APCTP winter school

26th APCTP Winter School on Fundamental Physics

Prof. Koenraad Schalm (Leiden university)
Title: A basic introduction to holographic duality and condensed matter applications
References
- Lecture notes: Mon. Tue. Wed.
- General reference: basically part of ch 4,5,6,8,10,11 of the book "Holographic Duality in Condensed Matter Physics"

Prof. Johanna Erdmenger (University of Würzburg)
Title: Kondo physics: from CMT to holography
References
- Introduction to Gauge/Gravity Duality (TASI Lectures 2017)
- Conformal Field Theory Approach to the Kondo Effect

Prof. Kantaro Ohmori (University of Tokyo)
Title: Topological Aspects of Symmetry in Low Dimensions
References:
- Lecture note by Kantaro Ohmori (will be updated during the school)
- Notes by Yuji Tachikawa: the first half of Yuji’s lecture is about the big framework the most of researchers assume (but not necessarily proven), which I will omit. The second half of Yuji's will serve as an advanced version of this lecture.
- Notes by Edward Witten: Not many overlap with this lecture but a good entry point to the field I think.
Abstract: In this lecture we will study the symmetry and its anomaly in low-dimensional, i.e. 0+1d and 1+1d, quantum field theories. In 0+1-dimensional quantum field theory, a.k.a quantum mechanics, the Wigner’s theorem tells that a global symmetry forms a group and acts on the Hilbert (state) space as a projective representation. We will see example with non-trivial projective phases and how it can be related to symmetry protected topological phases in 1+1-dimensions. We then see how the story are generalized/changed in 1+1-dimensional (relativistic) quantum field theory, where the locality of the theory plays an important role. Time permits, we also see how the inclusion of fermions affects the story.