Triangle Seminars
Thursday, 1 May 2025
Interacting Fields at Spatial Infinity
📍 London
Priyadarshi Paul
(Queen Mary University of London)
Abstract:
We study the properties of massive fields extrapolated to the blowup of spatial infinity (\hat{i}^0), extending the program initiated in arXiv:2207.06406. Although the motivation is to understand holography in the quantum theory of gravity for asymptotically flat spacetime, in this work we do not include dynamical gravity. Instead, we focus on understanding boundary operators in the fixed background for free as well as interacting theory. In the free theory, we find an explicit representation of boundary two-point functions and boundary-to-bulk two-point functions. We also present an HKLL-type reconstruction formula for local bulk operators in terms of smeared boundary operators. We study interacting Wightman correlators and find that, generically, interacting massive fields decay slower than free fields as one approaches \hat{i}^0. We propose that meaningful correlators at \hat{i}^0 can be obtained through an LSZ-like prescription that isolates the on-shell part of bulk Wightman correlators before extrapolating them to \hat{i}^0. We show that a natural basis for operators at \hat{i}^0, defined via this prescription, is given by the average of "in" and "out" operators defined at i^− and i^+ respectively. Therefore, correlators at \hat{i}^0 and cross correlators between \hat{i}^0, i^− and i^+ can be represented within the class of asymptotic observables studied by Caron-Huot et al. in arXiv:2308.02125. We present several sample calculations. In the future, we plan to couple dynamical gravity to the theory and see how it helps us understand holography.
We study the properties of massive fields extrapolated to the blowup of spatial infinity (\hat{i}^0), extending the program initiated in arXiv:2207.06406. Although the motivation is to understand holography in the quantum theory of gravity for asymptotically flat spacetime, in this work we do not include dynamical gravity. Instead, we focus on understanding boundary operators in the fixed background for free as well as interacting theory. In the free theory, we find an explicit representation of boundary two-point functions and boundary-to-bulk two-point functions. We also present an HKLL-type reconstruction formula for local bulk operators in terms of smeared boundary operators. We study interacting Wightman correlators and find that, generically, interacting massive fields decay slower than free fields as one approaches \hat{i}^0. We propose that meaningful correlators at \hat{i}^0 can be obtained through an LSZ-like prescription that isolates the on-shell part of bulk Wightman correlators before extrapolating them to \hat{i}^0. We show that a natural basis for operators at \hat{i}^0, defined via this prescription, is given by the average of "in" and "out" operators defined at i^− and i^+ respectively. Therefore, correlators at \hat{i}^0 and cross correlators between \hat{i}^0, i^− and i^+ can be represented within the class of asymptotic observables studied by Caron-Huot et al. in arXiv:2308.02125. We present several sample calculations. In the future, we plan to couple dynamical gravity to the theory and see how it helps us understand holography.
Posted by: QMW