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Register a new userAn Introduction to Effective Field Theories
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Riccardo Penco
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These notes are an overview of effective field theory (EFT) methods. I discuss toy model EFTs, chiral perturbation theory, Fermi liquid theory, and non-relativistic QED, and use these examples to introduce a variety of EFT concepts, including: matching a tree and loop level; summation of large logarithms; naturalness problems; spurion fields; coset construction; Wess-Zumino-Witten terms; chiral and gauge anomalies; field rephasings; and method of regions. These lecture notes were prepared for the 2nd Joint ICTP-Trieste/ICTP-SAIFR school on Particle Physics, Sao Paulo, Brazil, June 22 - July 3, 2020.
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We develop the idea that renormalization, decoupling of heavy particle effects from low energy physics and the construction of effective field theories are intimately linked to the momentum space entanglement of disparate modes of an interacting quantum field theory. Using unitary transformations to decouple these modes at the perturbative level, we show in a scalar field theoretical model with light and heavy fields, how renormalization may be consistently implemented and how the low energy effective field theory can be constructed. We also obtain a renormalization group equation in this framework and apply it to the scalar field theoretical model.
In this work we investigate the interaction between spin-zero and spin-one monopoles by making use of an effective field theory based on two-body and four-body interaction parts. In particular, we analyze the formation of bound state of monopole-antimonopole (i.e. monopolium). The magnetic-charge conjugation symmetry is studied in analogy to the usual charge conjugation to define a particle basis, for which we find bound-state solutions with relatively small binding energies and which allows us to identify the bounds on the parameters in the effective Lagrangians. Estimations of their masses, binding energies and scattering lengths are performed as functions of monopole masses and interaction strength in a specific renormalization scheme. We also examine the general validity of the approach and the feasibility of detecting the monopolium.
We show that in a spontaneously broken effective gauge field theory, quantized in a general background $R_xi$-gauge, also the background fields undergo a non-linear (albeit background-gauge invariant) field redefinition induced by radiative corrections. This redefinition proves to be crucial in order to renormalize the coupling constants of gauge-invariant operators in a gauge-independent way. The classical background-quantum splitting is also in general non-linearly deformed (in a non gauge-invariant way) by radiative corrections. Remarkably, such deformations vanish in the Landau gauge, to all orders in the loop expansion.
The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential $simleft(Phi^daggerPhi-frac{v^2}2right)^N$ with $N$ arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields $X_{1,2}$, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the $Ntoinfty$ case.
This is the introductory chapter to the volume. We review the main idea of the localization technique and its brief history both in geometry and in QFT. We discuss localization in diverse dimensions and give an overview of the major applications of the localization calculations for supersymmetric theories. We explain the focus of the present volume.
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