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Register a new userUniversality classes for horizon instabilities
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We introduce a notion of universality classes for the Gregory-Laflamme instability and determine, in the supergravity approximation, the stability of a variety of solutions, including the non-extremal D3-brane, M2-brane, and M5-brane. These three non-dilatonic branes cross over from instability to stability at a certain non-extremal mass. Numerical analysis suggests that the wavelength of the shortest unstable mode diverges as one approaches the cross-over point from above, with a simple critical exponent which is the same in all three cases.
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We study nuclear symmetry energy of dense matter using holographic QCD. We calculate it in a various holographic QCD models and show that the scaling index of the symmetry energy in dense medium is almost invariant under the smooth deformation of the metric as well as the embedding shape of the probe brane. We find that the scaling index depends only on the dimensionality of the branes and space-time. Therefore the scaling index of the symmetry energy characterizes the universality classes of holographic QCD models. We suggest that the scaling index might be also related to the non-fermi liquid behavior of the interacting nucleons.
We study how universality classes of O(N)-symmetric models depend continuously on the dimension d and the number of field components N. We observe, from a renormalization group perspective, how the implications of the Mermin-Wagner-Hohenberg theorem set in as we gradually deform theory space towards d=2. For fractal dimension in the range 2<d<3 we observe, for any N bigger than or equal to 1, a finite family of multi-critical effective potentials of increasing order. Apart for the N=1 case, these disappear in d=2 consistently with the Mermin-Wagner-Hohenberg theorem. Finally, we study O(N=0)-universality classes and find an infinite family of these in two dimensions.
We show that the diffeomorphism anomaly together with the trace anomaly reveal a chiral Virasoro algebra near the event horizon of a black hole. This algebra is the same irrespective of whether the anomaly is covariant or consistent, thereby manifesting its universal character and the fact that only the outgoing modes are relevant near the horizon. Our analysis therefore clarifies the role of the trace anomaly in the diffeomorphism anomaly approach cite{wilczek, isowilczek, shailesh, shailesh2, sunandan, sunandan10, rabin10} to the Hawking radiation.
In this work we propose a statistical approach to handling sources of theoretical uncertainty in string theory models of inflation. By viewing a model of inflation as a probabilistic graph, we show that there is an inevitable information bottleneck between the ultraviolet input of the theory and observables, as a simple consequence of the data processing theorem. This information bottleneck can result in strong hierarchies in the sensitivity of observables to the parameters of the underlying model and hence universal predictions with respect to at least some microphysical considerations. We also find other intriguing behaviour, such as sharp transitions in the predictions when certain hyperparameters cross a critical value. We develop a robust numerical approach to studying these behaviours by adapting methods often seen in the context of machine learning. We first test our approach by applying it to well known examples of universality, sharp transitions, and concentration phenomena in random matrix theory. We then apply the method to inflation with axion monodromy. We find universality with respect to a number of model parameters and that consistency with observational constraints implies that with very high probability certain perturbative corrections are non-negligible.
We show that the cosmological evolution of a scalar field in a potential can be obtained from a renormalisation group equation. The slow roll regime of inflation models is understood in this context as the slow evolution close to a fixed point, described by the methods of renormalisation group. This explains in part the universality observed in the predictions of a certain number of inflation models. We illustrate this behavior on a certain number of examples and discuss it in the context of the AdS/CFT correspondence.
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