Do We Live in the Swampland?

TL;DR

The paper investigates whether the Standard Model, potentially with minimal extensions, can be UV-completed within quantum gravity given the swampland conjectures, focusing on quintessence, the Higgs sector, and the QCD axion. It derives a no-go result for simple Higgs-sector modifications and argues that the QCD axion is generically incompatible with the conjectures unless sophisticated loopholes are invoked, many of which face serious theoretical constraints. By systematically testing loopholes and considering beyond-Higgs ideas (SUSY breaking, multi-valued potentials), the authors discuss the broader phenomenological implications for CP violation and inflation. They also propose a potential modification to the swampland criterion to reconcile these tensions, highlighting ongoing uncertainty in connecting quantum gravity constraints with low-energy phenomenology.

Abstract

A low-energy effective theory is said to be in the swampland if it does not have any consistent UV completion inside a theory of quantum gravity. The natural question is if the standard model of particle physics, possibly with some minimal extensions, are in the swampland or not. We discuss this question in view of the recent swampland conjectures. We prove a no-go theorem concerning the modification of the Higgs sector. Moreover, we find that QCD axion is incompatible with the recent swampland conjectures, unless some sophisticated possibilities are considered. We discuss the implications of this result for spontaneous breaking of CP symmetry. We comment on dynamical supersymmetry breaking as well as the issue of multi-valuedness of the potential.

Figures (1)

• Figure 1: We can foliate the $D$-dimensional configuration space by a set of $L_{\hat{n}}$ with $\hat{n} \in S^{D-1}$ starting with $P_B$ and ending at $P_C$. Here we show the case of $D=2$, where $\hat{n}\in S^1$ is a point of the circle, namely specifies the direction in the neighborhood of the point $P_B$.