MSc Defense by Jichao Li

One-point functions in ABJM theory

As an analogy study of the domain version of $\mathcal{N}=4$ super Yang-Mills theory, this thesis focuses on the ABJM theory with a 1/2-BPS domain wall. We first review integrability methods for solving the spectrum of the $\mathfrak{su}(2)$ Heisenberg spin spin chains, such as the Coordinate Bethe ansatz and the Algebraic Bethe ansatz. As a generalization, we analyze the nested Bethe ansatz for the $\mathfrak{su}(n)$ fundamental spin chain. 

For solving the Bethe equations efficiently and automatically eliminating all nonphysical solution, we introduce the Rational $Q$-system for several types of spin chain. Among these, our focus is on the $\mathfrak{su}(4)$ alternating spin chain, which plays a significant role in ABJM theory.

Next, we review the original ABJM theory and its spectrum integrability. The two-loop dilatation operator in the scalar sector of ABJM theory can be identified with the Hamiltonian of $\mathfrak{su}(4)$ alternating spin chain. Thus, the spectrum of ABJM theory can be solved using the Bethe ansatz. Finally, we study the tree-level one-point functions in the 1/2-BPS domain wall version of ABJM theory. The domain wall corresponds to an integrable matrix product state, leading to a compact determinant formula for the one-point functions in spin chain language. 

Supervisor: Charlotte Kristjansen

Censor: Marta Orselli