Introduction to the Spectrum of N=4 SYM and the Quantum Spectral Curve

TL;DR

This review introduces the Quantum Spectral Curve as a powerful non-perturbative tool for analyzing the spectrum of N=4 Super Yang-Mills theory, emphasizing pedagogical explanations and future applications.

Contribution

It provides a comprehensive, accessible introduction to the Quantum Spectral Curve for N=4 SYM, including examples, exercises, and potential future research directions.

Findings

The QSC offers a non-perturbative approach to N=4 SYM spectrum.

Examples demonstrate the application of QSC to specific problems.

Future applications of QSC are outlined.

Abstract

This review is based on the lectures given by the author at the Les Houches Summer School 2016. It describes the recently developed Quantum Spectral Curve (QSC) for a non-perturbative planar spectrum of N=4 Super Yang-Mills theory in a pedagogical way starting from the harmonic oscillator and avoiding a long historical path. We give many examples and provide exercises. At the end we give a list of the recent and possible future applications of the QSC.