Date Thesis Awarded
Honors Thesis -- Open Access
Bachelors of Science (BS)
Christopher D. Carone
Quantum Chromodynamics (QCD), the theory of the strong force describing quark interactions, is notoriously difficult to make calculations with because of properties such as confinement and asymptotic freedom. A model was developed several years ago using the Anti-de-Sitter/Conformal-Field-Theory (AdS/CFT) Correspondence conjectured by Juan Maldacena in terms of String Theory. In this paper, we first describe QCD and its associated chiral symmetry, and then develop Holographic QCD (or AdS/QCD), the model based on the AdS/CFT correspondence. We then describe the phenomenon of pion condensation to exhibit one discrepancy AdS/QCD shows from expectations. Using the model, we then derive the Gell-Mann-Oakes-Renner (GOR) relation for a real chiral condensate. In the derivation, we make a small detour to define the pion decay constant using the AdS/CFT correspondence. We then relax the assumption that the chiral condensate is real and derive a generalized GOR relation for a complex chiral condensate. After finding some unexpected results in the complex GOR relation, we attempt to find the cause of our problems and try a new field decomposition to reproduce our desired results.
Wilcox, Ronald James, "The Pion in AdS/QCD" (2011). Undergraduate Honors Theses. William & Mary. Paper 350.
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