Alessio Rocci1* and Thomas Van Riet2 1*Theoretische Natuurkunde (VUB) and the International Solvay Institutes; Applied Physics research group (APHY), Pleinlaan 2, Brussels, 1050, Belgium. 2Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200d- box 2415, 3001, Leuven, Belgium. *Corresponding author(s). E-mail(s): Alessio.Rocci@vub.be; Contributing authors: thomas.vanriet@kuleuven.be; Abstract This paper analyzes the effective field theory perspective on modern physics through the lens of the quantum theory of gravitational interaction. The historical part argues that the search for a theory of quantum gravity stimulated the change in outlook that characterizes the modern approach to the Standard Model of particle physics and General Relativity. We present some landmarks covering a long period, i.e., from the beginning of the 1930s until 1994, when, according to Steven Weinberg, the modern bottom-up approach to General Relativity began. Starting from the first attempt to apply the quantum field theory techniques to quantize Einstein’s theory perturbatively, we explore its developments and interaction with the top-down approach encoded by String Theory. In the last part of the paper, we focus on this last approach to describe the relationship between our modern understanding of String Theory and Effective Field Theory in today’s panorama. To this end, the non-historical part briefly explains the modern concepts of moduli stabilization and Swampland to understand another change in focus that explains the present framework where some string theorists move.
Weinberg suggested replacing the renormalizability criterion with the concept of asymptotic safety for the following reasons. He started considering critical phenomena, i.e., quantum eld theory at a non-zero temperature in four dimensions. He pointed out that critical phenomena are conveniently described in terms of an eective Euclidean three-dimensional eld theory (Weinberg, 1976; p. 8). Then, he analyzed the role of the cut-o introduced to choose the eective Hamiltonian. The coupling constant will depend on the cut-o, while physical quantities remain cut-o independent for all theories, renormalizable or not. Weinberg pointed out that in this approach to quantum eld theories, the temperature and similar parameters enter the theory only as initial conditions, determining the coupling constant values for some values of the cut-o. He nally concluded that Each particular physical theory with a particular value of the temperature is represented by a trajectory in coupling-constant s
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..] Dierent points on a given trajectory do not represent dierent theories, but only dierent Hamiltonians, corresponding to dierent cut-os (Weinberg, 1976; p. 16). From this perspective, renormalizability does not play any special role. Weinberg underlined this fact as follows. In this formalism, a renormalizable theory merely corresponds to a subset of trajectories (characterized by a few renormalized coupling constants) for which all but a few of the couplings vanish (at least in perturbation theory)
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Springer Nature 2021 LATEX template GR-EFT-Strings as (Weinberg, 1976; p. 33). Hence, Weinberg suggested that asymptotic safety can provide a rationale for picking physically acceptable quantum eld theories, which may either explain renormalizability or else replace it (Weinberg, 1976; p. 34).
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Weinbergs suggestion was soon analyzed in the context of QG. Two years later, Jaume Julve Perez and Mario Tonin considered a renormalizable but perturbatively non-unitary model of QG. The authors discussed the higher derivative theory that Stelle proved to be renormalizable, even if it was plagued by the occurrence of massive Weyl ghosts (Julve and Tonin, 1978; p. 137), which Tonin was used to jokingly call poltergeists (Lechner, 2022). Julve and Tonin tried to understand if one-loop corrections could push their masses to innity and restore the unitarity of the model. The need to modify the standard action by adding terms quadratic in the curvature tensor (Julve and Tonin, 1978; p. 137) had become accepted. However, the authors still considered their model as a candidate for a fundamental theory. They calculated the one-loop counterterms and analyzed the equations of the renormalization group with the hope of nding some possible mechanism which hopefully could rule out the ghosts (
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