International Journal of Modern Physics A

We systematically revisit the description of D-branes on orbifolds and the classification of their charges via K-theory. We include enough details to make the results accessible to both physicists and mathematicians interested in these topics. The minimally charged branes predicted by K-theory in ℤ_N orbifolds with N odd are only BPS. We confirm this result using the boundary state formalism for ℤ₃. For ℤ_N × ℤ_N orbifolds with N odd, in the untwisted case and with discrete torsion whose class is a generator of H³(ℤ/N × ℤ/N,ℤ), we show that the K-theory classification of charges agrees with the boundary state approach, largely developed by Gaberdiel and collaborators, including the types of representation on the Chan–Paton factors.

We study the system formed by a gas of black holes and strings within a microcanonical formulation. The density of mass levels grows asymptotically as , (i = 1,…,N). We derive the microcanonical content of the system: entropy, equation of state, number of components N, temperature T and specific heat. The pressure and the specific heat are negative reflecting the gravitational unstability and a nonhomogeneous configuration. The asymptotic behavior of the temperature for large masses emerges as the Hawking temperature of the system (classical or semiclassical phase) in which the classical black hole behavior dominates, while for small masses (quantum black hole or string behavior) the temperature becomes the string temperature which emerges as the critical temperature of the system. At low masses, a phase transition takes place showing the passage from the classical (black hole) to quantum (string) behavior. Within a microcanonical field theory formulation, the propagator describing the string–particle–black hole system is derived and from it the interacting four-point scattering amplitude of the system is obtained. For high masses it behaves asymptotically as the degeneracy of states ρ(m) of the system (i.e. duality or crossing symmetry). The microcanonical propagator and partition function are derived from a (Nambu–Goto) formulation of the N-extended objects and the mass spectrum of the black hole–string system is obtained: for small masses (quantum behavior) these yield the usual pure string scattering amplitude and string–particle spectrum ; for growing mass the spectrum describes all the intermediate states up to the pure black hole behavior. The different black hole behaviors according to the different mass ranges: classical, semiclassical and quantum or string behaviors are present in the model.

The issue of space–time gauge invariance for the bosonic string has been earlier addressed using the loop variable formalism. In this paper the question of obtaining a gauge invariant action for the open bosonic string is discussed. The derivative with respect to ln a (where a is a worldsheet cutoff) of the partition function — which is first normalized by dividing by the integral of the two-point function of a marginal operator — is a candidate for the action. Applied to the zero-momentum tachyon it gives a tachyon potential that is similar to those that have been obtained using Witten's background independent formalism. This procedure is easily made gauge invariant in the loop variable formalism by replacing ln a by Σ which is the generalization of the Liouville mode that occurs in this formalism. We also describe a method of resumming the Taylor expansion that is done in the loop variable formalism. This allows one to see the pole structure of string amplitudes that would not be visible in the original loop variable formalism.

We introduce a rotation invariant short distance cutoff in the theory of an ideal fluid in three space dimensions, by requiring momenta to take values in a sphere. This leads to an algebra of functions in position space that is noncommutative. Nevertheless it is possible to find appropriate analogues of the Euler equations of an ideal fluid. The system still has a Hamiltonian structure. It is hoped that this will be useful in the study of possible singularities in the evolution of Euler (or Navier–Stokes) equations in three dimensions.

We use a lattice formulation to study the spectra of the Dirac and the Dirac–Kähler operators on the 2-sphere. This lattice formulation uses differentiation matrices which yield exact values for the derivatives of polynomials, preserving the Leibniz rule in subspaces of polynomials of low degree and therefore, this formulation can be used to study the fermion–boson symmetry on the lattice. In this context, we find that the free Dirac and Dirac–Kähler operators on the 2-sphere exhibit fermionic as well as bosonic-like eigensolutions for which the corresponding eigenvalues and the number of states are computed. In the Dirac case these solutions appear in doublets, except for the bosonic mode with zero eigenvalue, indicating the possible existence of a supersymmetry of the square of the Dirac operator.

We examine resonances for two systems consisting of a particle coupled to a massless boson's field. The field is the free field in the whole space. In the first system, the particle is confined inside a ball. We show that besides the usual energy levels of the particle, which have become complex through the coupling to the field, other resonances are to be taken into account if the ball's radius is comparable to the particle's Compton wavelength. In the second system, the particle is in a finite-depth square-well potential. We study the way the resonances' energy and width depend on the extent of the uncoupled particle's wave functions. In both cases, we limit ourselves to considering two levels of the particle only.

We study the radiative lepton flavor violating l_i → l_jγ decays in the two-Higgs doublet model, respecting the Randall–Sundrum scenario and estimate the contributions of the KK modes of left- (right-)handed charged lepton doublets (singlets) on the branching ratios. We observe that the branching ratios are sensitive to the contributions of the charged lepton KK modes.

The reduction formulas for Dirac fermions is derived using the exact solutions of free Dirac equation on de Sitter space–time. In the framework of the perturbation theory one studies the Green functions and derives the scattering amplitude in the first orders of perturbation theory.

We show in this paper how to construct Symanzik polynomials and the Schwinger parametric representation of Feynman amplitudes for gauge theories in a generic covariant gauge. The complete Mellin representation of such amplitudes is then established in terms of invariants (squared sums of external momenta and squared masses). From the scaling of the invariants by a parameter we extend for the present situation a theorem on asymptotic expansions, previously proven for the case of scalar field theories, valid for both ultraviolet or infrared behaviors of Feynman amplitudes.