The Mandelstam Institute for Theoretical Physics will host the 15th Joburg School on Theoretical Physics from 1-5 December 2025. The school is aimed at MSc and PhD students who already have a solid background in Quantum Field Theory and General Relativity. Postdoc students and staff working in the field are also welcome to attend.
The school aims to provide pedagogical introductions to a variety of exciting recent developments in string theory with broader applications. These include:
- Trace relations, branes and holography
- Quantum chaos in low dimensional gravity
- Planar integrability in supersymmetric gauge theory
There will be +/- 6 1-hour lectures per topic.
Lecturers
- Ji Hoon Lee (ETH Zurich)
- Jeremy van der Heijden (University of British Columbia, Vancouver)
- Costas Zoubos (University of Pretoria)
Abstracts
Trace relations, branes and holography
In these lectures, I will discuss a holographic relation between the states of giant graviton branes in anti-de Sitter space and trace relations in the dual gauge theory, and study the implications of this connection for holography at finite N. In a computation of the partition function of BPS states in AdS5 x S5, we will find that the maximal giant is an unstable saddle point and that its states contribute negatively to the partition function. The cohomological treatment of trace relations in N=4 SYM suggests that these D-brane states can be regarded as bulk duals of trace relations. We suggest that the Lefschetz trace formula, which computes bulk observables as an alternating sum of the expectation values in an ensemble of states built on each classical open string vacuum, may be a useful way to formulate the holographic map at finite N. The final lecture will extend these ideas to AdS3 duals of symmetric orbifold CFTs. In this context, we show that a sum over one-loop partition functions of an infinite set of bulk geometries that are asymptotic to AdS3 x S3 x M4 reproduces the integer spectrum of chiral primaries in the symmetric orbifold at finite N.
Quantum chaos in low dimensional gravity
These lectures will provide an introduction to the physics of quantum chaos and its connection to two-dimensional quantum gravity. We will begin by reviewing the basic concepts of quantum chaos, focusing on the universality of spectral statistics, through the example of random matrix theory. Special attention will be given to computational tools such as the spectral form factor, which provide practical ways to probe chaotic dynamics in quantum systems.
The second part of the lectures will focus on two-dimensional gravity, in particular Jackiw–Teitelboim (JT) gravity, which offers a remarkably rich yet tractable setting to study quantum aspects of spacetime. We will discuss how the inclusion of nontrivial topology—so-called spacetime wormholes—leads to results that agree with the predictions of random matrix theory. This correspondence raises fundamental questions about the nature of two-dimensional holography, in particular, to what extent the underlying microscopic theory is captured by gravity.
To explore some of these questions, we will study the very late-time regime of quantum chaos using a powerful method based on supersymmetry. We will then ask whether there is an interpretation of these structures within the gravitational setting, leading to a novel geometric framework for describing late-time quantum chaos that goes beyond JT gravity. We will conclude by commenting on the implications of these ideas for more realistic models of quantum gravity.
Together, these lectures aim to provide both a conceptual overview and a technical toolkit for understanding the interplay between quantum chaos and two-dimensional gravity.
Planar integrability in supersymmetric gauge theory
I will provide an overview of how the spectrum of certain four-dimensional supersymmetric gauge theories can be mapped, in the planar limit, to the solution of one-dimensional Heisenberg-type spin chains, and how that, in turn, is related to classical string solutions on the AdS/CFT-dual backgrounds. After discussing the simplifications brought about by the planar limit and superconformal invariance, and also introducing some needed aspects of AdS/CFT, I will consider the one-loop mixing problem of the N=4 Super-Yang-Mills theory and how it can be approached using techniques from integrable systems. In particular, the Bethe Ansatz for the XXX chain will be discussed in detail. In order to extend these one-loop results to general values of the couping, one needs additional input from the dual AdS/CFT side. Therefore I will then discuss the integrability of classical string solutions on AdS_5xS^5 and how they provide the information needed to find the equations describing the spectral problem at general coupling. These provide the exact coupling dependence of certain non-protected operators, such as the Konishi operator, which is a spectacular achievement for a nontrivial 4-dimensional gauge theory. If time allows, I will discuss how far these results can be extended to cases with less supersymmetry or to cases where defects are present.
Venue
University of the Witwatersrand (WITS)
Support
During the school, lunch will be provided. There will also be funding for accommodation and subsistence for students from South African universities other than WITS who wish to participate in the school. Please indicate on the registration form if support is required.
Organisers
Pallab Basu, Kevin Goldstein, Vishnu Jejjala, Anosh Joseph, Sam van Leuven, João Rodrigues, Costas Zoubos
Contact
For any queries, please contact Sam van Leuven at: sam.vanleuven@wits.ac.za
Acknowledgements
The organisers thank NITheCS for generously funding the school and WITS for their support.
