Conformal Anomaly via AdS/CFT Duality

TL;DR

This paper explores the conformal anomaly in the context of AdS/CFT duality, deriving c-functions from supergravity calculations to understand RG flows and central charges in dual conformal field theories.

Contribution

It introduces a method to derive c-functions from dilatonic supergravity by calculating the conformal anomaly, extending understanding of RG flows in dual CFTs.

Findings

Derived dilaton-dependent conformal anomalies in 3 and 5-dimensional supergravity.

Proposed candidate c-functions from dilatonic gravity and analyzed their properties.

Connected conformal anomalies to central charges and RG flow characteristics.

Abstract

AdS/CFT duality is a conjectured dual correspondence between the large $N$ limit of Conformal Field Theory (CFT) in $d$-dimensions and the supergravity (SUGRA) in $d+1$-dimensional Anti de Sitter (AdS) space. By using this conjecture, we can study various properties of large $N$ CFT by simple calculations in SUGRA. Recently much attention has been paid to the Renormalization Group (RG) flow viewed from the SUGRA side. Such RG flow in CFT is known to be characterized by the c-function which connects CFTs with different central charges. Therefore, we are interested in deriving this c-function from SUGRA with the help of AdS/CFT correspondence. To derive the c-function, we calculate the conformal anomaly (CA) in SUGRA, since it is closely related to the central charge. In this thesis, we discuss the various aspects of CA from AdS/CFT duality, especially for the cases of SUGRA in 3 and 5-dimensions which correspond to 2 and 4-dimensional CFTs, respectively. It is known that the bosonic part of SUGRA with scalar (dilaton) and arbitrary scalar potential describes the special RG flows in dual quantum field theory. So we calculate dilaton-dependent CA from dilatonic gravity with arbitrary potential. After that, we propose candidates of c-functions from such dilatonic gravity and investigate the properties of them.