Spring 2021 Series
- 1 and 8 March: Nikolay Gromov, From Spin Chain to AdS/CFT with Mathematica
In this introductory lecture we describe the XXX Heisenberg spin chain, study its spectrum, wavefunctions and discuss integrability of the system. Some examples are given with simple Mathematica code. We also discuss applications to AdS/CFT correspondence.
Some derivations are formulated in the form of step-by-step exercises. They can be solved either with Mathematica or by hand.
A quick introduction to Mathematica is provided in a separate video here.
See the link below for the reading list and problem set. The mathematica notebook used in the video is also included as heisenbergexport.nb.
Some derivations are formulated in the form of step-by-step exercises. They can be solved either with Mathematica or by hand.
A quick introduction to Mathematica is provided in a separate video here.
See the link below for the reading list and problem set. The mathematica notebook used in the video is also included as heisenbergexport.nb.
nikolay_gromov_01_mar.pdf |
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- 8 and 15 March: Toby Wiseman, Gravity and Black Holes in AdS
Gravity in asymptotic AdS spacetimes behaves in many ways quite differently to the usual asymptotically flat situation we are usually introduced to. It is very important in understanding the AdS-CFT correspondence, and many of these differences to the flat setting have important implications. In this lecture and the problem sheet I will introduce AdS spacetime, asymptotic AdS spacetimes and then focus on the physics of black holes in AdS. For the simplest static black holes we will explore their behaviour, the implications for AdS-CFT and introduce some basic calculational tools to study them.
See the file below for a reading list and problem set.
See the file below for a reading list and problem set.
toby_wiseman_08_mar.pdf |
- 15 and 22 March: Olalla Castro Alvaredo, Entanglement in 1+1D Quantum Field Theory
In this short course I will introduce branch point twist fields and explain how they emerge in the context of computing entanglement measures in 1+1D. I will focus on massive 1+1D integrable quantum field theory (IQFT) and also comment on some well-known results in conformal field theory (CFT).
The talk will be structured into three main parts:
First, I will introduce entanglement measures, focussing on the entanglement entropy, explain how these measures relate to partition functions in multi-sheeted Riemann surfaces and how these, in turn, may be expressed as correlators of branch point twist fields.
Second, I will show how several well-known results in CFT and IQFT are very easily derived in this branch point twist field picture and how they can also be recovered numerically in a quantum spin chain.
Finally, I will explain how more involved computations with branch point twist fields may be performed by exploiting form factor technology and will end the talk by showing an example of one such calculation.
See the file below for a reading list and problem set.
The talk will be structured into three main parts:
First, I will introduce entanglement measures, focussing on the entanglement entropy, explain how these measures relate to partition functions in multi-sheeted Riemann surfaces and how these, in turn, may be expressed as correlators of branch point twist fields.
Second, I will show how several well-known results in CFT and IQFT are very easily derived in this branch point twist field picture and how they can also be recovered numerically in a quantum spin chain.
Finally, I will explain how more involved computations with branch point twist fields may be performed by exploiting form factor technology and will end the talk by showing an example of one such calculation.
See the file below for a reading list and problem set.
olalla_castro_alvaredo_15_mar.pdf |
- 22 and 29 March: Costis Papageorgakis, A Crash course on the Conformal Index
See the files below for lecture slides, and a reading list-cum-problem set, as well as a mathematica notebook. The solutions have been made available via the slack channel. There is a second video to help with the problem sheet and notebook prepared by Nikolay Gromov here.
index_ps.pdf |
costis_22__mar_solutions_1.pdf |
costis_22__mar_solutions_2.pdf |
lecture_on_superconformal_index.pdf |
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