Holographic technicolor models and their S-parameter

TL;DR

This paper calculates the S-parameter in various holographic technicolor models, providing a general method and specific results for different models, revealing how the parameter depends on model parameters and techniquark masses.

Contribution

It introduces a generalized holographic recipe for computing the S-parameter and applies it to multiple models, including confining and non-confining theories, with detailed quantitative results.

Findings

S-parameter proportional to N_{TC} with model-specific coefficients

Divergent S-parameter in one of the models

Dependence of S-parameter on techniquark mass and model parameters

Abstract

We study the Peskin-Takeuchi S-parameter of holographic technicolor models. We present the recipe for computing the parameter in a generalized holographic setup. We then apply it to several holographic models that include: (a) the Sakai-Sugimoto model and (b) its non-compactified cousin, (c) a non-critical analog of (a) based on near extremal AdS_6 background, (d) the KMMW model which is similar to model (a) but with D6 and anti-D6 flavor branes replacing the D8 and anti-D8 branes, (e) a model based on D5 branes compactified on two S^1s with D7 and anti-7 probe branes and (f) the conifold model with the same probe branes as in (e). The models are gravity duals of gauge theories with U(N_{TC}) gauge theory and with a breakdown of a flavor symmetry U(N_{TF})xU(N_{TF}) to U_V(N_{TF}). The models (a), (c),(d) and (e) are duals of a confining gauge theories whereas (b) and (f) associate with non confining models. The S-parameter was found to be S=sN_{TC} where s is given by 0.017\lambda_{TC}, 0.016\lambda_{TC}, 0.095, 0.50 and 0.043 for the (a),(b),(c),(d), (f) models respectively and for model (e) s is divergent. These results are valid in the large N_{TC} and large \lambda_{TC} limit. We further derive the dependence of the S-parameter on the "string endpoint" mass of the techniquarks for the various models. We compute the masses of the low lying vector technimesons.