Conformal Theories with an IR cutoff

TL;DR

This paper proposes that in conformal SU(N) gauge theories with an IR cutoff, meson propagators exhibit a power-law corrected Yukawa decay, and verifies this through numerical simulations for specific flavor numbers.

Contribution

It introduces a new perspective on meson propagator behavior in conformal theories with an IR cutoff and provides numerical verification for specific cases.

Findings

Meson propagators follow a power-law corrected Yukawa decay in the conformal region.

Transition between conformal and confining phases is first order.

Numerical results confirm the theoretical predictions for N_f=7 and N_f=16 cases.

Abstract

We give a new perspective on the dynamics of conformal theories realized in the SU(N) gauge theory, when the number of flavors N_f is within the conformal window. Motivated by the RG argument on conformal theories with a finite IR cutoff \Lambda_{IR}, we conjecture that the propagator of a meson G_H(t) on a lattice behaves at large t as a power-law corrected Yukawa-type decaying form G_H(t) = c_H \exp{(-m_H t)}/t^{\alpha_H} instead of the exponentially decaying form c_H\exp{(-m_H t)}, in the small quark mass region where m_H \le c \Lambda_{IR}: m_H is the mass of the ground state hadron in the channel H and c is a constant of order 1. The transition between the "conformal region" and the "confining region" is a first order transition. Our numerical results verify the predictions for the N_f=7 case and the N_f=16 case in the SU(3) gauge theory with the fundamental representation.