Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality

We study operators in four-dimensional gauge theories which are localized on a straight line, create electric and magnetic flux, and in the UV limit break the conformal invariance in the minimal possible way. We call them Wilson-'t Hooft operators, since in the purely electric case they reduce to the well-known Wilson loops, while in general they may carry 't Hooft magnetic flux. We show that to any such operator one can associate a maximally symmetric boundary condition for gauge fields on AdS^2\times S^2. We show that Wilson-'t Hooft operators are classifed by a pair of weights (electric and magnetic) for the gauge group and its magnetic dual, modulo the action of the Weyl group. If the magnetic weight does not belong to the coroot lattice of the gauge group, the corresponding operator is topologically nontrivial (carries nonvanishing 't Hooft magnetic flux). We explain how the spectrum of Wilson-'t Hooft operators transforms under the shift of the theta-angle by 2\pi. We show that, depending on the gauge group, either SL(2,Z) or one of its congruence subgroups acts in a natural way on the set of Wilson-'t Hooft operators. This can be regarded as evidence for the S-duality of N=4 super-Yang-Mills theory. We also compute the one-point function of the stress-energy tensor in the presence of a Wilson-'t Hooft operator at weak coupling.Comment: 32 pages, latex. v2: references added. v3: numerical factors corrected, other minor change

Aproximative solutions to the neutrino oscillation problem in matter

We present approximative solutions to the neutrino evolution equation calculated by different methods. In a two neutrino framework, using the physical parameters which gives the main effects to neutrino oscillations from nu{e} to another flavors for L=3000Km and E=1GeV, the results for the transition probability calculated by using series solutions, by to take the neutrino evolution operator as a product of ordered partial operators and by numerical methods, for a linearly and sinusoidally varying matter density are compared. The extension to an arbitrary density profile is discussed and the evolution operator as a product of partial operators in the three neutrino case is obtained.Comment: 12 pages, 5 figure

Solving simple quaternionic differential equations

The renewed interest in investigating quaternionic quantum mechanics, in particular tunneling effects, and the recent results on quaternionic differential operators motivate the study of resolution methods for quaternionic differential equations. In this paper, by using the real matrix representation of left/right acting quaternionic operators, we prove existence and uniqueness for quaternionic initial value problems, discuss the reduction of order for quaternionic homogeneous differential equations and extend to the non-commutative case the method of variation of parameters. We also show that the standard Wronskian cannot uniquely be extended to the quaternionic case. Nevertheless, the absolute value of the complex Wronskian admits a non-commutative extension for quaternionic functions of one real variable. Linear dependence and independence of solutions of homogeneous (right) H-linear differential equations is then related to this new functional. Our discussion is, for simplicity, presented for quaternionic second order differential equations. This involves no loss of generality. Definitions and results can be readily extended to the n-order case.Comment: 9 pages, AMS-Te

Wave-like Solutions for Bianchi type-I cosmologies in 5D

We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: homothetic, conformal and "wave-like". In this work we present the most general wave-like solutions to the 5D field equations. Using the standard technique based on Campbell's theorem, they generate a large number of anisotropic cosmological models of Bianchi type-I, which can be applied to our universe after the big-bang, when anisotropies could have played an important role. We present a complete review of all possible cases of self-similar anisotropic cosmologies in 5D. Our analysis extends a number of previous studies on wave-like solutions in 5D with spatial spherical symmetry

Renormalization Group Flow and Fragmentation in the Self-Gravitating Thermal Gas

The self-gravitating thermal gas (non-relativistic particles of mass m at temperature T) is exactly equivalent to a field theory with a single scalar field phi(x) and exponential self-interaction. We build up perturbation theory around a space dependent stationary point phi_0(r) in a finite size domain delta \leq r \leq R ,(delta << R), which is relevant for astrophysical applica- tions (interstellar medium,galaxy distributions).We compute the correlations of the gravitational potential (phi) and of the density and find that they scale; the latter scales as 1/r^2. A rich structure emerges in the two-point correl- tors from the phi fluctuations around phi_0(r). The n-point correlators are explicitly computed to the one-loop level.The relevant effective coupling turns out to be lambda=4 pi G m^2 / (T R). The renormalization group equations (RGE) for the n-point correlator are derived and the RG flow for the effective coupling lambda(tau) [tau = ln(R/delta), explicitly obtained.A novel dependence on tau emerges here.lambda(tau) vanishes each time tau approaches discrete values tau=tau_n = 2 pi n/sqrt7-0, n=0,1,2, ...Such RG infrared stable behavior [lambda(tau) decreasing with increasing tau] is here connected with low density self-similar fractal structures fitting one into another.For scales smaller than the points tau_n, ultraviolet unstable behaviour appears which we connect to Jeans' unstable behaviour, growing density and fragmentation. Remarkably, we get a hierarchy of scales and Jeans lengths following the geometric progression R_n=R_0 e^{2 pi n /sqrt7} = R_0 [10.749087...]^n . A hierarchy of this type is expected for non-spherical geometries,with a rate different from e^{2 n/sqrt7}.Comment: LaTex, 31 pages, 11 .ps figure

Exterior spacetime for stellar models in 5-dimensional Kaluza-Klein gravity

It is well-known that Birkhoff's theorem is no longer valid in theories with more than four dimensions. Thus, in these theories the effective 4-dimensional picture allows the existence of different possible, non-Schwarzschild, scenarios for the description of the spacetime outside of a spherical star, contrary to general relativity in 4D. We investigate the exterior spacetime of a spherically symmetric star in the context of Kaluza-Klein gravity. We take a well-known family of static spherically symmetric solutions of the Einstein equations in an empty five-dimensional universe, and analyze possible stellar exteriors that are conformal to the metric induced on four-dimensional hypersurfaces orthogonal to the extra dimension. All these exteriors are continuously matched with the interior of the star. Then, without making any assumptions about the interior solution, we prove the following statement: the condition that in the weak-field limit we recover the usual Newtonian physics singles out an unique exterior. This exterior is "similar" to Scharzschild vacuum in the sense that it has no effect on gravitational interactions. However, it is more realistic because instead of being absolutely empty, it is consistent with the existence of quantum zero-point fields. We also examine the question of how would the deviation from the Schwarzschild vacuum exterior affect the parameters of a neutron star. In the context of a model star of uniform density, we show that the general relativity upper limit M/R < 4/9 is significantly increased as we go away from the Schwarzschild vacuum exterior. We find that, in principle, the compactness limit of a star can be larger than 1/2, without being a black hole. The generality of our approach is also discussed.Comment: Typos corrected. Accepted for publication in Classical and Quantum Gravit

Warm alpha-nucleon matter

The properties of warm dilute alpha-nucleon matter are studied in a variational approach in the Thomas-Fermi approximation starting from an effective two-body nucleon-nucleon interaction. The equation of state, symmetry energy, incompressibility of the said matter as well as the alpha fraction are in consonance with those evaluated from the virial approach that sets a bench-mark for such calculations at low densities.Comment: 10 pages, 10 figures, Phys. Rev C (in press