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Abstract It is believed that Euclidean Yang–Mills theories behave like the massless Gaussian free field (GFF) at short distances. This makes it impossible to define the main observables for these theories—the Wilson loop observables—in dimensions greater than two, because line integrals of the GFF do not exist in such dimensions. Taking forward a proposal of Charalambous and Gross, this article shows that it is possible to define Euclidean Yang–Mills theories on the 3D unit torus as ‘random distributional gauge orbits’, provided that they indeed behave like the GFF in a certain sense. One of the main technical tools is the existence of the Yang–Mills heat flow on the 3D torus starting from GFF-like initial data, which is established in a companion paper. A key consequence of this construction is that under the GFF assumption, one can define a notion of ‘regularized Wilson loop observables’ for Euclidean Yang–Mills theories on the 3D unit torus.
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Abstract We apply for the first time orbit-averaged Monte Carlo star cluster simulations to study tidal tail and stellar stream formation from globular clusters (GCs), assuming a circular orbit in a time-independent spherical Galactic potential. Treating energetically unbound bodies—potential escapers (PEs)—as collisionless enables this fast but spherically symmetric method to capture asymmetric extratidal phenomena with exquisite detail. Reproducing stream features such as epicyclic overdensities, we show how
returning tidal tails can form after the stream fully circumnavigates the Galaxy, enhancing the stream's velocity dispersion by several kilometers per second in our ideal case. While a truly clumpy, asymmetric, and evolving Galactic potential would greatly diffuse such tails, they warrant scrutiny as potentially excellent constraints on the Galaxy’s history and substructure. Reexamining the escape timescale Δt of PEs, we find new behavior related to chaotic scattering in the three-body problem; the Δt distribution features sharp plateaus corresponding to distinct locally smooth patches of the chaotic saddle separating the phase-space basins of escape. We study for the first time Δt in an evolving cluster, finding that for PEs with (low, high) Jacobi energyE J, flatter than for a static cluster ( ). Accounting for cluster mass loss and internal evolution lowers the median Δt from ∼10 Gyr to ≲100 Myr. We finally outline potential improvements to escape in the Monte Carlo method intended to enable the first large grids of tidal tail/stellar stream models from full GC simulations and detailed comparison to stream observations. -
ABSTRACT The motion of the centre of mass of a coalescing binary black hole (BBH) in a gravitational potential, imprints a line-of-sight acceleration (LOSA) on to the emitted gravitational-wave (GW) signal. The acceleration could be sufficiently large in dense stellar environments, such as globular clusters (GCs), to be detectable with next-generation space-based detectors. In this work, we use outputs of the cluster monte carlo (cmc) simulations of dense star clusters to forecast the distribution of detectable LOSAs in DECIGO and LISA eras. We study the effect of cluster properties – metallicity, virial and galactocentric radii – on the distribution of detectable accelerations, account for cosmologically motivated distributions of cluster formation times, masses, and metallicities, and also incorporate the delay time between the formation of BBHs and their merger in our analysis. We find that larger metallicities provide a larger fraction of detectable accelerations by virtue of a greater abundance of relatively lighter BBHs, which allow a higher number of GW cycles in the detectable frequency band. Conversely, smaller metallicities result in fewer detections, most of which come from relatively more massive BBHs with fewer cycles but larger LOSAs. We similarly find correlations between the virial radii of the clusters and the fractions of detectable accelerations. Our work, therefore, provides an important science case for space-based GW detectors in the context of probing GC properties via the detection of LOSAs of merging BBHs.