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Register a new userBlack hole mass dynamics and renormalization group evolution
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We examine the real-time dynamics of a system of one or more black holes interacting with long wavelength gravitational fields. We find that the (classical) renormalizability of the effective field theory that describes this system necessitates the introduction of a time dependent mass counterterm, and consequently the mass parameter must be promoted to a dynamical degree of freedom. To track the time evolution of this dynamical mass, we compute the expectation value of the energy-momentum tensor within the in-in formalism, and fix the time dependence by imposing energy-momentum conservation. Mass renormalization induces logarithmic ultraviolet divergences at quadratic order in the gravitational coupling, leading to a new time-dependent renormalization group (RG) equation for the mass parameter. We solve this RG equation and use the result to predict heretofore unknown high order logarithms in the energy distribution of gravitational radiation emitted from the system.
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As an extension of the weak perturbation theory obtained in recent analysis on infinite-derivative non-local non-Abelian gauge theories motivated from p-adic string field theory, and postulated as direction of UV-completion in 4-D Quantum Field Theory (QFT), here we investigate the confinement conditions and $beta-$function in the strong coupling regime. We extend the confinement criterion, previously obtained by Kugo and Ojima for the local theory based on the Becchi-Rouet-Stora-Tyutin (BRST) invariance, to the non-local theory, by using a set of exact solutions of the corresponding local theory. We show that the infinite-derivatives which are active in the UV provides finite contributions also in the infrared (IR) limit and provide a proof of confinement, granted by the absence of the Landau pole. The main difference with the local case is that the IR fixed point is moved to infinity. We also show that in the limit of the energy scale of non-locality $M rightarrow infty$ we reproduce the local theory results and see how asymptotic freedom is properly recovered.
We construct an effective field theory (EFT) model that describes matter field interactions with Schwarzschild mini-black-holes (SBHs), treated as a scalar field, $B_0(x)$. Fermion interactions with SBHs require a random complex spurion field, $theta_{ij}$, which we interpret as the EFT description of holographic information, which is correlated with the SBH as a composite system. We consider Hawkings virtual black hole vacuum (VBH) as a Higgs phase, $langle B_0 rangle =V$. Integrating sterile neutrino loops, the field $theta_{ij}$ is promoted to a dynamical field, necessarily developing a tachyonic instability and acquiring a VEV of order the Planck scale. For $N$ sterile neutrinos this breaks the vacuum to $SU(N)times U(1)/SO(N)$ with $N$ degenerate Majorana masses, and $(1/2)N(N+1)$ Nambu-Goldstone neutrino-Majorons. The model suggests many scalars fields, corresponding to all fermion bilinears, may exist bound nonperturbatively by gravity.
We reconstruct the complete fermionic orbit of the non-extremal BTZ black hole by acting with finite supersymmetry transformations. The solution satisfies the exact supergravity equations of motion to all orders in the fermonic expansion and the final result is given in terms of fermionic bilinears. By fluid/gravity correspondence, we derive linearized Navier-Stokes equations and a set of new differential equations from Rarita-Schwinger equation. We compute the boundary energy-momentum tensor and we interpret the result as a perfect fluid with a modified definition of fluid velocity. Finally, we derive the modified expression for the entropy of the black hole in terms of the fermionic bilinears.
Casimir energy is calculated for 5D scalar theory in the {it warped} geometry. A new regularization, called {it sphere lattice regularization}, is taken. The regularized configuration is {it closed-string like}. We numerically evaluate $La$(4D UV-cutoff), $om$(5D bulk curvature, extra space UV-boundary parameter) and $T$(extra space IR-boundary parameter) dependence of Casimir energy. 5D Casimir energy is {it finitely} obtained after the {it proper renormalization procedure.} The {it warp parameter} $om$ suffers from the {it renormalization effect}. Regarding Casimir energy as the main contribution to the cosmological term, we examine the dark energy problem.
Perturbation theory is a crucial tool for many physical systems, when exact solutions are not available, or nonperturbative numerical solutions are intractable. Naive perturbation theory often fails on long timescales, leading to secularly growing solutions. These divergences have been treated with a variety of techniques, including the powerful dynamical renormalization group (DRG). Most of the existing DRG approaches rely on having analytic solutions up to some order in perturbation theory. However, sometimes the equations can only be solved numerically. We reformulate the DRG in the language of differential geometry, which allows us to apply it to numerical solutions of the background and perturbation equations. This formulation also enables us to use the DRG in systems with background parameter flows, and therefore, extend our results to any order in perturbation theory. As an example, we apply this method to calculate the soliton-like solutions of the Korteweg-de Vries equation deformed by adding a small damping term. We numerically construct DRG solutions which are valid on secular time scales, long after naive perturbation theory has broken down.
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