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Physics and mathematics of the 1/N expansion

Applicant Mariño Beiras Marcos
Number 156995
Funding scheme Project funding (Div. I-III)
Research institution Département de Physique Théorique Université de Genève
Institution of higher education University of Geneva - GE
Main discipline Theoretical Physics
Start/End 01.10.2014 - 30.11.2017
Approved amount 385'577.00
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Keywords (4)

1/N expansion; Random matrices; String theory; Geometry

Lay Summary (Italian)

Lead
La cosiddetta espansione 1/N, fu introdotta negli anni '70 come strumento per studiare la teoria dei quark e dei gluoni. Grazie alla teoria delle stringhe, questo metodo si è rivelato particolarmente utile nello studio della gravità quantistica ed ha permesso di sviluppare nuove idee nel campo della matematica.In questo progetto studieremo gli aspetti fisici e matematici dell’espansione 1/N limitandoci a dei modelli semplici seppure di una certa importanza sia fisica sia matematica.
Lay summary

La sviluppo di una teoria che che concili la meccanica quantistica e la gravità è attualmente uno dei problemi più importanti della fisica teorica. Infatti, tra tutte le forze fondamentali presenti nell'universo, la gravità rimane per alcuni aspetti la più misteriosa. Una teoria della gravità quantistica porterebbe, per esempio, a una migliore comprensione della fisica dei buchi neri e del Big Bang.

Recentemente si è osservato che, in alcuni casi, la teoria delle stringhe fornisce una descrizione quantistica della gravità. Una tale descrizione viene fornita in modo radicale postulando che la gravità è un fenomeno collettivo che emerge da una teoria di campi quantistici. Più precisamente la gravità emerge dalla teoria dei campi quantistici come una sorta di limite termodinamico in cui il numero di gradi di libertà diventa molto grande. Quest'ultimo viene chiamato il limite a grande N ( o espansione 1/N)  e fu introdotto da 't Hooft negli anni ’70 come strumento per analizzare la cromodinamica quantistica.

Lo scopo principale di questo progetto di ricerca è di esplorare la matematica e la fisica dell'espansione 1/N. 
In particolare, il nostro obbiettivo è di studiare questo limite nel caso di alcuni modelli semplificati di cui si riesce a capire in dettaglio le proprietà. Questi modelli, nonostante la loro semplicità, hanno delle applicazioni concrete nel campo della gravità quantistica e possono servire come guida nella costruzione di modelli più realistici.

Una delle peculiarità del nostro progetto è il suo legame con la matematica. L’espansione 1/N  interessa molte aree della matematica, e spesso porta a nuove intuizioni che difficilmente si riuscirebbero ad avere seguendo metodi più convenzionali. In questo modo l’espansione 1/N ha portato a nuovi risultati nella teoria dei nodi e nella geometria enumerativa. 


Direct link to Lay Summary Last update: 14.10.2014

Responsible applicant and co-applicants

Employees

Publications

Publication
Holomorphic anomaly and quantum mechanics
Codesido Santiago, Marino Marcos (2018), Holomorphic anomaly and quantum mechanics, in J. Phys. A, 51(5), 055402.
Localization at large N in Chern-Simons-matter theories
Marino Marcos (2017), Localization at large N in Chern-Simons-matter theories, in JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 50(44), 443007.
Localization techniques in quantum field theories
Pestun Vasily, Zabzine Maxim, Benini Francesco, Dimofte Tudor, Dumitrescu Thomas T., Hosomichi Kazuo, Kim Seok, Lee Kimyeong, Le Floch Bruno, Marino Marcos, Minahan Joseph A., Morrison David R., Pasquetti Sara, Qiu Jian, Rastelli Leonardo, Razamat Shlomo S., Pufu Silvu S., Tachikawa Yuji, Willett Brian, Zarembo Konstantin (2017), Localization techniques in quantum field theories, in JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 50(44), 440301.
Exact eigenfunctions and the open topological string
Marino Marcos, Zakany Szabolcs (2017), Exact eigenfunctions and the open topological string, in JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 50(32), 325401.
Resurgence matches quantization
Couso-Santamaria Ricardo, Marino Marcos, Schiappa Ricardo (2017), Resurgence matches quantization, in JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 50(14), 145402.
Calabi-Yau geometry and electrons on 2d lattices
Hatsuda Yasuyuki, Sugimoto Yuji, Xu Zhaojie (2017), Calabi-Yau geometry and electrons on 2d lattices, in PHYSICAL REVIEW D, 95(8), 086004.
Spectral Theory and Mirror Curves of Higher Genus
Codesido Santiago, Grassi Alba, Marino Marcos (2017), Spectral Theory and Mirror Curves of Higher Genus, in ANNALES HENRI POINCARE, 18(2), 559-622.
Operators and higher genus mirror curves
Codesido Santiago, Gu Jie, Marino Marcos (2017), Operators and higher genus mirror curves, in JOURNAL OF HIGH ENERGY PHYSICS, (2), 092.
Topological Strings from Quantum Mechanics
Grassi Alba, Hatsuda Yasuyuki, Marino Marcos (2016), Topological Strings from Quantum Mechanics, in ANNALES HENRI POINCARE, 17(11), 3177-3235.
Matrix Models from Operators and Topological Strings, 2
Kashaev Rinat, Marino Marcos, Zakany Szabolcs (2016), Matrix Models from Operators and Topological Strings, 2, in ANNALES HENRI POINCARE, 17(10), 2741-2781.
Exact results for ABJ Wilson loops and open-closed duality
Hatsuda Yasuyuki, Okuyama Kazumi (2016), Exact results for ABJ Wilson loops and open-closed duality, in JOURNAL OF HIGH ENERGY PHYSICS, (10), 132.
Hofstadter's butterfly in quantum geometry
Hatsuda Yasuyuki, Katsura Hosho, Tachikawa Yuji (2016), Hofstadter's butterfly in quantum geometry, in NEW JOURNAL OF PHYSICS, 18, 103023.
Operators from Mirror Curves and the Quantum Dilogarithm
Kashaev Rinat, Marino Marcos (2016), Operators from Mirror Curves and the Quantum Dilogarithm, in COMMUNICATIONS IN MATHEMATICAL PHYSICS, 346(3), 967-994.
ABJM on ellipsoid and topological strings
Hatsuda Yasuyuki (2016), ABJM on ellipsoid and topological strings, in JOURNAL OF HIGH ENERGY PHYSICS, (7), 026.
Exact quantization conditions for cluster integrable systems
Franco Sebastian, Hatsuda Yasuyuki, Marino Marcos (2016), Exact quantization conditions for cluster integrable systems, in JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 063107.
Exact quantization conditions for the relativistic Toda lattice
Hatsuda Yasuyuki, Marino Marcos (2016), Exact quantization conditions for the relativistic Toda lattice, in JOURNAL OF HIGH ENERGY PHYSICS, (5), 133.
Matrix Models from Operators and Topological Strings
Marino Marcos, Zakany Szabolcs (2016), Matrix Models from Operators and Topological Strings, in ANNALES HENRI POINCARE, 17(5), 1075-1108.
Quantization conditions and functional equations in ABJ(M) theories
Grassi Alba, Hatsuda Yasuyuki, Marino Marcos (2016), Quantization conditions and functional equations in ABJ(M) theories, in JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 49(11), 115401.
Exact solutions to quantum spectral curves by topological string theory
Gu Jie, Klemm Albrecht, Marino Marcos, Reuter Jonas (2015), Exact solutions to quantum spectral curves by topological string theory, in JOURNAL OF HIGH ENERGY PHYSICS, (10), 025.

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Quantim fields, knots and integrable systems Talk given at a conference The spectral theory of quantum mirror curves 27.02.2017 ICMS, Edinburgh, Great Britain and Northern Ireland Mariño Beiras Marcos;
String theory: past and present Talk given at a conference Free fermions, strings, and the 1/N expansion 13.01.2017 ICTS, Bangalore, India Mariño Beiras Marcos;
String-Math 2016 Talk given at a conference Spectral theory and topological strings 27.06.2016 College de France, Paris, France Mariño Beiras Marcos;
New spaces for mathematics and physics Talk given at a conference Stringy geometry and emergent space 28.09.2015 IHP, Paris, France Mariño Beiras Marcos;


Associated projects

Number Title Start Funding scheme
175539 Quantum Mechanics, Geometry and Strings 01.12.2017 Project funding (Div. I-III)
141869 NCCR SwissMAP: The Mathematics of Physics (phase I) 01.07.2014 National Centres of Competence in Research (NCCRs)

Abstract

The 1/N expansion has been a fundamental tool in physics since their first use in statistical mechanics almost fifty years ago, and it was famously proposed by 't Hooft as a way to understand the dynamics of Yang-Mills theory and QCD. In the last fifteen years, the idea that the 1/N expansion leads to a string theory has been implemented in a concrete way in the AdS/CFT correspondence, opening new avenues to understand both the dynamics of gauge theories and the nature of gravity. It has led in addition to deep insights on mathematics, particularly in algebraic geometry and knot theory. The goal of this project is to understand the mathematical structures underlying the 1/N expansion, and its applications in different fields of physics and mathematics. The focus of the project will be on simplified models of the 1/N expansion which, on the one hand, have applications in quantum field theory and quantum gravity, and on the other hand, lead to interesting connections with mirror symmetry, random matrix theory, integrable systems, and other areas of modern mathematics.
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