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A generalized entropy arising in the context of superstatistics is obtained for an ideal gas. The curvature scalar associated to the thermodynamic space generated by this modified entropy is calculated using two formalisms of the geometric approach to thermodynamics. Using the curvature/interaction hypothesis of the geometric approach to thermodynamic geometry it is found that as a consequence of considering a generalized statistics, an effective interaction arises but the interaction is not enough to give a phase transition. This generalized entropy seems to be relevant in confinement or in systems with not so many degrees of freedom, so it could be interesting to use such entropies to characterize the thermodynamics of small systems., Comment: 7 pages, 5 figures

In the present work some geometric and topological implications of noncommutative Wilson loops are explored via the Seiberg-Witten map. In the abelian Chern-Simons theory on a three dimensional manifold, it is shown that the effect of noncommutativity is the appearance of $6^n$ new knots at the $n$-th order of the Seiberg-Witten expansion. These knots are trivial homology cycles which are Poincar\'e dual to the high-order Seiberg-Witten potentials. Moreover the linking number of a standard 1-cycle with the Poincar\'e dual of the gauge field is shown to be written as an expansion of the linking number of this 1-cycle with the Poincar\'e dual of the Seiberg-Witten gauge fields. In the process we explicitly compute the noncommutative 'Jones-Witten' invariants up to first order in the noncommutative parameter. Finally in order to exhibit a physical example, we apply these ideas explicitly to the Aharonov-Bohm effect. It is explicitly displayed at first order in the noncommutative parameter, we also show the relation to the noncommutative Landau levels., Comment: 19 pages, 1 figure

We propose a general method to find exact ground state solutions to the SU($N$) invariant matrix model arising from the quantization of the 11-dimensional supermembrane action in the light-cone gauge. We illustrate the method by applying it to lower dimensional models and for the SU(2) group. This approach can be used to find ground state solutions to the complete 9-dimensional model and for any SU($N$) group. The supercharges and the constraints related to the SU(2) symmetry are the relevant operators and they generate a multicomponent wave function. In the procedure, the fermionic degrees of freedom are represented by means of Dirac-like gamma matrices. We exhibit a relation between these finite $N$ matrix theory ground state solutions and SUSY quantum cosmology wave functions giving a possible physical significance to the theory even for finite $N$

Quantum cosmology is studied within the framework of the minimal quantum gravity theory proposed by Ho\v{r}ava. For this purpose we choose the Kantowski-Sachs (KS) model and construct the corresponding Wheeler-DeWitt equation. We study the solution to this equation in the ultraviolet limit for different values of the running parameter {\lambda} of the theory. It is observed that the wave packet for this Universe changes completely compared with the one observed in the infrared (general relativity) regime. We also look at the classical solutions by means of a WKB semiclassical approximation. It is observed that if {\lambda} takes its relativistic value {\lambda} = 1 a generalized KS metric is obtained which differs from the usual KS solution in general relativity by an additional term arising from the higher-order curvature terms in the action and which dominates the behavior of the solution for very small values of the time parameter. We discuss the physical properties of this solution by comparing it with the usual KS solution in general relativity. The resulting solution has no horizons but singularities., Comment: 9 pages, 4 figures, uses REVTeX 4.1, published in Physical Review D

A Wheeler-DeWitt equation for the Kantowski-Sachs model is derived within the framework of the minimal quantum gravity theory proposed by Ho\v{r}ava. We study the solution to this equation in the ultraviolet limit for the specific case where the {\lambda} parameter of the theory takes its relativistic value {\lambda} = 1. It is observed that the minisuperspace variables switch their role compared with their usual infrared (General Relativity) behavior., Comment: 5 pages, 2 figures. This work was presented at the 8th Workshop of the Gravitation and Mathematical Physics Division of the Mexican Physical Society, Tuxtla Gutierrez, Chiapas, Mexico, November 22-26, 2010

Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity $\beta$ can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and $F$-distributions of $\beta$. It is assumed that they depend only on $p_l$, the probability associated with the microscopic configuration of the system. For each of the three $\beta-$distributions we calculate the Boltzmann factors and show that they coincide for small variance of the fluctuations. For the Gamma distribution it is possible to calculate the entropy in a closed form, depending on $p_l$, and to obtain then an equation relating $p_l$ with $\beta E_l$. We also propose, as other examples, new entropies close related with the Kaniadakis and two possible Sharma-Mittal entropies. The entropies presented in this work do not depend on a constant parameter $q$ but on $p_l$. For the $p_l$-Gamma distribution and its corresponding $B_{p_l}(E)$ Boltzmann factor and the associated entropy, we show the validity of the saddle-point approximation. We also briefly discuss the generalization of one of the four Khinchin axioms to get this proposed entropy., Comment: 13 pages, 3 figures

A spectral action of Euclidean supergravity is proposed. We calculate up to $a_4$, the Seeley-Dewitt coefficients in the expansion of the spectral action associated to the supergravity Dirac operator. This is possible because in simple supergravity, as in pure gravity, a well defined and mathematically consistent Dirac operator can be constructed., Comment: 10pages, no figures, matches published version

We briefly study the dynamics at classical level of the Carrollian limit, with vanishing speed of light and no possible propagation of signals, for a simply effective action in a flat space with a open string tachyon as scalar field. The canonical analysis of the theory indicates that the equation of motion is of Dirac type contrary to non-relativistic case where the equation is of Schrodinger type. The ultimate intention is to analize the latter case with electromagnetic fluxes finding that in this case the open string tachyon cannot be interpreted as time., Comment: 4 pages, accepted for publication in Rev. Mex. Fis. 2010

The Wheeler-DeWitt (WDW) equation for the Kantowski-Sachs model can also be understood as the WDW-equation corresponding to the Schwarzschild black hole due to the well known diffeomorphism between these two metrics. The WDW-equation and its solutions are ``ignorant'' of the coordinate patch one is using, only by imposing coordinate conditions we can differentiate between cosmological and black hole models. At that point, the foliation parameter $t$ or $r$ will appear in the solution of interest. In this work we supersymmetrize this WDW-equation obtaining an extra term in the potential with two possible signs. The WKB method is then applied, given rise to two classical equations. It is shown that the event horizon can never be reached because, very near to it the extra term in the potential, for each one of the equations, is more relevant than the one that corresponds to Schwarzschild. One can then study the asymptotic cases in which one of the two terms in the Hamiltonian dominates the behavior. One of them corresponds to the usual Schwarzschild black hole. We will study here the other two asymptotic regions; they provide three solutions. All of them have a singularity in $r=0$ and depending on an integration constant $C$ they can also present a singularity in $r=C^2$. Neither of these solutions have a Newtonian limit. The black hole solution we study is analyzed between the singularity $r=C^2$ and a maximum radius $r_m$. We find an associated mass, considering the related cosmological solution inside $r=C^2$, and based on the holographic principle an entropy can be assigned to this asymptotic solution., Comment: 20 pages, REVTeX4, Accepted to be published in Physical Review D

A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the $\theta$-expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in $\theta$ for the Pleba\'nski action is explicitly obtained., Comment: 23+1 pages, no figures, corrected typos, references and Appendix B is added

In this letter we study the effects of a noncommutative minisuperspace, including matter degrees of freedom on a FRW universe with cosmological constant. In this setting the vacuum energy density can be calculated to be of the same order as the observed energy density of the universe., Comment: 4 pages, RevTex 4

Unified generalized Chaplygin gas models assuming an interaction between dark energy and dark matter fluids have been previously proposed. Following these ideas, we consider a particular relation between dark densities, which allows the possibility of a time varying equation of state for dark energy that crosses the phantom divide at a recent epoch. Moreover, these densities decay during all the evolution of the Universe, avoiding a Big Rip. We find also a scaling solution, i.e. these densities are asymptotically proportional in the future, which contributes to the solution of the coincidence problem., Comment: Improved version, 10 pages, 4 figures, References added

In this work, we develop and apply the WKB approximation to several examples of noncommutative quantum cosmology, obtaining the time evolution of the noncommutative universe, this is done starting from a noncommutative quantum formulation of cosmology where the noncommutativity is introduced by a deformation on the minisuperspace variables. This procedure gives a straightforward algorithm to incorporate noncommutativity to cosmology and inflation., Comment: Revtex4, 6 pages, no figures

In this paper we study noncommutative black holes. We use a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate the Hawking's temperature and entropy for the noncommutative Schwarzschild black hole., Comment: RevTeX 4, 5 pages, no figures, to appear in Phys. Rev. D

The influence of higher dimensions in noncommutative field theories is considered. For this purpose, we analyze the bosonic sector of a recently proposed 6 dimensional SU(3) orbifold model for the electroweak interactions. The corresponding noncommutative theory is constructed by means of the Seiberg-Witten map in 6D. We find in the reduced bosonic interactions in 4D theory, couplings which are new with respect to other known 4D noncommutative formulations of the Standard Model using the Seiberg-Witten map. Phenomenological implications due to the noncommutativity of extra dimensions are explored. In particular, assuming that the commutative model leads to the standard model values, a bound -5.63 10^{-8} GeV^{-2}< theta <1.06 10^{-7}GeV^{-2} on the corresponding noncommutativity scale is derived from current experimental constraints on the S and T oblique parameters. This bound is used to predict a possibly significant impact of noncommutativity effects of extra dimensions on the rare Higgs boson decay H-> gamma gamma., Comment: Latex file, 11 pages, 1 figure

A non-Abelian Born-Infeld theory is presented. The square root structure that characterizes the Dirac-Born-Infeld (DBI) action does not appear. The procedure is based on an Abelian theory proposed by Erwin Schr\"{o}dinger that, as he showed, is equivalent to Born-Infeld theory. We briefly mention other possible similar proposals. Our results could be of interest in connection with string theory and possible extensions of well known physical results in the usual Born-Infeld Abelian case., Comment: 9 pages, no figures, revtex4

The quantum mechanical analysis of the canonical hamiltonian description of the effective action of a SDp-brane in bosonic ten dimensional Type II supergravity in a homogeneous background is given. We find exact solutions for the corresponding quantum theory by solving the Wheeler-deWitt equation in the late-time limit of the rolling tachyon. The probability densities for several values of p are shown and their possible interpretation is discussed. In the process the effects of electromagnetic fields are also incorporated and it is shown that in this case the interpretation of tachyon regarded as ``matter clock'' is modified., Comment: 15 pages, 3 eps figures, revtex4

Using the ontological interpretation of quantum mechanics in a particular sense, we obtain the classical behaviour of the scale factor and two scalar fields, derived from a string effective action for the FRW time dependent model. Besides, the Wheeler-DeWitt equation is solved exactly. We speculate that the same procedure could also be applied to S-branes., Comment: 11 pages, To appear in Int. J. Mod. Phys. A

We formulate a noncommutative description of topological half-flat gravity in four dimensions. BRST symmetry of this topological gravity is deformed through a twisting of the usual BRST quantization of noncommutative gauge theories. Finally it is argued that resulting moduli space of instantons is characterized by the solutions of a noncommutative version of the Plebanski's heavenly equation., Comment: 12+1 pages, revtex4, no figures

Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use Seiberg-Witten map. It is shown that the noncommutative torsion constraint is solved by the vanishing of commutative torsion. Finally, the noncommutative corrections to the action are computed up to second order., Comment: 15+1 pages, LaTeX, no figures

The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler characteristic and the signature invariant are obtained. This gives us a way towards the description of noncommutative gravitational instantons as well as noncommutative local gravitational anomalies., Comment: 17+1 pages, LaTeX, no figures, some clarifications, comments and references added, style improved

We propose a model for noncommutative quantum cosmology by means of a deformation of minisuperspace. For the Kantowski-Sachs metric we are able to find the exact wave function. We construct wave packets and show that new quantum states that ``compete'' to be the most probable state appear, in clear contrast with the commutative case. A tunneling process could be possible among these states., Comment: 5 pages, 5 figures, revtex4 file, major style changes, to be published in PRL

Abelian Chern-Simons gauge theory is known to possess a `$S$-self-dual' action where its coupling constant $k$ is inverted {\it i.e.} $k \leftrightarrow {1 \over k}$. Here a vector non-abelian duality is found in the pure non-abelian Chern-Simons action at the classical level. The dimensional reduction of the dual Chern-Simons action to two-dimensions constitutes a dual Wess-Zumino-Witten action already given in the literature., Comment: 14+1 pages, LaTeX file, no figures, version to appear in Phys. Rev D

Strong/weak coupling duality in Chern-Simons supergravity is studied. It is argued that this duality can be regarded as an example of superduality. The use of supergroup techniques for the description of Chern-Simons supergravity greatly facilitates the analysis., Comment: 10+1 pages, latex, no figures

We report our recent results concerning d5 gauged supergravity (dilatonic gravity) considered on AdS background. The finite action on such background as well as d4 holographic conformal anomaly (via AdS/CFT correspondence) are found. In such formalism the bulk potential is kept to be arbitrary, dilaton dependent function. Holographic RG in such theory is briefly discussed. d5 AdS brane-world Universe induced by quantum effects of brane CFT is constructed. Such brane is spherical, hyperbolic or flat one. Hence, the possibility of quantum creation of inflationary brane-world Universe is shown., Comment: Proceedings of Londrina conference, April 2000, to appear

We overview some attempts to find S-duality analogues of non-supersymmetric Yang-Mills theory, in the context of gravity theories. The case of MacDowell-Mansouri gauge theory of gravity is discussed. Three-dimensional dimensional reductions from the topological gravitational sector in four dimensions, enable to recuperate the 2+1 Chern-Simons gravity and the corresponding S-dual theory, from the notion of self-duality in the four-dimensional theory., Comment: 8+1 pages, LaTeX file, no figures. Invited talk at the `Third Workshop on Gravitation and Mathematical Physics', Leon Gto. Mexico

Several eigenvalue equations that could describe quantum black holes have been proposed in the canonical quantum gravity approach. In this paper, we choose one of the simplest of these quantum equations to show how the usual Feynman's path integral method can be applied to obtain the corresponding statistical properties. We get a logarithmic correction to the Bekenstein-Hawking entropy as already obtained by other authors by other means., Comment: 7 pages, LaTeX, no figures

We review the anomaly induced effective action for dilaton coupled spinors and scalars in large N and s-wave approximation. It may be applied to study the following fundamental problems: construction of quantum corrected black holes (BHs), inducing of primordial wormholes in the early Universe (this effect is confirmed) and the solution of initial singularity problem. The recently discovered anti-evaporation of multiple horizon BHs is discussed. The existance of such primordial BHs may be interpreted as SUSY manifestation. Quantum corrections to BHs thermodynamics maybe also discussed within such scheme., Comment: LaTeX file and two eps files, to appear in MPLA, Brief Reviews

We study 2+1 Chern-Simons gravity at the classical action level. In particular we rederive the linear combinations of the ``standard'' and ``exotic'' Einstein actions, from the (anti) self-duality of the ``internal'' Lorentzian indices. The relation to a genuine four-dimensional (anti)self-dual topological theory greatly facilitates the analysis and its relation to hyperbolic three-dimensional geometry. Finally a non-abelian vector field ``dual'' action is also obtained., Comment: 16+1 pages, LaTeX file, no figures, clarifications and comments added, typos corrected and one reference added

Using large N, 4d anomaly induced one-loop effective action for conformally invariant matter (typical GUT multiplet) we study the possibility to induce the primordial spherically symmetric wormholes at the early Universe. The corresponding effective equations are obtained in two different coordinate frames. The numerical investigation of these equations is done for matter content corresponding to ${\cal N}=4$ SU(N) super Yang-Mills theory. For some choice of initial conditions, the induced wormhole solution with increasing throat radius and increasing red-shift function is found., Comment: LaTeX file, 11 pages, 2 eps files of figures, few misprints are corrected

Using s-wave and large N approximation the one-loop effective action for 2d dilaton coupled scalars and spinors which are obtained by spherical reduction of 4d minimal matter is found. Quantum effective equations for reduced Einstein gravity are written. Their analytical solutions corresponding to 4d Kantowski-Sachs (KS) Universe are presented. For quantum-corrected Einstein gravity we get non-singular KS cosmology which represents 1) quantum-corrected KS cosmology which existed on classical level or 2)purely quantum solution which had no classical limit. The analogy with Nariai BH is briefly mentioned. For purely induced gravity (no Einstein term) we found general analytical solution but all KS cosmologies under discussion are singular. The corresponding equations of motion are reformulated as classical mechanics problem of motion of unit mass particle in some potential V., Comment: LaTeX file, 16 pages, a few misprints are corrected

In the context of field theory two elements seem to be necessary to search for strong-weak coupling duality. First, a gauge theory formulation and second, supersymmetry. For gravitation these two elements are present in MacDowell-Mansouri supergravity. The search for an "effective duality" in this theory presents technical and conceptual problems that we discuss. Nevertheless, by means of a field theoretical approach, which in the abelian case coincides with $S$-duality, we exhibit a dual theory, with inverted couplings. This results in a supersymmetric non-linear sigma model of the Freedman-Townsend type., Comment: 16 pages, LaTeX file, no figures, minor comments and one reference added

Using one-loop effective action in large N and s-wave approximation we discuss the possibility to induce primordial wormholes at the early Universe. An analytical solution is found for self-consistent primordial wormhole with constant radius. Numerical study gives the wormhole solution with increasing throat radius and increasing red-shift function. There is also some indication to the possibility of a topological phase transition., Comment: LaTeX file, 2 eps figures, 9 pages, few misprints are corrected, numerics are changed

In this work we define a scalar product ``weighted'' with the scalar factor $R$ and show how to find a normalized wave function for the supersymmetric quantum FRW cosmological model using the idea of supersymmetry breaking selection rules under local n=2 conformal supersymmetry. We also calculate the expectation value of the scalar factor R in this model and its corresponding behaviour., Comment: 11 pages, 1 figure, revtex

Recently a strong-weak coupling duality in non-abelian non-supersymmetric theories in four dimensions has been found. An analogous procedure is reviewed, which allows to find the `dual action' to the gauge theory of dynamical gravity constructed by the MacDowell-Mansouri model plus the superposition of a $\Theta$ term., Comment: Invited paper to appear in the special issue of the `Journal of Chaos, Solitons and Fractals' on: "Superstrings, M,F,S,... Theory" (M.S. El Naschie and C. Castro, editors), 19 pages, LaTeX file, no figures

Strong-weak duality invariance can only be defined for particular sectors of supersymmetric Yang-Mills theories. Nevertheless, for full non-Abelian non-supersymmetric theories, dual theories with inverted couplings, have been found. We show that an analogous procedure allows to find the dual action to the gauge theory of gravity constructed by the MacDowell-Mansouri model plus the superposition of a $\Theta$ term., Comment: 9 pages, LaTeX, no figures

We draw parallels between the recently introduced ``Immirzi ambiguity'' of the Ashtekar-like formulation of canonical quantum gravity and other ambiguities that appear in Yang-Mills theories, like the $\theta$ ambiguity. We also discuss ambiguities in the Maxwell case, and implication for the loop quantization of these theories., Comment: 5 pages, revtex, no figures

For non-abelian non-supersymmetric gauge theories, generic dual theories have been constructed. In these theories the couplings appear inverted. However, they do not possess a Yang-Mills structure but rather are a kind of non-linear sigma model. It is shown that for a topological gravitational model an analog to this duality exists., Comment: LaTeX, 14 pages, no figures, minor corrections

After a short outline of the factorization and Grassmann picture of the one-dimensional (1D) Fokker-Planck (FP) equation, we consider a class of spatially-inhomogeneous solutions of the 2D FP equation with symmetric 2D (super)potentials. We show that the spatial inhomogeneities of that class of solutions can be attributed to underlying Grassmannian pseudo-degrees of freedom. Such an interpretation may also be applied to FP solutions in three and more dimensions., Comment: 5 pages in LaTex, no figures

Using a simple factorization scheme we obtain the recurrence-shift relations of the polynomial functions of Aldaya, Bisquert and Navarro-Salas (ABNS), F_n^N(\frac\omega c\sqrtN x), i.e., one-step first-order differential relations referring to N, as follows. Firstly, we apply the scheme to the polynomial degree confirming the recurrence relations of Aldaya, Bisquert and Navarro-Salas, but also obtaining another slightly modified pair. Secondly, the factorization scheme is applied to the Gegenbauer polynomials to get the recurrence relations with respect to their parameter. Next, we make use of Nagel's result, showing the connection between Gegenbauer polynomials and the ABNS functions, to write down the recurrence-shift relations for the latter ones. Such relations may be used in the study of the spatial structure of pair-creation processes in an Anti-de Sitter gravitational background, Comment: there is a short version in The IV Wigner Symposium book (World Scientific, 1996) pp. 466-469

A non-minimal coupling for spin $3/2$ fields is obtained. We use the fact that the Rarita-Schwinger field equations are the square root of the full linearized Einstein field equations in order to investigate the form of the interaction for the spin $3/2$ field with gauge fields. We deduce the form of the interaction terms for the electromagnetic and non-Abelian Yang-Mills fields by implementing appropiate energy momentum tensors on the linearized Einstein field equations. The interaction found for the electromagnetic case happens to coincide with the dipole term found by Ferrara {\it et al} by a very different procedure, namely by demanding $g=2$ at the tree level for the electromagnetic interaction of arbitrary spin particles. The same interaction is found by using the resource of linearized Supergravity N=2. For the case of the Yang-Mills field Supergravity N=4 is linearized, providing the already foreseen interaction., Comment: 16 pages, Latex

We find solutions for quantum Class A Bianchi models of the form $\rm \Psi=W e^{\pm \Phi}$ generalizing the results obtained by Moncrief and Ryan in standard quantum cosmology. For the II and IX Bianchi models there are other solutions $\rm \tilde\Phi_2$, $\rm \tilde\Phi_9$ to the Hamilton-Jacobi equation for which $\rm \Psi$ is necessarely zero, in contrast with solutions found in supersymmetric quantum cosmology., Comment: 15 pages, Latex

We work out the second solution of the DO superpotentials in the $R_0=0$ sector., Comment: Several changes in the text in order to make it more precise and correct, one more reference, mathematical results not affected

We show that asymmetric time-continuous discrete random walks can display bistability for equal values of Jauslin's shifting parameters. The bistability becomes more pronounced at increased asymmetry parameter, Comment: Follow-up note to hep-th/9411026[PRE 51, 5112 (May 95)], one fig. included

We provide a supersymmetric analysis of the Maxwell fisheye (MF) wave problem at zero energy. Working in the so-called $R_{0}=0$ sector, we obtain the corresponding superpartner (fermionic) MF effective potential within Witten's one-dimensional (radial) supersymmetric procedure., Comment: 5 pages in Latex, one figure not included has been published as Fig. 2 in Phys. Lett. A 208 (1995) 33-39

We present a supersymmetric analysis of the wave problem with a Demkov-Ostrovsky spherically symmetric class of focusing potentials at zero energy. Following a suggestion of L\'evai, we work in the so-called R_0=0 sector in order to obtain the superpartner (fermionic) potentials within Witten's supersymmetric procedure. General solutions of the superpotential for the known physical cases are given explicitly., Comment: 6 pp, LaTex

By adding the Pontrjagin topological invariant to the gauge theory of the de Sitter group proposed by MacDowell and Mansouri we obtain an action quadratic in the field-strengths, of the Chern-Simons type, from which the Ashtekar formulation is derived., Comment: 9 pages