Universität Wien

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

5.00 ECTS (3.00 SWS), SPL 26 - Physik
Continuous assessment of course work
Moodle
Mo 11.11. 09:15-10:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 15 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

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

Information

Aims, contents and method of the course

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.

Assessment and permitted materials

Evaluation will be based on two written exams.

Minimum requirements and assessment criteria

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

Examination topics

Content of the course

Reading list

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!

Association in the course directory

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

Last modified: Tu 08.10.2024 12:46