scholarly journals Factorization of log-corrections in AdS4/CFT3 from supergravity localization

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Kiril Hristov ◽  
Valentin Reys
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Degrees Of Freedom ◽  
Index Theorem ◽  
Partition Functions ◽  
Dual Theory ◽  
De Sitter ◽  
Logarithmic Corrections ◽  
The One ◽  
Supergravity Action

Abstract We use the Atiyah-Singer index theorem to derive the general form of the one-loop corrections to observables in asymptotically anti-de Sitter (AdS4) supersymmetric backgrounds of abelian gauged supergravity. Using the method of supergravity localization combined with the factorization of the supergravity action on fixed points (NUTs) and fixed two-manifolds (Bolts) we show that an analogous factorization takes place for the one-loop determinants of supergravity fields. This allows us to propose a general fixed-point formula for the logarithmic corrections to a large class of supersymmetric partition functions in the large N expansion of a given 3d dual theory. The corrections are uniquely fixed by some simple topological data pertaining to a particular background in the form of its regularized Euler characteristic χ, together with a single dynamical coefficient that counts the underlying degrees of freedom of the theory.

scholarly journals De Sitter entropy as holographic entanglement entropy

2021 ◽  
Author(s):  
Nikolaos Tetradis
Keyword(s):  
Effective Action ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
De Sitter Space ◽  
Conformal Anomaly ◽  
Dual Theory ◽  
De Sitter ◽  
Logarithmic Corrections ◽  
Holographic Entanglement Entropy ◽  
Gravitational Entropy

We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newton's constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.

scholarly journals Fixed Points on Active and Passive Dynamics of Active Hydraulic Mounts with Oscillating Coil Actuator

Actuators ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 225
Author(s):  
Rang-Lin Fan ◽  
Yu-Fei Dou ◽  
Fu-Liang Ma
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Amplitude Dependence ◽  
Compact Structure ◽  
Passive Dynamics ◽  
Frequency Bands ◽  
Local Loss

Active hydraulic mounts with an inertia track, decoupler membrane, and oscillating coil actuator (AHM-IT-DM-OCAs) have been studied extensively due their compact structure and large damping in the low-frequency band. This paper focuses on a comprehensive analysis of the active and passive dynamics and their fixed points in mid-low-frequency bands, which will be helpful for parameter identification. A unified lumped parameter mechanical model with two degrees-of-freedom is established. The inertia and damping forces of the decoupler/actuator mover may be neglected, and a nonlinear mathematical model can be obtained for mid-low-frequency bands. Theoretical analysis of active and passive dynamics for fluid-filled state reveals the amplitude dependence and a fixed point in passive dynamic stiffness in-phase or active real-frequency characteristics. The amplitude dependence of local loss at the fluid channel entrance and outlet induces the amplitude-dependent dynamics. The amplitude-dependent dynamics constitute a precondition for fixed points. A single fixed point in passive dynamics is experimentally validated, and a pair of fixed points in active dynamics for an AHM-IT-DM-OCA is newly revealed in an experiment, which presents a new issue for further analysis.

scholarly journals Information from quantum blackhole physics

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2337-2346
Author(s):  
T. R. Govindarajan
Keyword(s):  
Simons Theory ◽  
Partition Functions ◽  
Cosmological Horizon ◽  
Manifolds With Boundary ◽  
De Sitter ◽  
Asymptotic Regime ◽  
Logarithmic Corrections ◽  
Chern Simons ◽  
Chern Simons Theory

The study of BTZ blackhole physics and the cosmological horizon of 3D de Sitter spaces are carried out in unified way using the connections to the Chern Simons theory on three manifolds with boundary. The relations to CFT on the boundary is exploited to construct exact partition functions and obtain logarithmic corrections to Bekenstein formula in the asymptotic regime. Comments are made on the dS/CFT correspondence frising from these studies.

scholarly journals SIMPLE CURRENTS, MODULAR INVARIANTS AND FIXED POINTS

1990 ◽  
Vol 05 (15) ◽  
pp. 2903-2952 ◽  
Author(s):  
A.N. SCHELLEKENS ◽  
S. YANKIELOWICZ
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Fixed Points ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Modular Invariants ◽  
Simple Currents

We review the use of simple currents in constructing modular invariant partition functions and the problem of resolving their fixed points. We present some new results, in particular regarding fixed point resolution. Additional empirical evidence is provided in support of our conjecture that fixed points are always related to some conformal field theory. We complete the identification of the fixed point conformal field theories for all simply laced and most non-simply laced Kac-Moody algebras, for which the fixed point CFT’s turn out to be Kac-Moody algebras themselves. For the remaining non-simply laced ones we obtain spectra that appear to correspond to new non-unitary conformal field theories. The fusion rules of the simplest unidentified example are computed.

scholarly journals Time dependent couplings as observables in de Sitter space

2014 ◽  
Vol 29 (08) ◽  
pp. 1430016 ◽  
Author(s):  
Hiroyuki Kitamoto ◽  
Yoshihisa Kitazawa
Keyword(s):  
Physical Mechanism ◽  
Quantum Effect ◽  
De Sitter Space ◽  
Time Dependent ◽  
General Covariance ◽  
De Sitter ◽  
Scale Invariant ◽  
Logarithmic Corrections ◽  
Slow Roll ◽  
The One

We summarize and expand our investigations concerning the soft graviton effects on microscopic matter dynamics in de Sitter space. The physical couplings receive IR logarithmic corrections which are sensitive to the IR cutoff at the one-loop level. The scale invariant spectrum in the gravitational propagator at the super-horizon scale is the source of the de Sitter symmetry breaking. The quartic scalar, Yukawa and gauge couplings become time dependent and diminish with time. In contrast, the Newton's constant increases with time. We clarify the physical mechanism behind these effects in terms of the conformal mode dynamics in analogy with 2d quantum gravity. We show that they are the inevitable consequence of the general covariance and lead to gauge invariant predictions. We construct a simple model in which the cosmological constant is self-tuned to vanish due to UV–IR mixing effect. We also discuss phenomenological implications such as decaying Dark Energy and SUSY breaking at the inflation era. The quantum effect alters the classical slow roll picture in general, if the tensor-to-scalar ratio r is as small as 0.01.

scholarly journals AdS one-loop partition functions from bulk and edge characters

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Zimo Sun
Keyword(s):  
Partition Function ◽  
Integral Representation ◽  
Integral Transform ◽  
Integral Formula ◽  
Partition Functions ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Higher Spin ◽  
The One

Abstract We show that the one-loop partition function of any higher spin field in (d + 1)-dimensional Anti-de Sitter spacetime can be expressed as an integral transform of an SO(2, d) bulk character and an SO(2, d − 2) edge character. We apply this character integral formula to various higher-spin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters that lead to agreement with the predictions of HS/CFT holography. We also discuss the relation between the character integral representation and the Rindler-AdS thermal partition function.

Conley–Zehnder index and bifurcation of fixed points of Hamiltonian maps

2017 ◽  
Vol 38 (6) ◽  
pp. 2086-2107 ◽  
Author(s):  
YANXIA DENG ◽  
ZHIHONG XIA
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Detailed Analysis ◽  
Parameter Family ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Symplectic Diffeomorphisms ◽  
Higher Dimensional ◽  
The One

We study the bifurcations of fixed points of Hamiltonian maps and symplectic diffeomorphisms. We are particularly interested in the bifurcations where the Conley–Zehnder index of a fixed point changes. The main result is that when the Conley–Zehnder index of a fixed point increases (or decreases) by one or two, we observe that there are several bifurcation scenarios. Under some non-degeneracy conditions on the one-parameter family of maps, two, four or eight fixed points bifurcate from the original one. We give a relatively detailed analysis of the bifurcation in the two-dimensional case. We also show that higher-dimensional cases can be reduced to the two-dimensional case.

scholarly journals BIFURCATION FOR DYNAMICAL SYSTEMS OF PLANET–BELT INTERACTION

2003 ◽  
Vol 13 (03) ◽  
pp. 617-630 ◽  
Author(s):  
ING-GUEY JIANG ◽  
LI-CHIN YEH
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Points ◽  
Outer Edge ◽  
Asteroid Belt ◽  
Asymptotically Stable ◽  
Point Analysis ◽  
The One ◽  
Structurally Stable ◽  
Bifurcation Of Solutions

The dynamical systems of planet–belt interaction are studied by the fixed-point analysis, and the bifurcation of solutions on the parameter space is discussed. For most cases, our analytical and numerical results show that the locations of fixed points are determined by the parameters and these fixed points are either structurally stable or unstable. In addition to that, there are two special fixed points: The one on the inner edge of the belt is asymptotically stable and the one on the outer edge of the belt is unstable. This is consistent with the observational picture of Asteroid Belt between Mars and Jupiter: Mars moves steadily close to the inner edge but Jupiter is quite far from the outer edge.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

“Ambiguist” Statesmanship

Worldview ◽  
1960 ◽  
Vol 3 (9) ◽  
pp. 7-8
Author(s):  
Will Herberg
Keyword(s):  
Foreign Policy ◽  
Fixed Points ◽  
Natural Law ◽  
The Other ◽  
Moral Decision ◽  
Actual Situation ◽  
The Past ◽  
Mixed Feelings ◽  
Rational Mind ◽  
The One

John Courtney Murray's writing cannot fail to be profound and instructive, and I have profited greatly from it in the course of the past decade. But I must confess that his article, "Morality and Foreign Policy" (Worldview, May), leaves me in a strange confusion of mixed feelings. On the one hand, I can sympathize with what I might call the historical intention of the natural law philosophy he espouses, which I take to be the effort to establish enduring structures of meaning and value to serve as fixed points of moral decision in the complexities of the actual situation. On the other hand, I am rather put off by the calm assurance he exhibits when he deals with these matters, as though everything were at bottom unequivocally rational and unequivocally accessible to the rational mind. And I am really distressed at what seems to 3ie to be his woefully inadequate appreciation of the position of the "ambiguists," among whom I cannot deny I count myself.

Sign in / Sign up

Export Citation Format

Share Document