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)less than or similar to11 N-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.

Consistent irrelevant deformations of interacting conformal field theories

ANSELMI, DAMIANO
2003

Abstract

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)less than or similar to11 N-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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/78039
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