TASI Lectures on Effective Field Theories

TL;DR

This work surveys the framework and utility of effective field theories across three broad arenas. It first develops EFT foundations—matching, decoupling, RG methods, and nonrelativistic extensions such as HQET and NRQCD—emphasizing how UV details are encoded in local operators and how large logs are systematically resummed. It then extends EFT ideas to extra dimensions, explaining NDA, orbifolding, and AdS_5 constructions, and illustrating how higher-dimensional physics can influence 4D observables and unification. Together, the notes illustrate a cohesive set of tools for extracting low-energy predictions from theories with multiple scales, including those with extra spatial dimensions and curved backgrounds.

Abstract

These notes are a written version of a set of lectures given at TASI-02 on the topic of effective field theories. They are meant as an introduction to some of the latest techniques and applications in the field.

Figures (20)

• Figure 1: Tree level contributions to the full theory four point functions involving the heavy scalar (thick lines).
• Figure 2: One loop contributions to the full theory two point function.
• Figure 3: A partial list of the one loop contributions to the full theory four point functions.
• Figure 4: One loop contributions to the effective theory four point functions, with the dark circle representing an insertion of the derivative operator (\ref{['deriv']}).
• Figure 5: A diagram which contributes to a dimension six operator which is suppressed by $1/v^2$.