arXiv subjects
Publications and source records attributed to Henrique Boschi-Filho.
We correct the energy of the static strings in hep-th/0512295, for large quark anti-quark separation. This energy is a smooth function of the quark separation for any position of the infrared brane. The asymptotic behavior of this energy is that of the Cornell potential as stated in the article. However, this identification does not fixes the AdS radius.
A static string in an AdS Schwarzschild space is dual to a heavy quark anti-quark pair in a gauge theory at high temperature. This space is non confining in the sense that the energy is finite for infinite quark anti-quark separation. We introduce an infrared cut off in this space and calculate the corresponding string energy. We find a deconfining phase transition at a critical temperature T_C. Above T_C the string tension vanishes representing the deconfined phase. Below T_C we find a linear confining behavior for large quark anti-quark separation. This simple phenomenological model leads to the appropriate zero temperature limit, corresponding to the Cornell potential and also describes a thermal deconfining phase transition. However the temperature corrections to the string tension do not recover the expected results for low temperatures.
We review some recent results on phenomenological approaches to strong interactions inspired in gauge/string duality. In particular, we discuss how such models lead to very good estimates for hadronic masses.
We calculate the energy of a static string in an AdS slice between two D3-branes with orbifold condition. The energy for configurations with endpoints on a brane grows linearly for large separation between these points. The derivative of the energy has a discontinuity at some critical separation. Choosing a particular position for one of the branes we find configurations with smooth energy. In the limit where the other brane goes to infinity the energy has a Coulombian behaviour for short separations and can be identified with the Cornell potential for a quark anti-quark pair. This identification leads to effective values for the AdS radius, the string tension and the position of the infrared brane. These results suggest an approximate duality between static strings in an AdS slice and a heavy quark anti-quark configuration in a confining gauge theory.
The spectrum of light baryons and mesons has been reproduced recently by Brodsky and Teramond from a holographic dual to QCD inspired in the AdS/CFT correspondence. They associate fluctuations about the AdS geometry with four dimensional angular momenta of the dual QCD states. We use a similar approach to estimate masses of glueball states with different spins and their excitations. We consider Dirichlet and Neumann boundary conditions and find approximate linear Regge trajectories for these glueballs. In particular the Neumann case is consistent with the Pomeron trajectory.
We calculate static Wilson loops for a heavy quark anti-quark pair in different positions in the space generated by a large number of coincident D3-branes. Simple results are obtained from limiting cases of the geodesic shape. In particular, quark anti-quark static potentials for flat and AdS spaces are reproduced.
Inspired in the AdS/CFT correspondence one can look for dualities between string theory and non conformal field theories. Exact dualities in the non conformal case are intricate but approximations can be helpful in extracting physical results. A phenomenological approach consists in introducing a scale corresponding to the maximum value of the axial AdS coordinate. Here we show that this approach can reproduce the scaling of high energy glueball scattering amplitudes and also an approximation for the scalar glueball mass ratios.
We consider the BRST gauge fixing procedure of the noncommutative Yang-Mills theory and of the gauged U(N) Proca model. An extended Seiberg-Witten map involving ghosts, antighosts and auxiliary fields for non Abelian gauge theories is studied. We find that the extended map behaves differently for these models. For the Yang-Mills theory in the Lorentz gauge it was not possible to find a map that relates the gauge conditions in the noncommutative and ordinary theories. For the gauged Proca model we found a particular map relating the unitary gauge fixings in both formulations.
We obtain the Killing equations and the corresponding infinitesimal isometries for the ten dimensional space generated by a large number of coincident D3-branes. In a convenient limit this space becomes an $AdS_5\times S^5$ which is relevant for the AdS/CFT correspondence. In this case, using Poincare coordinates, we also write down the Killing equations and infinitesimal isometries. Then we obtain a simple realization of the isomorphism between $AdS$ isometries and the boundary conformal group.
The AdS/CFT correspondence is an exact duality between string theory in anti-de Sitter space and conformal field theories on its boundary. Inspired in this correspondence some relations between strings and non conformal field theories have been found. Exact dualities in the non conformal case are intricate but approximations can reproduce important physical results. A simple approximation consists in taking just a slice of the AdS space with a size related to an energy scale. Here we will discuss how this approach can be used to reproduce the scaling of high energy QCD scattering amplitudes. Also we show that very simple estimates for glueball mass ratios can emerge from such an approximation.
Recently Polchinski and Strassler reproduced the high energy QCD scaling at fixed angles from a gauge string duality inspired in AdS/CFT correspondence. In their approach a confining gauge theory is taken as approximately dual to an AdS space with an IR cut off. Considering such an approximation (AdS slice) we found a one to one holographic mapping between bulk and boundary scalar fields. Associating the bulk fields with dilatons and the boundary fields with glueballs of the confining gauge theory we also found the same high energy QCD scaling. Here, using this holographic mapping we give a simple estimate for the mass ratios of the glueballs assuming the AdS slice approximation to be valid at low energies. We also compare these results to those coming from supergravity and lattice QCD.
It has been shown by Polchinski and Strassler that the scaling of high energy QCD scattering amplitudes can be obtained from string theory. They considered an AdS slice as an approximation for the dual space of a confining gauge theory. Here we use this approximation to estimate in a very simple way the ratios of scalar glueball masses imposing Dirichlet boundary conditions on the string dilaton field. These ratios are in good agreement with the results in the literature. We also find that they do not depend on the size of the slice.
Physical consistency of quantum fields in anti-de Sitter space time requires that the space must be compactified by the inclusion of a boundary where appropriate conditions are imposed. An interpretation for the presence of this boundary is found taking AdS as a limiting case of the space generated by a large number of coincident branes. The compactification of AdS leads to a discretization of the spectrum of bulk fields. As a consequence, we find a one to one mapping between the quantum states of scalar fields in AdS bulk and boundary. Using this mapping as an approximation for the dual relation between string dilaton field and scalar QCD glueballs the high energy QCD scaling is reproduced. We also use this map to estimate the ratio of scalar glueball masses.
The AdS/CFT correspondence can be realized in spaces that are globally different but share the same asymptotic behavior. Two known cases are: a compact AdS space and the space generated by a large number of coincident branes. We discuss the physical consistency, in the sense of the Cauchy problem, of these two formulations. We show that the role of the boundary in the compact AdS space is equivalent to that of the flat asymptotic region in the brane space. We also show, by introducing a second coordinate chart for the pure AdS space, that a point at its spatial infinity corresponds to a horizon in the brane system.
An explicit holographic correspondence between $AdS$ bulk and boundary quantum states is found in the form of a one to one mapping between scalar field creation/annihilation operators. The mapping requires the introduction of arbitrary energy scales and exhibits an ultraviolet-infrared duality: a small regulating mass in the boundary theory corresponds to a large momentum cutoff in the bulk. In the massless (conformal) limit of the boundary theory the mapping covers the whole field spectrum of both theories. The mapping strongly depends on the discretization of the field spectrum of compactified $AdS$ space in Poincare coordinates.
Compactified AdS space can not be mapped into just one Poincare coordinate chart. This implies that the bulk field spectrum is discrete despite the infinite range of the coordinates. We discuss here why this discretization of the field spectrum seems to be a necessary ingredient for the holographic mapping. For the Randall Sundrum model we show that this discretization appears even without the second brane.
The quantization of a scalar field in anti de Sitter spacetime using Poincaré coordinates is considered. We find a discrete spectrum that is consistent with a possible mapping between bulk and boundary quantum states.
We discuss how the variational principle can be used as a criterion for choosing, among scalar field actions implying the same equation of motion, the appropriate one for the AdS/CFT correspondence.