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I study some classes of RG flows in three dimensions that are classically conformal and have manifest $g \rightarrow 1/g$ dualities. The RG flow interpolates between known (four-fermion, Wilson-Fischer, $\phi_3^6$) and new interacting fixed points. These models have two remarkable properties: $i$) the RG flow can be integrated for arbitrarily large values of the couplings g at each order of the $1/N$ expansion; $ii$) the duality symmetries are exact at each order of the $1/N$ expansion. I integrate the RG flow explicitly to the order ${\cal O}(1/N)$, write correlators at the leading-log level and study the interpolation between the fixed points. I examine how duality is implemented in the regularized theory and verified in the results of this paper.


Nucl.Phys. B658 (2003) 440 | DOI: 10.1016/S0550-3213(03)00174-3


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14B1 D. Anselmi

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Last update: May 9th 2015, 230 pages

Contents: Preface | 1. Functional integral | 2. Renormalization | 3. Renormalization group | 4. Gauge symmetry | 5. Canonical formalism | 6. Quantum electrodynamics | 7. Non-Abelian gauge field theories | Notation and useful formulas | References

Course on renormalization, taught in Pisa in 2015. (More chapters will be added later.)