Conformal Theories and Holographic Dualities

Annotation

 In this lecture course we discuss a key phenomenon of modern theoretical physics --  the holographic duality principle or the gauge/gravity duality. It states that a theory of non-Abelian gauge fields can be considered as a quantum gravity theory living in a space of one more dimension. We focus on a particular example of the holographic duality known as the AdS/CFT correspondence between conformal field theories (CFT) and gravitational theories in AdS space. The main topics include higher-dimensional CFT, quantum field theory in AdS space, group-theoretical analysis of (conformal) isometry algebras, examples of calculations in holographically dual theories with scalar and vector operator content.

Course plan

1. Spinning primary operators and correlation functions in higher-dimensional CFT.
2. Generalized Verma module for the conformal algebra.
3. Ambient description of primary operators and correlation functions.  
4. Operator product expansions and conformal blocks. Conformal bootstrap.
5. AdS spacetime: coordinates, isometry, Penrose diagrams, conformal boundary. 
6. Particles in AdS as representations of the AdS algebra. Dirac singleton.
7. Klein-Gordon scalar equation in AdS and conformal boundary behaviour. 
8. Witten diagrams and Green’s functions in AdS.
9. The Gubser-Klebanov-Polyakov-Witten prescription.
10. Holographic calculation of 2-point correlation functions of scalar and vector primary operators.

Literature

1. H. Nastase, Introduction to the AdS/CFT correspondence, Cambridge University press, 2015.
2. M. Ammon, J. Erdmenger, Gauge/gravity duality, foundations and applications, Cambridge University press, 2015.
3. S. Rychkov, 'EPFL Lectures on Conformal Field Theory in D>3 dimensions', Springer Briefs in Physics, 2016.....