UC Berkeley

Some of the most fundamental questions in theoretical physics can be formulated as puzzles of naturalness, such as the cosmological constant problem and the Higgs mass hierarchy problem. In condensed matter physics, the interpretation of the linear scaling of resistivity with temperature in the strange metal phase of high-temperature superconductors also arises as a naturalness puzzle. In this thesis, we explore the landscape of naturalness in nonrelativistic quantum field theories that exhibit anisotropic scaling in space and time. Such theories are referred to as the ``Aristotelian quantum field theories." In the simple case with scalars, we find that the constant shift symmetry is extended to a shift by a polynomial in spatial coordinates, which protects the technical naturalness of modes with a higher order dispersion. This discovery leads to a generalization of the relativistic Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem to multicritical cases in lower critical dimension. By breaking the polynomial shift symmetries in a hierarchy, we find novel cascading phenomena with large natural hierarchies between the scales at which the values of z change, leading to an evasion of the "no-go" consequences of the relativistic CHMW theorem. Based on these formal developments, we propose potential applications both to the Higgs mass hierarchy problem and to the problem of linear resistivity in strange metals. Finally, encouraged by these nonrelativistic surprises that already arise in simple systems with scalars, we move on to more complicated systems with gauge symmetries. We study the quantization of Horava gravity in 2+1 dimensions and compute the anomalous dimension of the cosmological constant at one loop. However, nonrelativistic naturalness in gravity is still largely unexplored. Whether or not such nonrelativsitic twists have any implications for important naturalness puzzles, such as the cosmological constant problem, remains as an intriguing question.