Universität Wien

260047 VU Supersymmetry - where geometry, algebra, and physics meet (2024W)

5.00 ECTS (3.00 SWS), SPL 26 - Physik
Prüfungsimmanente Lehrveranstaltung
Moodle

An/Abmeldung

Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").

Details

max. 15 Teilnehmer*innen
Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

  • Montag 07.10. 09:15 - 10:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 14.10. 09:15 - 10:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 21.10. 09:15 - 10:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 28.10. 09:15 - 10:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 04.11. 09:15 - 10:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 11.11. 09:15 - 10:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 18.11. 09:15 - 10:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 25.11. 09:15 - 10:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 02.12. 09:15 - 12:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 09.12. 09:15 - 12:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 16.12. 09:15 - 12:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 13.01. 09:15 - 12:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Montag 20.01. 09:15 - 12:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

Supersymmetry is a symmetry that links bosons and fermions. It has become a crucial tool for studying strongly coupled quantum field theories across various space-time dimensions and plays a significant role in string theory. This course aims to explore the mathematical structures underlying theories with extended supersymmetry and connect them to phenomena in quantum field theory.

Course Outline:
1. Supersymmetric Field Theories and Their Ground States/Vacua
2. The Higgs Mechanism, Higgs Vacua, and Their Counting via Hilbert Series
3. Geometry and Algebra of Kähler and Hyper-Kähler Spaces
4. Nilpotent Orbits of sl(N) and their partial order
5. Connecting Geometry and the Higgs Mechanism
6. Coulomb Vacua and the Role of Monopoles
7. Outlook and Future Directions

This course will showcase how classical physics (Higgs vacua) and quantum physics (Coulomb vacua) interact with sophisticated mathematics, such as hyper-Kähler singularities and their stratification. Every mathematical concept will be tied to a specific physical counterpart. The techniques introduced, drawn from geometry, algebra, and physics, have applications beyond the supersymmetric framework.

Lectures will be complemented by exercises designed to reinforce and deepen the material. A strong emphasis will be placed on mastering the computational techniques central to the study of supersymmetric field theories.

Students should be familiar with the content of “Advanced Quantum Mechanics” and have a solid understanding of core theoretical physics topics, particularly quantum mechanics, symmetries, and Noether’s theorem. While not mandatory, it is recommended that students have taken “Introduction to Supersymmetry” or at least “Advanced Particle Physics,” as these courses will provide helpful background for the more advanced topics covered.

Art der Leistungskontrolle und erlaubte Hilfsmittel

Evaluation will be based on two written exams.

Mindestanforderungen und Beurteilungsmaßstab

50% of the total points in the exams are required to pass.

Prüfungsstoff

Content of the course

Literatur

There is no single text book (yet) that covers the contents of this course. However, the following theses give a rough impression:
1) J. Grimminger, Imperial College London, 2018, MSc thesis <https://imperialcollegelondon.box.com/s/romi46yfr1wa6yyrj9979maostnp3h9q>
2) G. Kumaran, Imperial College London, 2022, MSc thesis <https://www.imperial.ac.uk/media/imperial-college/research-centres-and-groups/theoretical-physics/msc/dissertations/2022/Guhesh-Kumaran-Dissertation.pdf>

Don’t worry if you don’t understand everything right now—this course is here to help you learn!

Zuordnung im Vorlesungsverzeichnis

M-VAF A 2, M-VAF B, Doktorat Physics

Letzte Änderung: Di 08.10.2024 12:46