论文标题
具有增强对称性和软行为的非依赖性有效领域理论
Nonrelativistic effective field theories with enhanced symmetries and soft behavior
论文作者
论文摘要
我们系统地探索了具有本地$ S $ -MATRIX的非依赖性有效领域理论的景观，并增强了对称性和软行为。该探索是使用基于对称性论点的常规量子场理论方法进行的，并最近开发了壳递归关系。我们表明，与相对论的理论相反，在非依赖主义理论中散射幅度的软限制的增强通常不是对称性的副产品，而是需要额外的低能量数据。可以通过结合散射颗粒的对称性和分散关系来得出足够的增强散射幅度的条件。这对红外动力学产生了直接的后果，即不同类型的非依赖主义的Nambu-Goldstone玻色子可以表现出来。然后，我们使用自下而上的软启动方法来缩小具有一致的低能$ S $ -MATRIX的非依赖性有效野外理论的景观。我们恢复了一个复杂的Schrödinger-type标量的两个例外理论，即$ \ Mathbb {C} P^1 $ nonelear Sigma模型和Schrödinger-Dirac-dirac-of-born-of-born-of-born-of-born-of-born-infeld理论。此外，我们使用软递归来证明无需定理，排除了其他例外的schrödinger-type理论的存在。我们还证明，具有线性分散关系的单个真实标量的所有特殊理论都必须是Lorentz-Invariant。软递归使我们能够在具有增强的软限制的非依赖主义有效理论的景观上获得进一步的一般界限。最后，我们提出了具有技术自然的四分之一分散关系的复杂标量的新颖理论。总的来说，我们的工作代表了计划的第一步，该计划将散射幅度的发展扩展到没有洛伦兹不变的理论中。
We systematically explore the landscape of nonrelativistic effective field theories with a local $S$-matrix and enhanced symmetries and soft behavior. The exploration is carried out using both conventional quantum field theory methods based on symmetry arguments, and recently developed on-shell recursion relations. We show that, in contrary to relativistic theories, enhancement of the soft limit of scattering amplitudes in nonrelativistic theories is generally not a byproduct of symmetry alone, but requires additional low-energy data. Sufficient conditions for enhanced scattering amplitudes can be derived by combining symmetries and dispersion relations of the scattered particles. This has direct consequences for the infrared dynamics that different types of nonrelativistic Nambu-Goldstone bosons can exhibit. We then use a bottom-up soft bootstrap approach to narrow down the landscape of nonrelativistic effective field theories that possess a consistent low-energy $S$-matrix. We recover two exceptional theories of a complex Schrödinger-type scalar, namely the $\mathbb{C} P^1$ nonlinear sigma model and the Schrödinger-Dirac-Born-Infeld theory. Moreover, we use soft recursion to prove a no-go theorem ruling out the existence of other exceptional Schrödinger-type theories. We also prove that all exceptional theories of a single real scalar with a linear dispersion relation are necessarily Lorentz-invariant. Soft recursion allows us to obtain some further general bounds on the landscape of nonrelativistic effective theories with enhanced soft limits. Finally, we present a novel theory of a complex scalar with a technically natural quartic dispersion relation. Altogether, our work represents the first step of a program to extend the developments in the study of scattering amplitudes to theories without Lorentz invariance.
