Consistent irrelevant deformations of interacting conformal field theories

Details Consistent irrelevant deformations of interacting conformal field theories Consistent irrelevant deformations of interacting conformal field theories

2003-09-27

arxiv.org/abs/hep-th/0309251v2

JHEP 0310 (2003) 045

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 5 figures; reference updated - JHEP

Scientific paper

10.1088/1126-6708/2003/10/045

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.

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