Gravitación y Teoría de Campos

The anisotropic chiral BosonWe construct the theory of a chiral boson with anisotropic scaling, characterized by a dynamical exponent z that takes positive odd integer values. The action reduces to that of Floreanini and Jackiw in the isotropic case (z = 1). The standard free boson with Lifshitz scaling is recovered when both chiralities are nonlocally combined. Its canonical structure and symmetries are also analyzed. As in the isotropic case, the theory is also endowed with a current algebra. Noteworthy, the standard conformal symmetry is shown to be still present, but realized in a nonlocal way. The exact form of the partition function at finite temperature is obtained from the path integral, as well as from the trace over u(1) descendants. It is essentially given by the generating function of the number of partitions of an integer into zth powers, being a wellknown object in number theory. Thus, the asymptotic growth of the number of states at fixed energy, including subleading correc tions, can be obtained from the appropriate extension of the renowned result of Hardy and Ramanujan. 
Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimesThe analysis is performed in terms of twodimensional gauge fields for isl (2,R), being isomorphic to the Poincaré algebra in 3D. Although the algebra is not semisimple, the formulation can still be carried out à la DrinfeldSokolov because it admits a nondegenerate invariant bilinear metric. The hierarchy turns out to be biHamiltonian, labeled by a nonnegative integer k, and defined through a suitable generalization of the GelfandDikii polynomials. The symmetries of the hierarchy are explicitly found. For k ≥ 1, the corresponding conserved charges span an infinitedimensional Abelian algebra without central extensions, so that they are in involution; while in the case of k = 0, they generate the BMS3 algebra. In the special case of k = 1, by virtue of a suitable field redefinition and time scaling, the field equations are shown to be equivalent to the ones of a specific type of the HirotaSatsuma coupled KdV systems. For k ≥ 1, the hierarchy also includes the socalled perturbed KdV equations as a particular case. A wide class of analytic solutions is also explicitly constructed for a generic value of k. 