Neporuchové metody pro silně interagující teorie pole
| Název práce v češtině: | Neporuchové metody pro silně interagující teorie pole |
|---|---|
| Název v anglickém jazyce: | Non-perturbative methods for strongly coupled field theories |
| Klíčová slova: | CFT|konformní bootstrap|neporuchové metody|O(N) model|technika velkého N|AdS/BCFT |
| Klíčová slova anglicky: | CFT|conformal bootstrap|non-perturbative methods|O(N) model|large N|AdS/BCFT |
| Akademický rok vypsání: | 2024/2025 |
| Typ práce: | diplomová práce |
| Jazyk práce: | |
| Ústav: | Ústav částicové a jaderné fyziky (32-UCJF) |
| Vedoucí / školitel: | Mgr. Petr Vaško, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 17.02.2025 |
| Datum zadání: | 17.02.2025 |
| Datum potvrzení stud. oddělením: | 18.02.2025 |
| Konzultanti: | RNDr. Jiří Novotný, CSc. |
| Zásady pro vypracování |
| The aim of this thesis is to introduce the student to a set of (non)-perturbative methods that can be used to compute observables in strongly coupled QFTs. These include epsilon expansions, large N techniques, placing the QFT in AdS, and in particular the conformal bootstrap. The selected subset on which the greatest attention will be focused will depend on the student's interests.
The perfect testing ground for all the above mentioned approaches is the O(N) model that features a non-trivial phase structure and a strongly coupled critical point in dimensions 2<d<4.The special case N=1 known as the Ising model has been analyzed with great success via the conformal bootstrap (and the up to date most precise critical exponents have been obtained in this way). After getting familiar with the bootstrap algorithm and the necessary software, we could try to reproduce the simplest of these results. If time allows, the critical O(N) model can be studied in the presence of a boundary. Either by the conformal bootstrap [2] or by AdS methods [1]. |
| Seznam odborné literatury |
| [1] Dean Carmi, Lorenzo Di Pietro, and Shota Komatsu; "A Study of Quantum Field Theories in AdS at Finite Coupling"; JHEP, 2019
[2] Padaysi et al.; "The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap"; SciPost, 2022 [3] Pedro Liendo, Leonardo Rastelli, Balt van Rees; "The bootstrap program for boundary CFT"; JHEP 2013 [4] David Simmons-Duffin; "TASI lectures on the conformal bootstrap" [5] Shai Chester; "Weizman lectures on the numerical conformal bootstrap"; Phys.Rept., 2023 |