We study the supersymmetric partition function of a 2d linear $sigma$-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kahler modulus that varies along the other. This setup is inspired by
the dimensional reduction of a Janus configuration of 4d $mathcal{N}=4$ $U(1)$ Super-Yang-Mills theory compactified on a mapping torus ($T^2$ fibered over $S^1$) times a circle with an $SL(2,mathbb{Z})$ duality wall inserted on $S^1$, but our setup has minimal supersymmetry. The partition function depends on two independent elements of $SL(2,mathbb{Z})$, one describing the duality twist, and the other describing the geometry of the mapping torus. It is topological and can be written as a multivariate quadratic Gauss sum. By calculating the partition function in two different ways, we obtain identities relating different quadratic Gauss sums, generalizing the {it Landsberg-Schaar} relation. These identities are a subset of a collection of identities discovered by F. Deloup. Each identity contains a phase which is an eighth root of unity, and we show how it arises as a Berry phase in the supersymmetric Janus-like configuration. Supersymmetry requires the complex structure to vary along a semicircle in the upper half-plane, as shown by Gaiotto and Witten in a related context, and that semicircle plays an important role in reproducing the correct Berry phase.
Background : The emergence of hyperon degrees of freedom in neutron star matter has been associated to first order phase transitions in some phenomenological models, but conclusions on the possible physical existence of an instability in the strangen
ess sector are strongly model dependent. Purpose : The purpose of the present study is to assess whether strangeness instabilities are related to specific values of the largely unconstrained hyperon interactions, and to study the effect of the strange meson couplings on phenomenological properties of neutron stars and supernova matter, once these latter are fixed to fulfill the constraints imposed by hypernuclear data. Method : We consider a phenomenological RMF model sufficiently simple to allow a complete exploration of the parameter space. Results : We show that no instability at supersaturation density exists for the RMF model, as long as the parameter space is constrained by basic physical requirements. This is at variance with a non-relativistic functional, with a functional behavior fitted through ab-initio calculations. Once the study is extended to include the full octet, we show that the parameter space allows reasonable radii for canonical neutron stars as well as massive stars above two-solar mass, together with an important strangeness content of the order of 30%, slightly decreasing with increasing entropy, even in the absence of a strangeness driven phase transition. Conclusions : We conclude that the hyperon content of neutron stars and supernova matter cannot be established with present constraints, and is essentially governed by the unconstrained coupling to the strange isoscalar meson.
We model the gravitational collapse of heavy massive shells including its main quantum corrections. Among these corrections, quantum improvements coming from Quantum Einstein Gravity are taken into account, which provides us with an effective quantum
spacetime. Likewise, we consider dynamical Hawking radiation by modeling its back-reaction once the horizons have been generated. Our results point towards a picture of gravitational collapse in which the collapsing shell reaches a minimum non-zero radius (whose value depends on the shell initial conditions) with its mass only slightly reduced. Then, there is always a rebound after which most (or all) of the mass evaporates in the form of Hawking radiation. Since the mass never concentrates in a single point, no singularity appears.
It has been postulated that black holes could be created in particle collisions within the range of the available energies for nowadays colliders (LHC). In this paper we analyze the evaporation of a type of black holes that are candidates for this sp
ecific behaviour, namely, small black holes on a brane in a world with large extra-dimensions. We examine their evolution under the assumption that energy conservation is satisfied during the process and compare it with the standard evaporation approach. We claim that, rather than undergoing a quick total evaporation, black holes become quasi-stable. We comment on the (absence of) implications for safety of this result. We also discuss how the presence of black holes together with the correctness of the energy conservation approach might be experimentally verified.
We consider Hawking radiation as due to a tunneling process in a black hole were quantum corrections, derived from Quantum Einstein Gravity, are taken into account. The consequent derivation, satisfying conservation laws, leads to a deviation from an
exact thermal spectrum. The non-thermal radiation is shown to carry information out of the black hole. Under the appropriate approximation, a quantum corrected temperature is assigned to the black hole. The evolution of the quantum black hole as it evaporates is then described by taking into account the full implications of energy conservation as well as the back-scattered radiation. It is shown that, as a critical mass of the order of Plancks mass is reached, the evaporation process decelerates abruptly while the black hole mass decays towards this critical mass.
