is a survey of the relevant global properties of Spin(32)/Z_2 and its subgroups.
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