Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

Evaluating gravitational path integrals in the Lorentzian has been a long-standing challenge due to the numerical sign problem. We show that this challenge can be overcome in simplicial quantum gravity. By deforming the integration contour into the complex, the sign fluctuations can be suppressed, for instance using the holomorphic gradient flow algorithm. Working through simple models, we show that this algorithm enables efficient Monte Carlo simulations for Lorentzian simplicial quantum gravity. In order to allow complex deformations of the integration contour, we provide a manifestly holomorphic formula for Lorentzian simplicial gravity. This leads to a complex version of simplicial gravity that generalizes the Euclidean and Lorentzian cases. Outside the context of numerical computation, complex simplicial gravity is also relevant to studies of singularity resolving processes with complex semi-classical solutions. Along the way, we prove a complex version of the Gauss-Bonnet theorem, which may be of independent interest.

A compendium of sphere path integrals

We study the manifestly covariant and local 1-loop path integrals on Sd+1 for general massive, shift-symmetric and (partially) massless totally symmetric tensor fields of arbitrary spin s ≥ 0 in any dimensions d ≥ 2. After reviewing the cases of massless fields with spin s = 1, 2, we provide a detailed derivation for path integrals of massless fields of arbitrary integer spins s ≥ 1. Following the standard procedure of Wick-rotating the negative conformal modes, we find a higher spin analog of Polchinski’s phase for any integer spin s ≥ 2. The derivations for low-spin (s = 0, 1, 2) massive, shift-symmetric and partially massless fields are also carried out explicitly. Finally, we provide general prescriptions for general massive and shift-symmetric fields of arbitrary integer spins and partially massless fields of arbitrary integer spins and depths.

De Sitter Holography: Fluctuations, Anomalous Symmetry, and Wormholes

The Goheer–Kleban–Susskind no-go theorem says that the symmetry of de Sitter space is incompatible with finite entropy. The meaning and consequences of the theorem are discussed in light of recent developments in holography and gravitational path integrals. The relation between the GKS theorem, Boltzmann fluctuations, wormholes, and exponentially suppressed non-perturbative phenomena suggests that the classical symmetry between different static patches is broken and that eternal de Sitter space—if it exists at all—is an ensemble average.

Reinforcement Learning with Dynamic Movement Primitives for Obstacle Avoidance

Dynamic movement primitives (DMPs) are a robust framework for movement generation from demonstrations. This framework can be extended by adding a perturbing term to achieve obstacle avoidance without sacrificing stability. The additional term is usually constructed based on potential functions. Although different potentials are adopted to improve the performance of obstacle avoidance, the profiles of potentials are rarely incorporated into reinforcement learning (RL) framework. In this contribution, we present a RL based method to learn not only the profiles of potentials but also the shape parameters of a motion. The algorithm employed is PI2 (Policy Improvement with Path Integrals), a model-free, sampling-based learning method. By using the PI2, the profiles of potentials and the parameters of the DMPs are learned simultaneously; therefore, we can optimize obstacle avoidance while completing specified tasks. We validate the presented method in simulations and with a redundant robot arm in experiments.