Twistors and Quantum Field Theory: Strong fields, holography and beyond

这一提议涉及在非微扰环境下研究量子场论（QFT）的新策略。在一个平凡的真空周围，有互补的实验和理论激励来推动QFT超越标准摄动理论。接下来的实验将探索从量子电动力学到引力的强场效应，并且将全息原理扩展到渐近平坦时空的建议需要详细了解超越闵可夫斯基空间的QFT。这两个命令的基本量是s矩阵：编码渐近状态散射的算子。不幸的是，一旦引入强背景场或时空曲率，在s矩阵的现代方法中使用的绝大多数技术就会失效。扭曲理论提供了一个关键的例外，这是一个用复杂几何来编码物理的框架。我最近的工作已经证明，扭转理论可以在强场量子傅立叶变换中提供精确的前沿计算，并且与渐近平面全息的方法密切相关。这些突破为强背景下的QFT和渐近平坦时空的全息学的新方法打开了大门，并将扭曲理论本身推向了新的方向。该团队将提供最先进的散射振幅和物理观测（包括经典和量子）在强规范和引力背景下的计算，包括平面波，光束，瞬子和黑洞，直接与当前或即将进行的实验中的探测目标相关。我们将为渐近平坦时空的全息提供详细的自底向上的数据，并使用共形和全纯场论方法创建自顶向下的边界对偶模型。同时，我们将开发扭扭理论本身的新应用，在高自旋理论、高维和代数几何中。

This proposal concerns new strategies for the study of quantum field theory (QFT) in non-perturbative settings. There are complementary experimental and theoretical incentives for pushing QFT beyond standard perturbation theory around a trivial vacuum. Upcoming experiments will probe strong field effects from quantum electrodynamics to gravity, and proposals for extending the holographic principle to asymptotically flat spacetimes require detailed knowledge of QFT beyond Minkowski space. The fundamental quantity underlying these twin imperatives is the S-matrix: the operator encoding the scattering of asymptotic states.Unfortunately, the vast majority of techniques employed in modern approaches to the S-matrix break down as soon as strong background fields or spacetime curvature are introduced. A crucial exception to this is provided by twistor theory, a framework encoding physics in terms of complex geometry. My recent work has demonstrated that twistor theory can deliver precision frontier calculations in strong field QFT and is intimately connected with approaches to asymptotically flat holography. These breakthroughs open the door on new approaches to QFT in strong backgrounds and holography in asymptotically flat spacetimes, as well as pushing twistor theory itself in novel directions. The team will deliver state-of-the-art calculations for scattering amplitudes and physical observables (both classical and quantum) in strong gauge and gravitational backgrounds including plane waves, beams, instantons and black holes, directly linked to detection targets at current or upcoming experiments. We will provide detailed bottom-up data for holography in asymptotically flat spacetimes, as well as using conformal and holomorphic field theory methods to create top-down models for the boundary dual. In parallel, we will develop new applications for twistor theory in its own right, in higher-spin theories, higher-dimensions and algebraic geometry.