Dirac-Ramond Analysis, The Euler-Hirzebruch Indices, SuSy, And The Atiyah-Bott Theorem

Why should things be easy to understand?
~ Thomas Pynchon!

In this post, I will relate the Dirac-Ramond operator to the Euler and Hirzebruch indices in the context of string theory and connect some dots that lead us to supersymmetry and use the

The Seiberg-Witten Map, Emergent Gravity, AdS/CFT Duality, And Noncommutativity


Mathematical physics represents the purest image that the view of nature may generate for humanity; this image presents all the character of the product of art; it begets unity, it is true and has the quality of sublimity; this image is to physical nature what music is to the thousand noises of which the air is full ~ Théophile de Donder as quoted by Ilya Prigogine in his Autobiography given at the occasion of Prigogine's 1977 Nobel Prize in Chemistry.

I will just broad-stroke the topics involved here and try to inter-connect them and draw a 'deep' isomorphism at the end. Let me set the stage. One of the deepest aspects of the AdS/CFT duality is the notion that local symmetries may not be fundamental: the duality basically says that if we deform the CFT by source fields by adding: