# CERN Winter School on Strings and Fields 2017

Feb 6 – 10, 2017
CERN
Europe/Zurich timezone

### Support

Johanna Erdmenger:

Abstract:

The Kondo model  describes the interaction of a free electron gas with a magnetic impurity. It was decisive in the development of the renormalisation group (RG). In particular, it has features similar to QCD, such as a negative beta function, the breakdown of perturbation theory and the formation of a bound state at low energies. The Kondo model was solved using a variety of approaches, including boundary conformal field theory and a large N expansion. In the lectures I will briefly review this model and then move on to a recent realisation of a variant within gauge/gravity duality. Here, the magnetic impurity interacts with a strongly coupled electron system. I will explain how the gravity dual is constructed and discuss its physical properties. In particular, I will use it to calculate the entanglement entropy, quantum quenches and two-point functions. Finally, I will compare to some aspects of the related Sachdev-Ye-Kitaev (SYK) model.

1) Holographic Kondo model:

J. Erdmenger, C. Hoyos, A. O’Bannon, J. Wu: A holographic model of the Kondo effect. arXiv:1310.3271.

J. Erdmenger, M. Flory, C. Hoyos, M. Newrzella, J. Wu, Entanglement entropy in a holographic Kondo model. arXiv:1511.03666.

J. Erdmenger, C. Hoyos, A. O’Bannon, I. Papadimitriou, J. Probst, J. Wu, Holographic Kondo and Fano resonances. arXiv:1611.09368.

J. Erdmenger, C. Hoyos, A. O’Bannon, I. Papadimitriou, J. Probst, J. Wu, Two-point functions in a holographic Kondo model, arXiv:1612.02005.

J. Erdmenger, M. Flory, M. Newrzella, M. Strydom, J. Wu, Quantum quenches in a holographic Kondo model, arXiv:1612.06860.

2) Sachdev-Ye-Kitaev model:

S. Sachdev: Bekenstein-Hawking entropy and strange metals, arXiv:1506.05111.

S. Hartnoll, A. Lucas, S. Sachdev: Holographic quantum matter, arXiv:1612.07324, and references therein.

Joao Penedones:

Abstract:  In the first part of these lectures, we will start by reviewing the conformal bootstrap approach to conformal field theory (CFT). This approach leads to universal bounds on scaling dimensions and operator product expansion coefficients in CFT. We will then show that quantum field theory (QFT) in hyperbolic space can be studied using the same conformal bootstrap equations. In particular, in the flat space limit of hyperbolic space one obtains universal bounds on coupling constants in QFT.

In the second part of these lectures, we will discuss how analyticity, unitarity and crossing symmetry of scattering amplitudes can be used to derive the same bounds.

It would be useful if the students knew the basics of the conformal bootstrap. The following lecture notes are a good introduction to the subject:

https://arxiv.org/abs/1601.05000

https://arxiv.org/abs/1602.07982

Ashoke Sen:

https://indico.cern.ch/event/565320/attachments/1403279/2142937/revout.pdf

Alberto Zaffaroni:

Abstract: In these series of lectures I  discuss how localization techniques can be applied to the counting of micro-states of a class of AdS black holes using holography. I  first give a general overview of localization as a method for computing exact quantities in supersymmetric field theories. I  then apply the method to a specific class of supersymmetric there dimensional theories.
I will provide few examples for finite and large N and  applications to dualities. Finally, I evaluate a topologically twisted partition function for the ABJM theory and show that it correctly reproduces the entropy of a class of dyonic black holes in AdS4. Time permitting, I discuss
generalizations to other dimensions.

General references: everything you want to know about localization is in arXiv 1608.02952

Specific references: arXiv 1504.03698, 1511.04085, 1605.06120.