Thirty-Ninth Meeting of the North British Mathematical Physics Seminar

Galileons satisfy equations of motion with terms containing only second order derivatives of the fields. They have many intriguing properties, derivation from Lagrangian hierarchies, implicit solutions, dualities etc, and have become new players in cosmological models.

The study of the worldsheet S-matrix for AdS_5 x S^5 strings was a key step in the complete determination of the spectrum of anomalous dimensions for planar N=4 super-Yang-Mills gauge theory. To go beyond the spectral problem it is important to consider higher-point worldsheet correlation functions and one approach is the study of form factors. We will discuss the calculation of form factors in the two-dimensional light-cone gauge-fixed string theory and their connection to four-dimensional gauge theory three-point functions.

We present the collective coordinate approximation to model the dynamics of two interacting nonlinear Schrodinger (NLS) solitons; and discuss the accuracy of this approximation by comparing our results to those of the full numerical simulations.

We consider a class of phenomenological modified gravity models where the terms added to the standard Einstein-Hilbert Lagrangian are just a function of the metric only. For linearized perturbations around an isotropic space-time, this class of models is entirely specified by a rank 4 tensor that encodes possibly time-dependent masses for the gravitons. This tensor has the same symmetries as an elasticity tensor, suggesting an interpretation of massive gravity as an effective rigidity of space-time. If we choose a form for this tensor which is compatible with the symmetries of FRW and enforce full reparameterization invariance, then the only theory possible is a cosmological constant. However, in the case where the theory is only time translation invariant, the ghost-free massive gravity theory is equivalent to the elastic dark energy scenario with the extra Lorentz violating vector giving rise to 2 transverse and 1 longitudinal degrees of freedom, whereas when one demands spatial translation invariance one is left with a theory where the entropy perturbation is not gauge invariant.

Reporting on work in progress with A. Konechny, I will talk about the important role redundant operators play in the renormalization of 2d QFTs. The analysis is performed both via the study of the local renormalization anomaly equation as well as in explicit conformal perturbation theory. Our results reveal the existence of a symmetry on coupling space due to the redundant operators, indicating that physical quantities such as the c-function and the beta-functions should depend only on equivalence classes of couplings under this symmetry. Partial progress towards the study of the geometry of coupling space as well as illustrating examples will be presented.