Selected topics in AdS/CFT correspondence

(NTMF082, winter term 2022/23)


Lecturer: David Kubiznak (

Institute of Theoretical Physics, MFF UK

Dotation: 2/1, oral exam



We will cover the basics of the gauge/gravity duality, including some of the following aspects: holographic RG flows, fluid/gravity correspondence, applications to condensed matter systems, holographic entanglement entropy, and recent advances in understanding the black hole information paradox. For PhD and Mgr students – basic knowledge of general relativity and quantum field theory is required.


Preliminary topics



You will be asked one theoretical and one computational question out of the following two sets. You will have 30 minutes to prepare your answers. After that, we will discuss your answers together with some (un)related problems. The discussion should last about 30 minutes, after which I will provide my feedback to you.

·     Here is the List of exam questions


Additional reading

·        Study text (will be updated as the course progresses)

·        Gauge/gravity duality: Foundations and applications, M. Ammon and J. Erdmenger, Cambridge University Press, 2015.

·        Holographic entanglement entropy: An overview, T. Nishioka, S. Ryu, T. Takayanagi, J. Phys. A 42 (2009) 504008; ArXiv:0905.0932.

·        The entropy of Hawking radiation, A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, A. Tajdini, Rev. Mod. Phys. 93 (2021) 3, 035002; ArXiv:2006.6872.


·      Lecture 1: Black hole thermodynamics

·      Lecture 2: Properties of Hawking radiation, Black hole info paradox, AdS action

·      Lecture 3: Hawking-Page phase transition, Classical p-branes

·      Lecture 4: Superstrings and D-branes

·      Lecture 5: AdS/CFT conjecture

·      Lecture 6: CFT propaganda & AdS primer

·      Lecture 7: State operator correspondence, Correlation functions

·      Lecture 8: 2-point function calculation, Holographic renormalization

·      Lecture 9: Conformal anomaly, Wilson loops

·      Lecture 10: Finite temperature, holographic hydrodynamics

·      Lecture 11: Fluid/gravity correspondence, Entanglement entropy

·      Lecture 12: Black hole information paradox


Lectures and tutorials

Mondays, 13:10-15:35, A1032UTF (Troja, UTF)


·       Tutorial 1: Actions and boundary terms   Solutions T1

·       Tutorial 2: Euclidean magic – Unruh radiation Solutions T2

·       Tutorial 3: Strings and Throats  Solutions T3

·       Tutorial 4: Feelings for D-branes  Solutions T4

·       Tutorial 5: Conformal symmetry   Solutions T5

·       Tutorial 6: Energy momentum tensor   Solutions T6

·       Tutorial 7: Holographic renormalization 1   Solutions T7

·       Tutorial 8: Holographic renormalization 2

·       Tutorial 9: Wilson loops: quark-antiquark potential   Solutions T9

·       Tutorial 10: Finite temperature AdS/CFT   Solutions T10

·       Tutorial 11: Calculating eta/s   Solutions T11