Center for Theoretical Physics

In recent years, detailed studies of three-pion systems have become possible in lattice QCD. This has in turn led to interest in 3-to-3 scattering of pions in the chiral perturbation theory framework. In addition to being an interesting study of multi-meson dynamics in its own right, it provides a valuable handle on finite-volume effects and the pion mass dependence, thus complementing the lattice results. I present our derivation of the next-to-leading order amplitude for this process, as well as its conversion into the three-particle K-matrix, which enables direct comparison to the lattice. Our results significantly improve the agreement between theory and lattice, which was poor when only leading-order effects were taken into account.

The theory of modular flow has proved extremely useful for applying thermodynamic reasoning to out-of-equilibrium states in quantum field theory. However, the standard proofs of the fundamental theorems of modular flow use machinery from Fourier analysis on Banach spaces, and as such are not especially transparent to an audience of physicists. In this article, I present a construction of modular flow that differs from existing treatments. The main pedagogical contribution is that I start with thermal physics via the KMS condition, and derive the modular operator as the only operator that could generate a thermal arrow of time, rather than starting with the modular operator as the fundamental object of the theory. The main technical contribution is a new proof of the fundamental theorem stating that modular flow is a symmetry. The new proof circumvents the delicate issues of Fourier analysis that appear in previous treatments, but is still mathematically rigorous.

Decades of analytic and computational work have demonstrated that a charge immersed in a hot plasma is screened. For both Abelian and non-Abelian interactions, the characteristic screening length \(1/m_D\) is set by the so-called Debye mass \(m_D \sim g_s T\), proportional to the plasma temperature \(T\) and the dimensionless gauge coupling \(g_s\). One of the most interesting naturally occurring examples is the quark-gluon plasma (QGP) that filled the early universe prior to the QCD confinement phase transition at \(t_{\rm QCD} \sim 10^{-5}\,{\rm s}\). During this early epoch, regimes of strong spacetime curvature are of significant cosmological interest, such as near primordial black holes (PBHs). However, the typical description of Debye screening only applies within Minkowski spacetime, and is therefore insufficient to describe the dynamics of charged plasmas near PBHs or other primordial features. We construct an effective field theory for soft modes of the gauge field \(A_\mu^a\) to give a full description of Debye screening in non-Abelian plasmas within arbitrary curved spacetimes, recovering a temperature-dependent Debye mass that exhibits gravitational redshift. We then apply our results to some scenarios of cosmological interest: an expanding FLRW universe and the vicinity of a PBH immersed in a hot QGP.

We derive an effective field theory (EFT) for cosmological Lyman alpha forest fluctuations valid for the power spectrum at the one-loop order. The ``bottom-up'' EFT expansion at the level of the transmitted flux is identical to the line-of-sight dependent bias model first derived by Desjacques et al. We confirm this result by a ``top-down'' derivation based on the exponential map of the optical depth field. Specifically, we show that the combination of the exponential map and conditions of renormalizability generates the same EFT expansion as the ``bottom-up'' approach. In passing, we point out inconsistencies of the tree-level perturbative expansion of the exponential map without counterterms. To facilitate practical applications, we generalize the FFTLog method for efficient calculations of one-loop integrals from new line-of-sight dependent operators. Finally, we compare the one-loop EFT model against data from the Sherwood hydrodynamic simulation. The theory fits the data with sub percent accuracy up to \(k= \) 3 \(h\)Mpc\(^{-1}\) at \(z= 2.8\) for both 3D and 1D correlations. Our model can be readily used for cosmological full-shape analyses of Lyman alpha forest data.