skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • NSF Public Access
  • Search Results
  • Stability of saddles and choices of contour in the Euclidean path integral for linearized gravity: dependence on the DeWitt parameter
Title: Stability of saddles and choices of contour in the Euclidean path integral for linearized gravity: dependence on the DeWitt parameter
A<sc>bstract</sc> Due to the conformal factor problem, the definition of the Euclidean gravitational path integral requires a non-trivial choice of contour. The present work examines a generalization of a recently proposed rule-of-thumb [1] for selecting this contour at quadratic order about a saddle. The original proposal depended on the choice of an indefinite-signature metric on the space of perturbations, which was taken to be a DeWitt metric with parameterα= – 1. This choice was made to match previous results, but was otherwise admittedlyad hoc. To begin to investigate the physics associated with the choice of such a metric, we now explore contours defined using analogous prescriptions forα≠ – 1. We study such contours for Euclidean gravity linearized about AdS-Schwarzschild black holes in reflecting cavities with thermal (canonical ensemble) boundary conditions, and we compare path-integral stability of the associated saddles with thermodynamic stability of the classical spacetimes. While the contour generally depends on the choice of DeWitt parameterα, the precise agreement between these two notions of stability found atα= – 1 continues to hold over the finite interval (– 2, – 2/d), wheredis the dimension of the bulk spacetime. This agreement manifestly fails forα> – 2/dwhen the DeWitt metric becomes positive definite. However, we also find dramatic failures forα< – 2 that correlate with breakdowns of the de Donder-like gauge condition defined byα, and at which the relevant fluctuation operator fails to be diagonalizable. This provides criteria that may be useful in predicting metrics on the space of perturbations that give physically-useful contours in more general settings. Along the way, we also identify an interesting error in [1], though we show this error to be harmless.  more » « less
Award ID(s):
2107939
PAR ID:
10511715
Author(s) / Creator(s):
; ;
Publisher / Repository:
Springer
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2024
Issue:
5
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; (, Journal of High Energy Physics)
    A<sc>bstract</sc> Gravitational Rényi computations have traditionally been described in the language of Euclidean path integrals. In the semiclassical limit, such calculations are governed by Euclidean (or, more generally, complex) saddle-point geometries. We emphasize here that, at least in simple contexts, the Euclidean approach suggests an alternative formulation in terms of the bulk quantum wavefunction. Since this alternate formulation can be directly applied to the real-time quantum theory, it is insensitive to subtleties involved in defining the Euclidean path integral. In particular, it can be consistent with many different choices of integration contour. Despite the fact that self-adjoint operators in the associated real-time quantum theory have real eigenvalues, we note that the bulk wavefunction encodes the Euclidean (or complex) Rényi geometries that would arise in any Euclidean path integral. As a result, for any given quantum state, the appropriate real-time path integral yields both Rényi entropies and associated complex saddle-point geometries that agree with Euclidean methods. After brief explanations of these general points, we use JT gravity to illustrate the associated real-time computations in detail. 
    more » « less
  2. (, Journal of High Energy Physics)
    A bstract Thermal partition functions for gravitational systems have traditionally been studied using Euclidean path integrals. But in Euclidean signature the gravitational action suffers from the conformal factor problem, which renders the action unbounded below. This makes it difficult to take the Euclidean formulation as fundamental. However, despite their familiar association with periodic imaginary time, thermal gravitational partition functions can also be described by real-time path integrals over contours defined by real Lorentzian metrics. The one caveat is that we should allow certain codimension-2 singularities analogous to the familiar Euclidean conical singularities. With this understanding, we show that the usual Euclidean-signature black holes (or their complex rotating analogues) define saddle points for the real-time path integrals that compute our partition functions. Furthermore, when the black holes have positive specific heat, we provide evidence that a codimension-2 subcontour of our real Lorentz-signature contour of integration can be deformed so as to show that these black holes saddles contribute with non-zero weight to the semiclassical limit, and that the same is then true of the remaining two integrals. 
    more » « less
  3. ; ; (, ACM Transactions on Algorithms)
    This article presentsuniversalalgorithms for clustering problems, including the widely studiedk-median,k-means, andk-center objectives. The input is a metric space containing allpotentialclient locations. The algorithm must selectkcluster centers such that they are a good solution foranysubset of clients that actually realize. Specifically, we aim for lowregret, defined as the maximum over all subsets of the difference between the cost of the algorithm’s solution and that of an optimal solution. A universal algorithm’s solutionSolfor a clustering problem is said to be an α , β-approximation if for all subsets of clientsC′, it satisfiessol(C′) ≤ α ċopt(C′) + β ċmr, whereopt(C′ is the cost of the optimal solution for clients (C′) andmris the minimum regret achievable by any solution. Our main results are universal algorithms for the standard clustering objectives ofk-median,k-means, andk-center that achieve (O(1),O(1))-approximations. These results are obtained via a novel framework for universal algorithms using linear programming (LP) relaxations. These results generalize to other ℓp-objectives and the setting where some subset of the clients arefixed. We also give hardness results showing that (α, β)-approximation is NP-hard if α or β is at most a certain constant, even for the widely studied special case of Euclidean metric spaces. This shows that in some sense, (O(1),O(1))-approximation is the strongest type of guarantee obtainable for universal clustering. 
    more » « less
  4. ; ; ; ; ; (, The Astrophysical Journal)
    Abstract We present Keck Cosmic Web Imager Lyαintegral field spectroscopy of the fields surrounding 14 damped Lyαabsorbers (DLAs) atz≈ 2. Of these 14 DLAs, nine have high metallicities ([M/H] > − 0.3), and four of those nine feature a CO-emitting galaxy at an impact parameter ≲30 kpc. Our search reaches median Lyαline flux sensitivities of ∼2 × 10−17erg s−1cm−2over apertures of ∼6 kpc and out to impact parameters of ∼50 kpc. We recover the Lyαflux of three known Lyα-emitting Hi-selected galaxies in our sample. In addition, we find two Lyαemitters at impact parameters of ≈50–70 kpc from the high-metallicity DLA atz≈ 1.96 toward QSO B0551-366. This field also contains a massive CO-emitting galaxy at an impact parameter of ≈15 kpc. Apart from the field with QSO B0551-366, we do not detect significant Lyαemission in any of the remaining eight high-metallicity DLA fields. Considering the depth of our observations and our ability to recover previously known Lyαemitters, we conclude that Hi-selected galaxies associated with high-metallicity DLAs atz≈ 2 are dusty and therefore might feature low Lyαescape fractions. Our results indicate that complementary approaches—using Lyα, CO, Hα, and [Cii] 158μm emission—are necessary to identify the wide range of galaxy types associated withz≈ 2 DLAs. 
    more » « less
  5. ; ; ; (, The Astrophysical Journal Letters)
    Abstract In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a nonthermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameterσ≫ 1) quickly evolves into a state with ultrarelativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponentαin the power-law particle-energy distribution function,f(γ)dγ∝γ−αdγ, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponentαis in good agreement with the numerical results. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email