Miguel Á. Vázquez-Mozo

Comments on noncommutative gravity

Abstract 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.

Critical formation of trapped surfaces in the collision of gravitational shock waves

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.

Thermal effects in perturbative noncommutative gauge theories

The thermodynamics of gauge theories on the noncommutative plane is studied in perturbation theory. For U(1) noncommutative Yang-Mills we compute the first quantum correction to the ideal gas free energy density and study their behavior in the low and high temperature regimes. Since the noncommutativity scale effectively cutoff interactions at large distances, the theory is regular in the infrared. In the case of U(N) noncommutative Yang-Mills we evaluate the two-loop free energy density and find that it depends on the noncommutativity parameter through the contribution of non-planar diagrams.

On nonanticommutative Script N = 2 sigma-models in two dimensions

We study nonanticommutative deformations of N = 2 two-dimensional eu- clidean sigma models. We flnd that these theories are described by simple deformations of Zuminos 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 fleld. In the case of nonanticommutative deformations preserving euclidean invariance, we flnd that a continuation of the deformed supersymmetry algebra to lorentzian signature leads to a rather intriguing central extension of the ordinary (2,2) superalgebra.

The double copy structure of soft gravitons

A bstractThe subleading corrections to factorization theorems for soft bremsstrahlung in nonabelian gauge theories and gravity are investigated in the case of a five point amplitude with four scalars. Building on recent results, we write the action of the angular momentum operators on scattering amplitudes as derivatives with respect to the Mandelstam invariants to uncover a double copy structure in the contribution of the soft graviton to the amplitude, both in the leading term and the first correction. Using our approach, we study Gribov’s theorem as extended to nonabelian gauge theories and gravity by Lipatov, and find that subleading corrections can be obtained from those to Low’s theorem by dropping the terms with derivatives with respect to the center-of-mass energy, which are suppressed at high energies. In this case, the emitted gravitons are not necessarily soft.

Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction

A bstractIn this note we study the applicability of the color-kinematics duality to the scattering of two distinguishable scalar matter particles with gluon emission in QCD, or graviton emission in Einstein gravity. Previous analysis suggested that direct use of the Bern-Carrasco-Johansson double-copy prescription to matter amplitudes does not reproduce the gravitational amplitude in multi-Regge kinematics. This situation, however, can be avoided by extensions to the gauge theory, while maintaning the same Regge limit. Here we present two examples of these extensions: the introduction of a scalar contact interaction and the relaxation of the distinguishability of the scalars. In both cases new diagrams allow for a full reconstruction of the correct Regge limit on the gravitational side. Both modifications correspond to theories obtained by dimensional reduction from higher-dimensional gauge theories.

M-theory resolution of four-dimensional cosmological singularities via U-duality

Abstract We consider cosmological solutions of string and M-theory compactified to four dimensions by giving a general prescription to construct four-dimensional modular cosmologies with two commuting Killing vectors from vacuum solutions. By lifting these solutions to higher dimensions we analyze the existence of cosmological singularities and find that, in the case of non-closed Friedmann-Robertson-Walker universes, curvature singularities are removed from the higher-dimensional model when only one of the extra dimensions is time-varying. By studying the moduli space of compactifications of M-theory resulting in homogeneous cosmologies in four dimensions we show that U-duality transformations map singular cosmologies into non-singular ones.

Color-Kinematics Duality and the Regge Limit of Inelastic Amplitudes

A bstractWe 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 Johansson. 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.

Initial conditions and the structure of the singularity in pre - big bang cosmology

We propose a picture, within the pre-big-bang approach, in which the universe emerges from a bath of plane gravitational and dilatonic waves. The waves interact gravitationally breaking the exact plane symmetry and lead generically to gravitational collapse resulting in a singularity with Kasner-like structure. The analytic relations between the Kasner exponents and the initial data are evaluated explicitly and it is shown that pre-big-bang inflation may occur within a dense set of initial data. Finally, we argue that plane waves carry zero gravitational entropy and thus are, from a thermodynamical point of view, good candidates for the universe to emerge from.

Colliding AdS gravitational shock waves in various dimensions and holography

The formation of marginally trapped surfaces in the off-center collision of two shock waves on AdSD (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 AdSD 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.