We consider monopole and dyon classical solutions of the Yang-Mills-Higgs system coupled to gravity in asymptotically anti-de Sitter space. We discuss both singular and regular solutions to the second order equations of motion showing that singular Wu-Yang like dyons can be found, the resulting metric being of the Reissner-Nördstrom type (with cosmological constant). Concerning regular solutions, we analyze the conditions under which they can be constructed discussing, for vanishing coupling constant, the main distinctive features related to the anti-de Sitter asymptotic condition; in particular, we find in this case that the v.e.v. of the Higgs scalar, | H(∞)|, should be quantized in units of the natural mass scale 1/e r 0 (related to the cosmological constant) according to | H(∞)| 2 = m(m + 1)(e r 0 ) −2 , with m ∈ Z.

We find monopole solutions for a spontaneously broken SU (2)-Higgs system coupled to gravity in asymptotically anti-de Siter space. We present new analytic and numerical results discussing, in particular, how the gravitational instability of self-gravitating monopoles depends on the value of the cosmological constant. * CONICET † Associate CICBA

We explicitly construct bases for meromorphic /l-differentials over genus g Riemann surfaces. With the help of these bases we introduce a new operator formalism over Riemann surfaces which closely resembles the operator formalism on the sphere. As an application we calculate the propagators for bc systems with arbitrary integer or half-integer λ (in the Ramond and Neveu-Schwarz sectors). We also give explicit expressions for the zero modes and for the Teichmύller deformations for a generic Riemann surface.

We construct a dyon solution for a Yang-Mills-Higgs theory in a 4 dimensional Schwarzschild-anti-de Sitter black hole background with temperature T. We then apply the AdS/CFT correspondence to describe the strong coupling regime of a 2 + 1 quantum field theory which undergoes a phase transition exhibiting the condensation of a composite charge operator below a critical temperature T c .

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 compute analytically the solution to the perturbation equation for the vev deformation case by generalizing the usual matching method to higher orders and find the propagator of the boundary theory operator defined through the AdS-CFT correspondence. We show that, contrary to what happens at the leading order of the matching method, the next-to-leading order presents a simple pole at q 2 = 0 in accordance with the Goldstone theorem applied to a spontaneously broken dilatation invariance.1 borut.bajc@ijs.si 2

We present a self-gravitating dyon solution of the Einstein-YangMills-Higgs equations of motion in asymptotically AdS space. The back reaction of gauge and Higgs fields on the space-time geometry leads to the metric of an asymptotically AdS black hole. Using the gauge/gravity correspondence we analyze relevant properties of the finite temperature quantum field theory defined on the boundary. In particular we identify an order operator, characterize a phase transition of the dual theory on the border and also compute the expectation value of the finite temperature Wilson loop.

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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.