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Random Tensors and Field Theory

Project description

Theoretical descriptions and practical applications of a new class of field theories

Advanced mathematical formulations are fundamental to our descriptions of complex physical systems, particularly in the fields of quantum mechanics and condensed matter. Perturbation techniques can make the complex more simple, enabling approximate solutions to problems without exact solutions starting from exact solutions to simpler problems. Perturbative large-N (or 1/N) expansion is a particular case of this. Its application to tensors led to the exciting discovery of a new class of mathematical models or field theories, the melonic theories. EU funding of the RTFT project will enable the scientist who made the discovery to explore the topic in much greater depth.


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.

Host institution

Net EU contribution
€ 1 493 934,54
69117 Heidelberg

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Baden-Württemberg Karlsruhe Heidelberg, Stadtkreis
Activity type
Higher or Secondary Education Establishments
Total cost
€ 1 493 934,54

Beneficiaries (2)