Title Generalized symmetries and tensor gauge theories Title (english) Generalizirane simetrije i tenzorske baždarne teorije Author Sara Zeko 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 Defense date and country 2024-10-22, Croatia Scientific / art field, NATURAL SCIENCES Abstract This work investigates the intricate relationships between generalized global symmetries and tensor gauge theories, particularly focusing on the interpretation of the graviton as a Nambu-Goldstone boson for a spontaneously broken generalized global symmetry. The first sections present a review of ordinary and higher-form symmetries, guided by the example of the free Maxwell theory. The central aim is to understand how higher-dimensional objects, naturally extend symmetry principles and manifest
... More in various physical contexts. We introduce the generalization of global symmetries through familiar ordinary symmetries. Higher-form symmetries are symmetries that lead to higher-form conserved currents. They are discussed within the examples of free Maxwell theory and its electric-magnetic duality. The topological aspects of higher-form symmetries are provided, too. Furthermore, other developments in the generalization of symmetry principles are briefly presented, such as highergroup symmetries (like 2-group symmetries) and non-invertible symmetries. 2-group symmetries, i.e. symmetries that allow for the mixing of background gauge fields under their respective gauge transformations are considered through the simplest Abelian case where we have shown how it is derived from ordinary product flavor symmetry by gauging. Another notable generalization discussed in this work is non-invertible symmetries. Unlike traditional symmetries, which are invertible (i.e., they can be undone by applying the inverse transformation), non-invertible symmetry operators do not have inverses. These symmetries arise in systems where the usual group structure of symmetries breaks down. Instead of standard group multiplication rules, the operators that implement such symmetry obey some other fusion rules. For theories exhibiting some duality, the global symmetries must match - this is also true for higher-form symmetries. The dualization procedure is done in detail for the Maxwell theory and is later abbreviated to a recipe that works for Maxwell-like Lagrangians and is shown for, not only the free Maxwell theory but also for some non-linear theories of electrodynamics. The theory of linearized gravity is a tensor gauge theory pivotal to this work. Tensor gauge theories generalize conventional gauge theories by employing higher-rank tensors. The core of the thesis lies in the chapter "Graviton as a Nambu-Goldstone boson." This section explores the idea that the graviton, the quantum of the gravitational field, can be seen as a Nambu- Goldstone boson. Through the lens of linearized gravity, the massless mode of the metric perturbation is reinterpreted as arising from a spontaneously broken higher-form symmetry, specifically a biform symmetry. This perspective not only provides a fresh outlook on the nature of the graviton but also highlights the role of symmetry breaking in understanding massless spin-2 particles in gauge theory. Concluding with the recent developments, we have also presented potential avenues for future exploration regarding the graviton as a NambuGoldstone boson. Less Abstract (croatian) Rad istražuje složene odnose između generaliziranih globalnih simetrija i tenzorskih baždarnih teorija, posebno se fokusirajući na interpretaciju gravitona kao Nambu-Goldstoneovog bozona za spontano slomljenu generaliziranu globalnu simetriju. Prvi dijelovi predstavljaju pregled običnih simetrija te simetrija viših formi, vođeni primjerom slobodne Maxwellove teorije. Središnji cilj je razumjeti kako višedimenzionalni objekti prirodno proširuju principe simetrije te kako se one manifestiraju u
... More raznim fizikalnim kontekstima. Uvodimo poopćenje globalnih simetrija kroz poznate obične simetrije. Simetrije viših formi su simetrije koje dovode do sačuvanih struja viših formi. O njima se raspravlja kroz primjer slobodne Maxwellove teorije i njezine elektromagnetske dualnosti. Također su navedeni topološki aspekti simetrije viših formi. Nadalje, kratko su predstavljeni i drugi razvoji u generalizaciji principa simetrije, kao što su simetrije više-grupe (poput 2-grupne simetrije) i neinvertibilne simetrije. 2-grupne simetrije, tj. simetrije koje omogućuju miješanje pozadinskih baždarnih polja pod njihovim odgovarajućim baždarnim transformacijama, razmatrane su kroz najjednostavniji abelovski slučaj gdje smo pokazali kako one proizlaze iz obične produktne simetrije okusa baždarenjem. Druga značajna generalizacija koja se raspravlja u ovom radu su neinvertibilne simetrije. Za razliku od tradicionalnih simetrija, koje su invertibilne (tj. mogu se poništiti primjenom inverzne transformacije), operatori neinvertibilnih simetrija nemaju inverze. Ove simetrije nastaju u sustavima gdje uobičajena grupna struktura simetrija propada. Umjesto standardnih pravila množenja generatora, operatori koji implementiraju takvu simetriju poštuju neka druga pravila fuzije. Za teorije koje pokazuju dualnost, globalne simetrije moraju se podudarati - to vrijedi i za simetrije viših formi. Postupak dualizacije detaljno je objašnjen za Maxwellovu teoriju i kasnije je skraćen na recept koji djeluje za lagranžijane slične Maxwellovom, a prikazan je, ne samo za slobodnu Maxwellovu teoriju, nego i za neke nelinearne elektrodinamičke teorije. Teorija linearizirane gravitacije je tenzorska baždarna teorija ključna za ovaj rad. Tenzorske baždarne teorije generaliziraju konvencionalne baždane teorije koristeći tenzore višeg ranga. Cilj rada leži u poglavlju "Graviton kao Nambu-Goldstoneov bozon", gdje se istražuje ideja da se graviton, kvant gravitacijskog polja, može promatrati kao Nambu-Goldstoneov bozon. Kroz prizmu linearizirane gravitacije, bezmaseni mod perturbacije metrike reinterpretira se kao rezultat spontano slomljene simetrije više forme, konkretno biformne simetrije. Ova perspektiva ne samo da pruža nov pogled na prirodu gravitona, već također ističe ulogu narušenja simetrije u razumijevanju bezmasenih spin-2 čestica u baždarnoj teoriji. Zaključujući s nedavnim napretcima, također smo predstavili potencijalni put za buduće istraživanje gravitona kao Nambu-Goldstoneova bozona. Less Keywords
generalized symmetries
higher-form symmetries
free Maxwell theory
linearized gravity
graviton
gauge theories
dualities
’t Hooft anomalies
Keywords (croatian)
generalizirane simetrije
simetrije viših formi
slobodna Maxwellova teorija
linearizirana gravitacija
graviton
baždarne teorije
dualnost
’t Hooftove anomalije
Language english URN:NBN urn:nbn:hr:217:328785 Study programme Title: The University Integrated Undergraduate and Graduate Programme in Physics; Research Physics; specializations in: Research Physics Type of resource Text File origin Born digital Access conditions Open access Terms of use Created on 2025-02-01 08:58:29
