Positivity in Multifield Effective Field Theories,Physical Review Letters

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Positivity in Multifield Effective Field Theories
Physical Review Letters ( IF 8.1 ) Pub Date : 2021-09-17 , DOI: 10.1103/physrevlett.127.121601
Xu Li ₁ , Hao Xu _{2,

3} , Chengjie Yang ₁ , Cen Zhang _{1,

4} , Shuang-Yong Zhou _{2,

3}

Affiliation

We discuss the general method for obtaining full positivity bounds on multifield 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 three 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.

中文翻译：

多场有效场理论中的正性

我们讨论了在多场有效场理论 (EFT) 上获得完全正界的一般方法。虽然领先的正向正边界通常来自两个（叠加的）外部状态的弹性散射，但我们表明，对于包含三个或更多低能量模式的通用 EFT，这种方法只能给出不完整的边界。然后，我们将允许的参数空间识别为谱面体的对偶，由振幅的交叉对称性构成，并表明为给定数量的模式找到最佳边界等价于几何问题：找到谱面体的极值射线。我们展示了如何在简单情况下分析地完成此操作，并在更复杂的情况下将其数值公式化为半定规划 (SDP) 问题。我们用粒子物理学和宇宙学中的许多动机良好的例子来证明这种方法，包括标量、矢量、费米子和引力子的 EFT。在所有这些情况下，我们发现 SDP 方法导致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 方法在数值上更有效。

更新日期：2021-09-17

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