Conformal Quantum Field Theory in D-dimensions

Alexander A. Belavin, Yaroslav Pugai, Alexander B. Zamolodchikov

Volume 1 is a collection of reprinted works of Alexei Zamolodchikov who was a prominent theoretical physicist of his time. It contains his works on conformal field theories, 2D quantum gravity, and Liouville theory. These original contributions of Alexei Zamolodchikov have a profound effect on shaping the fast developing areas of theoretical physics. His ideas are expressed lucidly, such as the recursive relation for conformal blocks and the structure of conformal bootstrap in Liouville theory, including the boundary Liouville theory. These ideas are at the foundation of the subject and they are of great interest to a wide community of physicists and mathematicians working in diverse areas. This volume is a part of the 2-volume collection of remarkable research papers that can be used as an advanced textbook by graduate students specializing in string theory, conformal field theory and integrable models of QFT. It is also highly relevant to experts in these fields. Volume 2 includes Alexei Zamolodchikov's works on non-perturbative methods in 2D quantum field theory, and on integrable models.

Efim S. Fradkin, M.Ya. Palchik

Takanori Anegawa, Norihiro Iizuka, Daniel Kabat

We previously proposed that entanglement across a planar surface can be obtained from the partition function on a Euclidean hourglass geometry. Here we extend the prescription to spherical entangling surfaces in conformal field theory. We use the prescription to evaluate log terms in the entropy of a conformal field theory in two dimensions, a conformally coupled scalar in four dimensions, and a Maxwell field in four dimensions. For Maxwell we reproduce the extractable entropy obtained by Soni and Trivedi. We take this as evidence that the hourglass prescription provides a Euclidean technique for evaluating extractable entropy in quantum field theory.

Paolo Furlan, Galen M. Sotkov, Ivan T. Todorov

Luis Álvarez-Gaumé

Koushik Bar, Supervisors Dr. Sunandan Gangopadhyay, Prasanta Kumar Panigrahi

These features the study of conformal quantum field theories, in dimensions greater than two dimension and very special case of two dimensions. Over the last two decades, the understanding and mathematical formulation of such theories has developed to a very mature state, and conformal field theory (CFT) has in uenced both mathematics and physics. As such, it can be considered a prototype example for a constructive interplay between these two subjects. The main feature of a conformal field theory is the invariance under conformal transformations. We also review the development in the field of entanglement entropy, the holographic aspect of it, and the AdS/CFT conjuncture. Describe the Ruy-Takayangai conjecture of Entanglement Entropy and study the reconstruction of the AdS metric using the same for two different case, which are, 1+1 CFT in Infinite Line, and 1+1 CFT in compact circle.