AdS4/CFT3 : ABJM Theory, Brane Geometry, Correlators and Mellin Space

Abstract

This thesis delves into the $AdS_4/CFT_3$ correspondence (M-theory on $AdS_4 \times S^7 / \mathbb{Z}_k$ $\leftrightarrow$ ABJM theory) in a comprehensive and detailed manner. The ABJM theory i.e. $\mathcal{N} = 6$ $U(N)_k \times U(N)_{-k}$ Chern-Simons matter theory, is presented in $\mathcal{N} = 2$ superspace, with explicit demonstration of R-symmetry invariance. The associated brane configuration in type IIB string theory is examined, and the low-energy effective field content is shown to align with that of the ABJM theory, by considering string modes and boundary conditions in a new intuitive perspective on brane intersection boundaries and staged compactification. The consequent lift to M-theory, along with the resulting geometry and its Killing spinors in 11D supergravity, is thoroughly analyzed. The $AdS_4/CFT_3$ statement is then articulated, and its implications are explored, with a focus on the computational machinery of Witten diagrams, first in position space and subsequently in the more convenient Mellin space. The thesis culminates with the computation of the four-point function of the stress-tensor multiplet superconformal primary, incorporating contributions from additional short multiplets involving Spin-3 and Spin-4 exchanges not previously considered in the literature. These computations hold significant practical implications for the M-theory S-matrix. As an overall remark, the streamlined nature of this comprehensive work also aims to inspire fresh insights from $AdS_4/CFT_3$, a duality that probes the non-perturbative aspects of M-theory; a theory that, if it exists, is a promising candidate for the theory of everything, yet remains shrouded in Mystery with much still unknown.