Talks

The next hope to constrain cosmological parameters observationally is in surveys of the large scale structure (LSS) of the universe. LSS has the potential to rival the CMB in cosmological constraints because the number of modes scales like the volume, but the nonlinear clustering due to gravity makes it more difficult to extract primordial parameters. In order to take full advantage of the constraining power of LSS, we must understand it in the quasi-nonlinear regime. The effective field theory (EFT) of LSS provides a consistent way to perturbatively predict the clustering of matter at large distances. In this talk, I will discuss the status of the EFT of LSS and present recent work describing the inclusion of baryons in the EFT approach, including comparisons to N-body simulations.

Solitons in a ferromagnet have interesting dynamics because atomic magnetic moments behave like little gyroscopes. A domain wall in a magnetic wire can be modeled as a bead on a string: it has two soft modes, position and orientation. This "bead" rotates when it is pushed and moves when twisted.

From that one can deduce that the angular momentum is proportional to the domain wall's coordinate and the linear momentum to its azimuthal angle. In fact, the definition of conserved momenta for magnetic solitons has been discussed in the scientific literature for 40 years. A naive attempt to derive them from the application of Noether's theorem yields unphysical, gauge-dependent answers. To resolve this problem, we exploit a similarity between the dynamics of a ferromagnetic soliton and that of a charged particle in a magnetic field. For the latter, canonical momentum is also gauge-dependent and thus unphysical; the physical momentum is the generator of magnetic translations, a symmetry combining physical translations with gauge transformations. We use this analogy to unambiguously define conserved momenta for ferromagnetic solitons.

I consider the Standard Model as an effective field theory (EFT) at the electroweak scale $v$. At the scale $f\geq v$ I assume a new, strong interaction that breaks the electroweak symmetry dynamically. The Higgs boson arises as a composite pseudo-Nambu-Goldstone boson in these scenarios and is therefore naturally light $(m_{h}\sim v)$. Based on these assumptions and the value of $\xi=v^{2}/f^{2}$, I explain the systematics that governs the effective expansion:\\

For $\xi=\mathcal{O}(1)$ the effective theory is given by a loop expansion, equivalent to an expansion in chiral dimensions (similar to chiral perturbation theory). I will briefly discuss the operators that arise at next-to-leading order ($\mathcal{O}(f^{2} / \Lambda^{2})\simeq \mathcal{O}(1/16\pi^{2})$). On the other hand, in the decoupling limit where $\xi\rightarrow 0$, an expansion in canonical dimension is recovered. The case where $\xi$ is small but non-zero is of phenomenological interest. It leads to a double expansion in $\xi$ and $1/16\pi^{2}$, which captures the expected corrections of a strongly-interacting light Higgs to the Standard Model in a systematic way. \\

Further, I will apply the leading order chiral Lagrangian to current LHC Higgs data. I will show that this gives a QFT justification of the $\kappa$-framework, which is currently used as phenomenological signal-strength parametrization by the experiments at the LHC. I will also present a fit of the leading order chiral Lagrangian to the LHC Higgs data.