On the Renormalization of the Complex Scalar Free Field Theory

Polar coordinates are used for the complex scalar free field in D=4 dimensions. The resulting non renormalizable theory is healed by using a recently proposed symmetric subtraction procedure. The existence of the coordinates transformation is proved by construction.Comment: 27 pages, no figures, LaTe

Numerical Investigation of Two-Phase Flow through a Fault

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Off-shell renormalization in the presence of dimension 6 derivative operators. II. UV coefficients

The full off-shell one loop renormalization for all divergent amplitudes up to dimension 6 in the Abelian Higgs-Kibble model, supplemented with a maximally power counting violating higher-dimensional gauge-invariant derivative interaction $\sim g ~ \phi^\dagger \phi (D^\mu \phi)^\dagger D_\mu \phi$, is presented. This allows one to perform the complete renormalization of radiatively generated dimension 6 operators in the model at hand. We describe in details the technical tools required in order to disentangle the contribution to UV divergences parameterized by (generalized) non-polynomial field redefinitions. We also discuss how to extract the dependence of the $\beta$-function coefficients on the non-renormalizable coupling $g$ in one loop approximation, as well as the cohomological techniques (contractible pairs) required to efficiently separate the mixing of contributions associated to different higher-dimensional operators in a spontaneously broken effective field theory.Comment: 33 pages; revised version including the derivation of the one-loop beta function

Off-shell renormalization in the presence of dimension 6 derivative operators. I. General theory

The consistent recursive subtraction of UV divergences order by order in the loop expansion for spontaneously broken effective field theories with dimension-6 derivative operators is presented for an Abelian gauge group. We solve the Slavnov-Taylor identity to all orders in the loop expansion by homotopy techniques and a suitable choice of invariant field coordinates (named bleached variables) for the linearly realized gauge group. This allows one to disentangle the gauge-invariant contributions to off-shell 1-PI amplitudes from those associated with the gauge-fixing and (generalized) non-polynomial field redefinitions (that do appear already at one loop). The tools presented can be easily generalized to the non-Abelian case.Comment: 37 pages, 3 figures; updated version to match the published on

The Cosmological Slavnov-Taylor Identity from BRST Symmetry in Single-Field Inflation

The cosmological Slavnov-Taylor (ST) identity of the Einstein-Hilbert action coupled to a single inflaton field is obtained from the Becchi-Rouet-Stora-Tyutin (BRST) symmetry associated with diffeomorphism invariance in the Arnowitt-Deser-Misner (ADM) formalism. The consistency conditions between the correlators of the scalar and tensor modes in the squeezed limit are then derived from the ST identity, together with the softly broken conformal symmetry. Maldacena's original relations connecting the 2- and 3-point correlators at horizon crossing are recovered, as well as the next-to-leading corrections, controlled by the special conformal transformations.Comment: 38 pages, no figures. Corrected an error in the bispectrum relations, so that original Maldacena's results are now recovered. Added new sections on the extended discussions of the in-in formalism in the BRST approach and higher order corrections in the squeezed limit (special conformal transformations). Revised version accepted for publication in JCA

Off-shell renormalization in Higgs effective field theories

The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential $\sim\left(\Phi^\dagger\Phi-\frac{v^2}2\right)^N$ 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 $N\to\infty$ case.Comment: 33 pages, no figures. v3: complete one-loop off-shell renormalization for a BSM potential involving arbitrary powers of $\left(\phi^\dagger\phi-\frac{v^2}2\right)$ presented; Higgs wavefunction renormalization shown to be SM like; renormalization of the complete set of Higgs self-coupling in the $N\to\infty$ case discussed. v3 matches the published on