Bouatta, Nazim and Butterfield, Jeremy (2012) On emergence in gauge theories at the 't Hooft limit. [Preprint]

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Abstract
Quantum field theories are notoriously difficult to understand, physically as well as philosophically. The aim of this paper is to contribute to a better conceptual understanding of gauge quantum field theories, such as quantum chromodynamics, by discussing a famous physical limit, the 't Hooft limit, in which the theory concerned often simplifies.
The idea of the limit is that the number N of colours (or charges) goes to infinity. The
simplifications that can happen in this limit, and that we will consider, are: (i) the theory's Feynman diagrams can be drawn on a plane without lines intersecting (called `planarity'); and (ii) the theory, or a sector of it, becomes integrable, and indeed corresponds to a wellstudied system, viz. a spin chain. Planarity is important because it shows how a quantum field theory can exhibit extended, in particular stringlike, structures; in some cases, this gives a connection with string theory, and thus with gravity.
Previous philosophical literature about how one theory (or a sector, or regime, of a theory) might be emergent from, andor reduced to, another one has tended to emphasize cases, such as occur in statistical mechanics, where the system before the limit has finitely many degrees of freedom. But here, our quantum field theories, including those on the way to the 't Hooft limit, will have infinitely many degrees of freedom.
Nevertheless, we will show how a recent schema by Butterfield and taxonomy by Norton apply to the quantum field theories we consider; and we will classify three physical properties of our theories in these terms. These properties are planarity and integrability, as in (i) and (ii) above; and the behaviour of the betafunction reflecting, for example, asymptotic freedom.
Our discussion of these properties, especially the betafunction, will also relate to
recent philosophical debate about the propriety of assessing quantum field theories, whose rigorous existence is not yet proven.
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Item Type:  Preprint  

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Keywords:  Emergence, gauge theories, the 't Hooft limit, quantum chromodynamics, supersymmetry, planarity, integrability  
Subjects:  General Issues > Models and Idealization Specific Sciences > Physics > Quantum Field Theory General Issues > Reductionism/Holism Specific Sciences > Physics > Symmetries/Invariances 

Depositing User:  Jeremy Butterfield  
Date Deposited:  25 Aug 2012 15:27  
Last Modified:  25 Aug 2012 15:27  
Item ID:  9288  
URI:  http://philsciarchive.pitt.edu/id/eprint/9288 
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