From Singularities to Algebras to Pure Yang–Mills with Matter
Since the advent of dualities in string theory, it has been well-known that codimension 4 orbifold singularities that appear in extra-dimensional spaces, such as Calabi–Yau or G 2 spaces, may be interpreted as ADE gauge theories. As to orbifold singularities of higher codimension, there has not been an analog of this interpretation. Here we show how the search for such an analog led us from the singularities to the creation of Lie Algebras of the Third Kind (“LATKes”). We introduce an example of a LATKe that arises from the singularity C 3 ∕ Z 3, and prove it to be simple and unique. We explain that the uniqueness of the LATKe serves as a vacuum selection mechanism. We also show how the LATKe leads to a new kind of gauge theory in which the matter field arises naturally and which is tantalizingly close to the Standard Model of particle physics.
KeywordsGauge Theory Gauge Group Intersection Number Adjoint Representation Dynkin Diagram
The author is grateful to the organizers, and especially to V. Dobrev, for putting together such a vibrant, stimulating, and enjoyable workshop.
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