The large-N limit in field theory restricts the perturbative expansion to specific classes of Feynman diagrams. For vectors the restricted class of diagrams is simple, and one can analytically solve the models. For matrices, the large-N limit is simple in zero dimensions but is exceedingly complicated in higher dimensions. I proved that going one step up in the rank and considering tensor fields things simplify again, but not to the level of the vectors. I established the 1/N expansion of random tensors and discovered a new (and the last possible) universality class of large-N field theories: the melonic theories. As pointed out by Witten, these theories yield nontrivial, strongly coupled conformal field theories in the infrared. The aim of this project is to perform an exhaustive study of the melonic universality class of tensor field theories and their infrared conformal field theories. I aim to extend maximally the melonic universality class, study the renormalization group flow in melonic theories and apply them to the AdS/CFT correspondence and quantum critical metals.
Field of science
- /natural sciences/chemical sciences/inorganic chemistry/metals
Call for proposal
See other projects for this call