Thermodynamical phases of a regular SAdS black hole

This paper studies the thermodynamical stability of regular BHs in AdS5 background. We investigate off-shell free energy of the system as a function of temperature for different values of a "coupling constant" L=4 theta/l^2, where the cosmological constant is Lambda = -3/l^2 and \sqrt{theta} is a "minimal length". The parameter L admits a critical value, L_{inf}=0.2, corresponding to the appearance of an inflexion point in the Hawking temperature. In the weak-coupling regime L < L_{inf}, there are first order phase transitions at different temperatures. Unlike the Hawking-Page case, at temperature 0\le T \le T_{min} the ground state is populated by "cold" near-extremal BHs instead of a pure radiation. On the other hand, for L \g L_{inf} only large, thermodynamically stable, BHs exist.Comment: 12 pages; 6 Figures; accepted for publication in Int. J. Mod. Phys.

Zero-point length, extra-dimensions and string T-duality

In this paper, we are going to put in a single consistent framework apparently unrelated pieces of information, i.e. zero-point length, extra-dimensions, string T-duality. More in details we are going to introduce a modified Kaluza-Klein theory interpolating between (high-energy) string theory and (low-energy) quantum field theory. In our model zero-point length is a four dimensional ``virtual memory'' of compact extra-dimensions length scale. Such a scale turns out to be determined by T-duality inherited from the underlying fundamental string theory. From a low energy perspective short distance infinities are cut off by a minimal length which is proportional to the square root of the string slope, i.e. \sqrt{\alpha^\prime}. Thus, we provide a ``bridge'' between the ultra-relativistic string domain and the low energy arena of point-particle quantum field theory.Comment: 28 pages, Latex, no figures; two references adde

Un-spectral dimension and quantum spacetime phases

In this Letter, we propose a new scenario emerging from the conjectured presence of a minimal length $\ell$ in the spacetime fabric, on the one side, and the existence of a new scale invariant, continuous mass spectrum, of un-particles on the other side. We introduce the concept of \textit{un-spectral dimension} $\mathbb{D}_U$ of a $d$-dimensional, euclidean (quantum) spacetime, as the spectral dimension measured by an "un-particle" probe. We find a general expression for the un-spectral dimension $\mathbb{D}_U$ labelling different spacetime phases: a semi-classical phase, where ordinary spectral dimension gets contribution from the scaling dimension $d_U$ of the un-particle probe ; a critical "Planckian phase", where four-dimensional spacetime can be effectively considered two-dimensional when $d_U=1$; a "Trans-Planckian phase", which is accessible to un-particle probes only, where spacetime as we currently understand it looses its physical meaning.Comment: 5 pages, 1 figure, version matching that published by Physics Letters

Maxwell's equal area law and the Hawking-Page phase transition

In this paper we study the phases of a Schwarzschild black hole in the Anti deSitter background geometry. Exploiting fluid/gravity duality we construct the Maxwell equal area isotherm T=T* in the temperature-entropy plane, in order to eliminate negative heat capacity black hole configurations. The construction we present here is reminiscent of the isobar cut in the pressure-volume plane which eliminates un-physical part of the Van der Walls curves below the critical temperature. Our construction also modifies the Hawking-Page phase transition. Stable black holes are formed at the temperature T > T*, while pure radiation persists for T< T*. T* turns out to be below the standard Hawking-Page temperature and there are no unstable black holes as in the usual scenario. Also, we show that in order to reproduce the correct black hole entropy S=A/4, one has to write a black hole equation of state, i.e. P=P(V), in terms of the geometrical volume V=4\pi r^3/3.Comment: 15 pages, 4 Figures. Accepted for publication in Journal of Gravit

Confinement from gluodynamics in curved space-time

We determine the static potential for a heavy quark-antiquark pair from gluodynamics in curved space-time. Our calculation is done within the framework of the gauge-invariant, path-dependent, variables formalism. The potential energy is the sum of a Yukawa and a linear potential, leading to the confinement of static charges.Comment: 4 page

The Abelian Higgs model and a minimal length in an un-particle scenario

We consider both the Abelian Higgs model and the impact of a minimal length in the un-particle sector. It is shown that even if the Higgs field takes a non-vanishing v.e.v., gauge interaction keeps its long range character leading to an effective gauge symmetry restoration. The effect of a quantum gravity induced minimal length on a physical observable is then estimated by using a physically-based alternative to the usual Wilson loop approach. Interestingly, we obtain an ultraviolet finite interaction energy described by a confluent hyper-geometric function, which shows a remarkable richness of behavior.Comment: 6 pages. Tp appear in EP