Non-invertible symmetries and higher categories

master's thesis

• Title (croatian): Neinvertibilne simetrije i više kategorije
• Author: Zlatko Posavec
• Mentor: Athanasios Chatzistavrakidis (mentor)
• Mentor: Ivica Smolić (komentor)
• Committee member: Ivica Smolić (predsjednik povjerenstva)
• Committee member: Athanasios Chatzistavrakidis (član povjerenstva)
• Committee member: Maro Cvitan (član povjerenstva)
• Committee member: Krešimir Kumerički (član povjerenstva)
• Committee member: Sanjin Benić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2024-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

This Master’s Thesis describes the modern treatment of symmetries in quantum field theories which is the result of recent developments and a change in perspective on symmetries in which symmetries are given by topological operators of the theory. It outlines the basic notions of category theory used in the SymTFT construction as well as the basic aspects of Topological Quantum Field Theories (TQFTs) needed to tackle the subject without relying heavily on the string theory and Conformal Field Theory (CFT) machinery which is usually present in other papers on this subject. Lastly, it uses the Chern-Simons and BF theory to provide elementary examples of the SymTFT construction at work.

Abstract (croatian)

Ovaj diplomski rad izlaže moderan tretman simetrija u kvantnim teorijama polja koji je rezultat nedavnih napredovanja u razumijevanju simetrija iz nove perspektive u kojoj su simetrije dane topološkim operatorima teorije. Rad izlaže osnovne pojmove teorije kategorije korištene u SymTFT konstrukciji kao i osnovne aspekte topoloških kvantnih teorija polja (TQFT) koji su potrebani za svladavanje ove teme bez oslanjanja na mašineriju teorije struna i konformalnih teorija polja (CFT) koja je prisutna u većini radova na ovu temu. Konačno, korišteni su primjeri Chern-Simonsove i BF teorije kako bi se demonstrirala SymTFT konstrukcija.

• Keywords: SymTFT; symmetries; topology; TQFT; orbifold; compactification; generalized charges; extended operators; topological operators; defects; stacking; category; fusion categories
• Keywords (croatian): SymTFT; simetrije; topologija; TQFT; orbifold; kompaktifikacija; generalizirani naboji; prošireni operatori; topološki operatori; defekti; stog teorije; kategorija; fuzijska kategorija
• Language: english
• URN:NBN: urn:nbn:hr:217:501934
• Study programme: Title: The University Integrated Undergraduate and Graduate Programme in Physics; Research Physics; specializations in: Research Physics; Course: Research Physics; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: sveučilišni magistar fizike (sveučilišni magistar fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2025-01-31 13:14:59