Les Houches Lectures on Effective Field Theories and Gravitational Radiation

TL;DR

The paper presents Les Houches lectures on applying effective field theory to gravitational radiation from compact binaries, framing the problem with multiple separated scales and introducing a tower of EFTs to organize the post-Newtonian expansion. It develops a two-stage NRGR approach, first integrating out the internal structure to a point-particle EFT and then integrating out orbital-scale potential modes to obtain a radiation EFT with multipole degrees of freedom, enabling a controlled calculation of observables such as gravitational-wave power. Key results include explicit matching procedures, velocity-counting rules, and the emergence of the leading quadrupole radiation formula, along with an assessment of finite-size effects and their suppression. The framework provides a scalable and extensible toolkit for LIGO/LISA science and for future connections to numerical relativity and other astrophysical GW sources.

Abstract

These lectures give an overview of the uses of effective field theories in describing gravitational radiation sources for LIGO or LISA. The first lecture reviews some of the standard ideas of effective field theory (decoupling, matching, power counting) mostly in the context of a simple toy model. The second lecture sets up the problem of calculating gravitational wave emission from non-relativistic binary stars by constructing a tower of effective theories that separately describe each scale in the problem: the internal size of each binary constituent, the orbital separation, and the wavelength of radiated gravitons.

Figures (9)

• Figure 2: Leading order contribution to $\pi\pi\rightarrow\pi\pi$ scattering in the full theory. The intermediate double line corresponds to the $\rho$ field propagator.
• Figure 3: Feynman graphs contributing to the $\pi$ field self-energy in the full theory with a propagating $\rho$ field.
• Figure 4: Feynman graphs contributing to the $\pi$ field self-energy in the low energy EFT. Graph (b), including one insertion of the coupling $c_8$ vanishes in dimensional regularization.
• Figure 5: Construction of a low energy EFT for a theory with scales $\Lambda_1\gg \Lambda_2\gg\omega$.
• Figure 6: Feynman graphs contributing to the $\pi\pi\rightarrow\pi\pi$ in the effective theory. Graph (a) corresponds to one insertion of the dimension eight operator $(\partial_\mu\pi \partial^\mu\pi)^2$. Graphs (b), (c) correspond to insertions of a generic dimension ten and twelve operator, respectively. Note that the $\omega/\Lambda$ power counting scheme implies that the one-loop diagram (d) comes in at the same order as the tree graph (c).