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Register a new userExamining Instabilities Due to Driven Scalars in AdS
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Brad Cownden
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We extend the study of the non-linear perturbative theory of weakly turbulent energy cascades in AdS$_{d+1}$ to include solutions of driven systems, i.e. those with time-dependent sources on the AdS boundary. This necessitates the activation of non-normalizable modes in the linear solution for the massive bulk scalar field, which couple to the metric and normalizable scalar modes. We determine analytic expressions for secular terms in the renormalization flow equations for any mass, and for various driving functions. Finally, we numerically evaluate these sources for $d = 4$ and discuss what role these driven solutions play in the perturbative stability of AdS.
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Based on the new version of the gedanken experiment proposed by Sorce and Wald, we investigate the weak cosmic censorship conjecture (WCCC) for a Reissner-Nordstr{o}m-Anti-de Sitter (RN-AdS) black hole under the perturbation of extra matter fields. Firstly, we propose that the cosmological constant can be effectively derived from the matter fields and its value varies with the matter fields perturbing the black hole. Meanwhile, we assume that the perturbation satisfies the stability condition. This condition means that after a long time of the perturbation, the black hole solution also belongs to the family of the RN-AdS solution. After that, based on both the stability condition and the null energy condition, while using the off-shell variation method, the first-order and the second-order perturbation inequalities are derived respectively when the cosmological constant is considered as a dynamic variable. It is the first time to extend the two perturbation inequalities to contain the term of the press and volume of thermodynamics. Finally, we perform the two perturbation inequalities into testing the WCCC for the RN-AdS black hole under the second-order approximation of the perturbation. It is shown that if the variation of the cosmological constant is caused by the matter fields, while the stability condition and the null energy condition are all satisfied, the black hole cannot be destroyed after the perturbation. In other words, the WCCC for the RN-AdS black hole is valid under the second-order approximation of the perturbation.
In string models with brane supersymmetry breaking exponential potentials emerge at (closed-string) tree level but are not accompanied by tachyons. Potentials of this type have long been a source of embarrassment in flat space, but can have interesting implications for Cosmology. For instance, in ten dimensions the logarithmic slope |V/V| lies precisely at a critical value where the Lucchin--Matarrese attractor disappears while the scalar field is emph{forced} to climb up the potential when it emerges from the Big Bang. This type of behavior is in principle perturbative in the string coupling, persists after compactification, could have trapped scalar fields inside potential wells as a result of the cosmological evolution and could have also injected the inflationary phase of our Universe.
We describe in more detail the general relation uncovered in our previous work between boundary correlators in de Sitter (dS) and in Euclidean anti-de Sitter (EAdS) space, at any order in perturbation theory. Assuming the Bunch-Davies vacuum at early times, any given diagram contributing to a boundary correlator in dS can be expressed as a linear combination of Witten diagrams for the corresponding process in EAdS, where the relative coefficients are fixed by consistent on-shell factorisation in dS. These coefficients are given by certain sinusoidal factors which account for the change in coefficient of the contact sub-diagrams from EAdS to dS, which we argue encode (perturbative) unitary time evolution in dS. dS boundary correlators with Bunch-Davies initial conditions thus perturbatively have the same singularity structure as their Euclidean AdS counterparts and the identities between them allow to directly import the wealth of techniques, results and understanding from AdS to dS. This includes the Conformal Partial Wave expansion and, by going from single-valued Witten diagrams in EAdS to Lorentzian AdS, the Froissart-Gribov inversion formula. We give a few (among the many possible) applications both at tree and loop level. Such identities between boundary correlators in dS and EAdS are made manifest by the Mellin-Barnes representation of boundary correlators, which we point out is a useful tool in its own right as the analogue of the Fourier transform for the dilatation group. The Mellin-Barnes representation in particular makes manifest factorisation and dispersion formulas for bulk-to-bulk propagators in (EA)dS, which imply Cutkosky cutting rules and dispersion formulas for boundary correlators in (EA)dS. Our results are completely general and in particular apply to any interaction of (integer) spinning fields.
We calculate the emission and absorption rates of fixed scalars by the near-extremal five-dimensional black holes that have recently been modeled using intersecting D-branes. We find agreement between the semi-classical and D-brane computations. At low energies the fixed scalar absorption cross-section is smaller than for ordinary scalars and depends on other properties of the black hole than just the horizon area. In the D-brane description, fixed scalar absorption is suppressed because these scalars must split into at least four, rather than two, open strings running along the D-brane. Consequently, this comparison provides a more sensitive test of the effective string picture of the D-brane bound state than does the cross-section for ordinary scalars. In particular, it allows us to read off the value of the effective string tension. That value is precisely what is needed to reproduce the near-extremal 5-brane entropy.
The special properties of scalars having a mass such that the two possible dimensions of the dual scalar respect the unitarity and the Breitenlohner-Freedman bounds and their ratio is integral (``resonant scalars) are studied in the AdS/CFT correspondence. The role of logarithmic branches in the gravity theory is related to the existence of a trace anomaly and to a marginal deformation in the Conformal Field Theory. The existence of asymptotic charges for the conformal group in the gravity theory is interpreted in terms of the properties of the corresponding CFT.
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