多场EFT中的正性
Positivity in Multi-Field EFTs
摘要：
讨论了多场有效场论（EFT）正性全界的一般方法。虽然领先的顺序向前的正边界通常来自两个（叠加）外部状态的弹性散射，我们表明，对于一个通用的EFT包含3个或更多的低能量模式，这种方法只给出不完整的边界。然后，我们确定允许的参数空间作为对偶的一个spectrahedron，从交叉对称的振幅，并表明，找到一个给定数量的模式的最佳界限是相当于一个几何问题：找到极值射线的spectrahedron。我们将展示如何做到这一点，分析简单的情况下，和数值制定为半定规划（SDP）问题，更复杂的情况下。我们证明了这种方法与粒子物理学和宇宙学，包括标量，矢量，费米子和引力子的EFT的一些动机良好的例子。在所有这些情况下，我们发现SDP方法产生的结果要么改进了以前的结果，要么是全新的。我们还发现，SDP的方法是数值上更有效。
英文摘要：
We discuss the general method for obtaining full positivity bounds on multi-field effective field theories (EFTs). While the leading order forward positivity bounds are commonly derived from the elastic scattering of two (superposed) external states, we show that for a generic EFT containing 3 or more low-energy modes, this approach only gives incomplete bounds. We then identify the allowed parameter space as the dual to a spectrahedron, constructed from crossing symmetries of the amplitude, and show that finding the optimal bounds for a given number of modes is equivalent to a geometric problem: finding the extremal rays of a spectrahedron. We show how this is done analytically for simple cases, and numerically formulated as semidefinite programming (SDP) problems for more complicated cases. We demonstrate this approach with a number of well-motivated examples in particle physics and cosmology, including EFTs of scalars, vectors, fermions and gravitons. In all these cases, we find that the SDP approach leads to results that either improve the previous ones or are completely new. We also find that the SDP approach is numerically much more efficient.
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