Non standard parametrizations and adjoint invariants of classical groups

We obtain local parametrizations of classical non-compact Lie groups where adjoint invariants under maximal compact subgroups are manifest. Extension to non compact subgroups is straightforward. As a by-product parametrizations of the same type are obtained for compact groups. They are of physical interest in any theory gauge invariant under the adjoint action, typical examples being the two dimensional gauged Wess-Zumino-Witten-Novikov models where these coordinatizations become of extreme usefulness to get the background fields representing the vacuum expectation values of the massless modes of the associated (super) string theory.Comment: 11 pages, latex file, La Plata preprint Th-99/01. Minor changes in the introduction, version to appear in Physics Letters

A note on the non-commutative Chern-Simons model on manifolds with boundary

We study field theories defined in regions of the spatial non-commutative (NC) plane with a boundary present delimiting them, concentrating in particular on the U(1) NC Chern-Simons theory on the upper half plane. We find that classical consistency and gauge invariance lead necessary to the introduction of $K_0$-space of square integrable functions null together with all their derivatives at the origin. Furthermore the requirement of closure of $K_0$ under the *-product leads to the introduction of a novel notion of the *-product itself in regions where a boundary is present, that in turn yields the complexification of the gauge group and to consider chiral waves in one sense or other. The canonical quantization of the theory is sketched identifying the physical states and the physical operators. These last ones include ordinary NC Wilson lines starting and ending on the boundary that yield correlation functions depending on points on the one-dimensional boundary. We finally extend the definition of the *-product to a strip and comment on possible relevance of these results to finite Quantum Hall systems.Comment: 15 pages, references added, to appear in International Journal of Modern Physic

Scalar potentials, propagators and global symmetries in AdS/CFT

We study the transition of a scalar field in a fixed $AdS_{d+1}$ background between an extremum and a minimum of a potential. We first prove that two conditions must be met for the solution to exist. First, the potential involved cannot be generic, i.e. a fine-tuning of their parameters is mandatory. Second, at least in some region its second derivative must have a negative upper limit which depends only on the dimensionality $d$. We then calculate the boundary propagator for small momenta in two different ways: first in a WKB approximation, and second with the usual matching method, generalizing the known calculation to arbitrary order. Finally, we study a system with spontaneously broken non-Abelian global symmetry, and show in the holographic language why the Goldstone modes appear.Comment: 26 pages - Invited contribution for the Central European Journal of Physics, topical issue devoted to "Cosmology and Particle Physics beyond Standard Models". Some parts overlap with 1304.3051v1, which has been replaced by the published versio

Holographic phase transitions from higgsed, non abelian charged black holes

We find solutions of a gravity-Yang-Mills-Higgs theory in four dimensions that represent asymptotic anti-de Sitter charged black holes with partial/full gauge symmetry breaking. We then apply the AdS/CFT correspondence to study the strong coupling regime of a $2+1$ quantum field theory at temperature $T$ and finite chemical potential, which undergoes transitions to phases exhibiting the condensation of a composite charged vector operator below a critical temperature $T_c$, presumably describing $p+ip/p$-wave superconductors. In the case of $p+ip$-wave superconductors the transitions are always of second order. But for $p$-wave superconductors we determine the existence of a critical value $\alpha_c$ of the gravitational coupling (for fixed Higgs v.e.v. parameter $\hat m_W$) beyond which the transitions become of first order. As a by-product, we show that the $p$-wave phase is energetically favored over the $p+ip$ one, for any values of the parameters. We also find the ground state solutions corresponding to zero temperature. Such states are described by domain wall geometries that interpolate between $AdS_4$ spaces with different light velocities, and for a given $\hat m_{W}$, they exist below a critical value of the coupling. The behavior of the order parameter as function of the gravitational coupling near the critical coupling suggests the presence of second order quantum phase transitions. We finally study the dependence of the solution on the Higgs coupling, and find the existence of a critical value beyond which no condensed solution is present.Comment: 29 pages, 43 figure

The Shared Reward Dilemma

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma, namely the Prisoner's Dilemma. Specifically, for a group of players that collect payoffs by playing a pairwise Prisoner's Dilemma game with their partners, we consider an external entity that distributes a fixed reward equally among all cooperators. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared a vast variety of scenarios arises, including traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the $n$-player game as well as of its evolutionary dynamics.Comment: Major rewriting, new appendix, new figure

Rewarding cooperation in social dilemmas

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared we can cast a vast variety of scenarios, including traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the nplayer game as well as of the evolutionary dynamics. Beyond, we extend our analysis to a general class of public good games where competition among individuals with the same strategy exists.

Correlation functions in the non-commutative Wess-Zumino-Witten model

We develop a systematic perturbative expansion and compute the one-loop two-points, three-points and four-points correlation functions in a non-commutative version of the U(N) Wess-Zumino-Witten model in different regimes of the $\theta$-parameter showing in the first case a kind of phase transition around the value $\theta_c = \frac{\sqrt{p^2 + 4 m^2}}{\Lambda^2 p}$, where $\Lambda$ is a ultraviolet cut-off in a Schwinger regularization scheme. As a by-product we obtain the functions of the renormalization group, showing they are essentially the same as in the commutative case but applied to the whole U(N) fields; in particular there exists a critical point where they are null, in agreement with a recent background field computation of the beta-function, and the anomalous dimension of the Lie algebra-valued field operator agrees with the current algebra prediction. The non-renormalization of the level $k$ is explicitly verified from the four-points correlator, where a left-right non-invariant counter-term is needed to render finite the theory, that it is however null on-shell. These results give support to the equivalence of this model with the commutative one.Comment: 21 pages, latex, no figures, shortened version to appear in Physics Letters

About the stability of a D4 - anti D 4 system

We study a system of coincident $D4$ and $\bar D 4$ branes with non zero world-volume magnetic fields in the weak coupling limit. We show that the conditions for absence of tachyons in the spectrum coincide exactly with those found in hep-th/0206041, in the low energy effective theory approach, for the system to preserve a $\frac 14$ of the supersymmetries of the Type IIA string theory vacuum. We present further evidence about the stability of the system by computing the lowest order interaction amplitude from both open and closed channels, thus verifying the no force condition as well as the supersymmetric character of the spectrum. A brief discussion of the low energy effective five dimensional world-volume theory is given.Comment: 37 pages, latex file, no figures, heavy changes in language all along the paper, references added; to appear in Nuclear Physics