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Ground states of supersymmetric matrix models

Gian Michele Graf (1998/1999)

Séminaire Équations aux dérivées partielles

We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the d = 9 model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in d = 9 . Moreover, it would be unique. Other values of d , where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation. This seminar...

Quantum Cohomology and Crepant Resolutions: A Conjecture

Tom Coates, Yongbin Ruan (2013)

Annales de l’institut Fourier

We give an expository account of a conjecture, developed by Coates–Iritani–Tseng and Ruan, which relates the quantum cohomology of a Gorenstein orbifold 𝒳 to the quantum cohomology of a crepant resolution Y of 𝒳 . We explore some consequences of this conjecture, showing that it implies versions of both the Cohomological Crepant Resolution Conjecture and of the Crepant Resolution Conjectures of Ruan and Bryan–Graber. We also give a ‘quantized’ version of the conjecture, which determines higher-genus...

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