arXiv subjects
Publications and source records attributed to Miguel A. Vazquez-Mozo.
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String Theory.
We investigate tree-level five-point amplitudes in scalar-QCD expressed in terms of Sudakov variables and find the equivalent "gravitational" counterparts using the color-kinematics duality proposed by Bern, Carrasco, and Johannson. Taking the multi-Regge limit in the gravitational amplitudes, we show that those pieces in the coupling of two reggeized gravitons to one on-shell graviton directly stemming from the double copy of the vertex for two reggeized gluons to one on-shell gluon are universal and properly reproduced by the duality.
We study the collision of two Reissner-Nordström gravitational shock waves in AdS and show that the charge completely prevents the formation of marginally trapped surfaces of the Penrose type with topology S^(D-2), independently of the energy and the value of the impact parameter. In the case of head-on collisions, a numerical analysis shows that no trapped surfaces with topology S^1 \times S^(D-3) form either.
We identify a novel physical mechanism that may be responsible for energy release in $γ$-ray bursts. Radial perturbations in the neutron core, induced by its collision with collapsing outer layers during the early stages of supernova explosions, can trigger a gravitational shock, which can readily eject a small but significant fraction of the collapsing material at ultra-relativistic speeds. The development of such shocks is a strong-field effect arising in near-critical collapse in General Relativity and has been observed in numerical simulations in various contexts, including in particular radially perturbed neutron star collapse, albeit for a tiny range of initial conditions. Therefore, this effect can be easily missed in numerical simulations if the relevant parameter space is not exhaustively investigated. In the proposed picture, the observed rarity of $γ$-ray bursts would be explained if the relevant conditions for this mechanism appear in only about one in every $10^4-10^5$ core collapse supernovae. We also mention the possibility that near-critical collapse could play a role in powering the central engines of Active Galactic Nuclei.
The five-point amplitude for the scattering of two distinct scalars with the emission of one graviton in the final state is calculated in exact kinematics for Einstein-Hilbert gravity. The result, which satisfies the Steinmann relations, is expressed in Sudakov variables, finding that it corresponds to the sum of two gauge invariant contributions written in terms of a new two scalar - two graviton effective vertex. A similar calculation is carried out in Quantum Chromodynamics (QCD) for the scattering of two distinct quarks with one extra gluon in the final state. The effective vertices which appear in both cases are then evaluated in the multi-Regge limit reproducing the well-known result obtained by Lipatov where the Einstein-Hilbert graviton emission vertex can be written as the product of two QCD gluon emission vertices, up to corrections to preserve the Steinmann relations.
The formation of marginally trapped surfaces in the off-center collision of two shock waves on AdS_D (with D=4,5,6,7 and 8) is studied numerically. We focus on the case when the two waves collide with nonvanishing impact parameter while the sources are located at the same value of the holographic coordinate. In all cases a critical value of the impact parameter is found above which no trapped surface is formed. The numerical results show the existence of a simple scaling relation between the critical impact parameter and the energy of the colliding waves. Using the isometries of AdS_D we relate the solutions obtained to the ones describing the collision of two waves with a purely holographic impact parameter. This provides a gravitational dual for the head-on collision of two lumps of energy of unequal size.
We study the formation of marginally trapped surfaces in the head-on collision of two shock waves both in anti-de Sitter and Minkowski space-time in various dimensions as a function of the spread of the energy density in transverse space. For D=4 and D=5 it is shown that there exists a critical value of this spread above which no solution to the trapped surface equation is found. In four dimensions the trapped surface at criticality has a finite size, whereas in five the critical size vanishes. In both cases we find scaling relations characterized by critical exponents. Finally, when D>5 there is always a solution to the trapped surface equation for any transverse spread.
We study noncommutative deformations of Yang-Mills theories and show that these theories admit a infinite, continuous family of twisted star-gauge invariances. This family interpolates continuously between star-gauge and twisted gauge transformations. The possible physical role of these start-twisted invariances is discussed.
We study the possible holographic connection between the Regge limit in QCD and critical gravitational collapse of a perfect fluid in higher dimensions. We begin by analyzing the problem of critical gravitational collapse of a perfect fluid in any number of dimensions and numerically compute the associated Choptuik exponent in d=5, 6 and 7 for a range of values of the speed of sound of the fluid. Using continuous self-similarity as guiding principle, a holographic correspondence between this process and the phenomenon of parton saturation in high-energy scattering in QCD is proposed. This holographic connection relates strong gravitational physics in the bulk with (nonsupersymmetric) QCD at weak coupling in four dimensions.
We present holographic arguments to predict properties of strongly coupled gravitational systems in terms of weakly coupled gauge theories. In particular we relate the latest computed value for the Choptuik critical exponent in black hole formation in five dimensions, γ_{5D}=0.412 \pm 1%, to the saturation exponent of four-dimensional Yang-Mills theory in the Regge limit, γ_{BFKL}\simeq 0.410.
We study the possibility of obtaining noncommutative gravity dynamics from string theory in the Seiberg-Witten limit. We find that the resulting low-energy theory contains more interaction terms than those proposed in noncommutative deformations of gravity. The role of twisted diffeomorphisms in string theory is studied and it is found that they are not standard physical symmetries. It is argued that this might be the reason why twisted diffeomorphisms are not preserved by string theory in the low energy limit. Twisted gauge transformations are also discussed.
We study nonanticommutative deformations of N=2 two-dimensional Euclidean sigma models. We find that these theories are described by simple deformations of Zumino's Lagrangian and the holomorphic superpotential. Geometrically, this deformation can be interpreted as a fuzziness in target space controlled by the vacuum expectation value of the auxiliary field. In the case of nonanticommutative deformations preserving Euclidean invariance, we find that a continuation of the deformed supersymmetry algebra to Lorentzian signature leads to a rather intriguing central extension of the ordinary (2,2) superalgebra.
This is a semipopular introduction to the Special and General Theory of Relativity, with special emphasis on the geometrical aspects of both theories and their physical implications.