Recent theorems

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Archive for August 1998

We study higher spin tensor currents in quantum field theory. Scalar, spinor and vector fields admit unique “improved” currents of arbitrary spin, traceless and conserved. Off-criticality as well as at interacting fixed points conservation is violated and the dimension of the current is anomalous. In particular, currents $J^{(s,I)}$ with spin $s$ between 0 and 5 (and a second label $I$) appear in the operator product expansion of the stress tensor. The TT OPE is worked out in detail for free fields; projectors and invariants encoding the space-time structure are classified. The result is used to write and discuss the most general OPE for interacting conformal field theories and off-criticality. Higher spin central charges $c_{(s,I)}$ with arbitrary $s$ are defined by higher spin channels of the many-point T-correlators and central functions interpolating between the UV and IR limits are constructed. We compute the one-loop values of all $c_{(s,I)}$ and investigate the RG trajectories of quantum field theories in the conformal window following our approach. In particular, we discuss certain phenomena (perturbative and nonperturbative) that appear to be of interest, like the dynamical removal of the $I$-degeneracy. Finally, we address the problem of formulating an action principle for the RG trajectory connecting pairs of CFT’s as a way to go beyond perturbation theory.


Nucl.Phys. B541 (1999) 323-368 | DOI: 10.1016/S0550-3213(98)00783-4


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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.)