Uniqueness of Nash equilibria in quantum Cournot duopoly game

A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement of entanglement between strategic variables chosen by the competing firms is sufficiently large, the multiplicity of equilibria vanishes, and, (ii) the more strongly the strategic variables are entangled, the more closely the unique equilibrium approaches to the optimal one.Comment: 7 pages, 2 figure

Asymptotically hyperbolic manifolds with small mass

For asymptotically hyperbolic manifolds of dimension $n$ with scalar curvature at least equal to $-n(n-1)$ the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to hyperbolic space. In this paper we study asymptotically hyperbolic manifolds which are also conformally hyperbolic outside a ball of fixed radius, and for which the positive mass theorem holds. For such manifolds we show that the conformal factor tends to one as the mass tends to zero

Positive tension 3-branes in an AdS5AdS_{5} bulk

In this work, we review and extend the so-called consistency conditions for the existence of a braneworld scenario in arbitrary dimensions in the Brans-Dicke (BD) gravitational theory. After that, we consider the particular case of a five-dimensional scenario which seems to have phenomenological interesting implications. We show that, in the BD framework, it is possible to achieve necessary conditions pointing to the possibility of accommodating branes with positive tensions in an AdS bulk by the presence of the additional BD scalar field, avoiding in this way the necessity of including unstable objects in the compactification scheme. Furthermore, in the context of time variable brane tension, it is shown that the brane tension may change its sign, following the bulk cosmological constant sign.Comment: 15 pages, new version to appear in JHE

The Measure for the Multiverse and the Probability for Inflation

We investigate the measure problem in the framework of inflationary cosmology. The measure of the history space is constructed and applied to inflation models. Using this measure, it is shown that the probability for the generalized single field slow roll inflation to last for $N$ e-folds is suppressed by a factor $\exp(-3N)$, and the probability for the generalized $n$-field slow roll inflation is suppressed by a much larger factor $\exp(-3nN)$. Some non-inflationary models such as the cyclic model do not suffer from this difficulty.Comment: 16 page

SD-brane gravity fields and rolling tachyons

S(pacelike)D-branes are objects arising naturally in string theory when Dirichlet boundary conditions are imposed on the time direction. SD-brane physics is inherently time-dependent. Previous investigations of gravity fields of SD-branes have yielded undesirable naked spacelike singularities. We set up the problem of coupling the most relevant open-string tachyonic mode to massless closed-string modes in the bulk, with backreaction and Ramond-Ramond fields included. We find solutions numerically in a self-consistent approximation; our solutions are naturally asymptotically flat and time-reversal asymmetric. We find completely nonsingular evolution; in particular, the dilaton and curvature are well-behaved for all time. The essential mechanism for spacetime singularity resolution is the inclusion of full backreaction between the bulk fields and the rolling tachyon. Our analysis is not the final word on the story, because we have to make some significant approximations, most notably homogeneity of the tachyon on the unstable branes. Nonetheless, we provide significant progress in plugging a gaping hole in prior understanding of the gravity fields of SD-branes.Comment: References added. Analysis for much broader range of solutions presented. Conclusions unchanged. Time-reversal symmetric examples ruled out, new examples are provide

Off-shell extension of S-matrix elements and tachyonic effective actions

We show that the on-shell S-matrix elements of four open string massless scalars, two scalars and two tachyons, and four open string tachyons in the super string theory can be written in a unique form. We then propose an off-shell extension for the S-matrix element of four scalars which is consistent, in the low energy limit, with the Dirac-Born-Infeld effective action. Using a similar off-shell extension for the S-matrix element of two scalars and two tachyons and for the S-matrix element of four tachyons, we show that they are fully consistent with the tachyonic DBI action.Comment: Latex, 17 pages, v3:a paragraph comparing off-shell and on- shell amplitudes added, reference adde

Particle Motion Around Tachyon Monopole

Recently, Li and Liu have studied global monoole of tachyon in a four dimensional static space-time. We analyze the motion of massless and massive particles around tachyon monopole. Interestingly, for the bending of light rays due to tachyon monopole instead of getting angle of deficit we find angle of surplus. Also we find that the tachyon monopole exerts an attractive gravitational force towards matter.Comment: 14 pages, 7 figure

Noncommutative Topological Theories of Gravity

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 improve

Non-Z2\mathbb{Z}_{2} symmetric braneworlds in scalar tensorial gravity

We obtain, via the Gauss-Codazzi formalism, the expression of the effective Einstein-Brans-Dicke projected equations in a non-$\mathbb{Z}_{2}$ symmetric braneworld scenario which presents hybrid compactification. It is shown that the functional form of such equations resembles the one in the Einstein's case, except by the fact that they bring extra informations in the context of exotic compactifications.Comment: 12 pages, LATEX file, no figures. Accepted for publication in the European Physical Journal