Irrelevant Deformations Research Articles

Holographic flavor transport in Schrödinger spacetime

We use gauge-gravity duality to study the transport properties of a finite density of charge carriers in a strongly-coupled theory with non-relativistic symmetry. The field theory is N=4 supersymmetric SU(Nc) Yang-Mills theory in the limit of large Nc and with large 't Hooft coupling, deformed by an irrelevant operator, coupled to a number Nf of massive N=2 supersymmetric hypermultiplets in the fundamental representation of the gauge group, i.e. flavor fields. The irrelevant deformation breaks the relativistic conformal group down to the Schroedinger group, which has non-relativistic scale invariance with dynamical exponent z=2. Introducing a finite baryon number density of the flavor fields provides us with charge carriers. We compute the associated DC and AC conductivities using the dual gravitational description of probe D7-branes in an asymptotically Schroedinger spacetime. We generically find that in the infrared the conductivity exhibits scaling with temperature or frequency that is relativistic, while in the ultraviolet the scalings appear to be non-relativistic with dynamical exponent z=2, as expected in the presence of the irrelevant deformation.

Identification Method for Flexure and Shear Behavior of Cantilever Structures

This article presents an original identification method for the assessment of flexure and shear stiffness of cantilever structures or shear wall buildings. Required data include an initial (theoretical) model, an estimation of lumped mass values (by floor) and an experimental evaluation of two eigenvalues (modal frequencies and their modal shapes). The method estimates coefficients whenever flexural (EI) or shear (GA) values are relevant or irrelevant. An initial formula includes both shear and flexural components. Furthermore, particular developments are carried out for particular cases of irrelevant shear or flexural deformations. A numerical simulation of a real chimney is performed to study the effectiveness of the methodology in identifying damage under noise conditions. A dynamic-test experiment is carried out on a steel cantilever which suffers damage in two sections. The result obtained from the application of the proposed methodology is satisfactory in both numerical and experimental cases, identifying precisely the stiffness changes in the system.

Identification des rigidités résiduelles de systèmes à murs porteurs chaînés

ABSTRACT This article presents an identification method for the assessment of flexure and shear stiffness of shear wall buildings. Required data includes an initial (theoretical) model, the estimation of lumped mass values (by floor) and the experimental evaluation of one or two eigenvalues (modal frequency and its modal shapes). The method estimates stiffness whenever flexural (EI) or shear (GA) values are relevant or are irrelevant. An initial formula includes both shear and flexural components. Furthermore, particular developments are carried out for particular cases of irrelevant shear or flexural deformations. The method is applied for two numerical examples showing its simple implementation. The numeric errors are very small, in the order of 10−18 up to 10−12 in the case of structures with 5 up to 12 stories.

SL(2,Bbb Z) action on three-dimensional CFTs and holography

We show that there is a natural action of SL(2,Z) on the two-point functions of the energy momentum tensor and of higher-spin conserved currents in three-dimensional CFTs. The dynamics behind the S-operation of SL(2,Z) is that of an irrelevant current-current deformation and we point out its similarity to the dynamics of a wide class of three-dimensional CFTs. The holographic interpretation of our results raises the possibility that many three-dimensional CFTs have duals on AdS4 with SL(2,Z) duality properties at the linearized level.

Consistent irrelevant deformations of interacting conformal field theories

I show that under certain conditions it is possible to define consistent irrelevant deformations of interacting conformal field theories. The deformations are finite or have a unique running scale ("quasi-finite"). They are made of an infinite number of lagrangian terms and a finite number of independent parameters that renormalize coherently. The coefficients of the irrelevant terms are determined imposing that the beta functions of the dimensionless combinations of couplings vanish ("quasi-finiteness equations"). The expansion in powers of the energy is meaningful for energies much smaller than an effective Planck mass. Multiple deformations can be considered also. I study the general conditions to have non-trivial solutions. As an example, I construct the Pauli deformation of the IR fixed point of massless non-Abelian Yang-Mills theory with N_c colors and N_f <~ 11N_c/2 flavors and compute the couplings of the term F^3 and the four-fermion vertices. Another interesting application is the construction of finite chiral irrelevant deformations of N=2 and N=4 superconformal field theories. The results of this paper suggest that power-counting non-renormalizable theories might play a role in the description of fundamental physics.