scholarly journals Background field method and generalized field redefinitions in effective field theories

2021 ◽  
Vol 136 (6) ◽  
Author(s):  
A. Quadri
Keyword(s):  
Effective Field Theories ◽  
Background Field ◽  
Field Method ◽  
Effective Field ◽  
Field Theories ◽  
Background Field Method

scholarly journals Consistent higher order $$ \sigma \left(\mathcal{GG}\to h\right) $$, $$ \Gamma \left(h\to \mathcal{GG}\right) $$ and Γ(h → γγ) in geoSMEFT

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Tyler Corbett ◽  
Adam Martin ◽  
Michael Trott
Keyword(s):  
Background Field ◽  
Field Method ◽  
Effective Field ◽  
Leading Order ◽  
The Standard Model ◽  
Gauge Fixing ◽  
Complete Set ◽  
Background Field Method ◽  
The One ◽  
Geometric Formulation

Abstract We report consistent results for Γ(h → γγ), $$ \sigma \left(\mathcal{GG}\to h\right) $$ σ GG → h and $$ \Gamma \left(h\to \mathcal{GG}\right) $$ Γ h → GG in the Standard Model Effective Field Theory (SMEFT) perturbing the SM by corrections $$ \mathcal{O}\left({\overline{\upsilon}}_T^2/16{\pi}^2{\Lambda}^2\right) $$ O υ ¯ T 2 / 16 π 2 Λ 2 in the Background Field Method (BFM) approach to gauge fixing, and to $$ \mathcal{O}\left({\overline{\upsilon}}_T^4/{\Lambda}^4\right) $$ O υ ¯ T 4 / Λ 4 using the geometric formulation of the SMEFT. We combine and modify recent results in the literature into a complete set of consistent results, uniforming conventions, and simultaneously complete the one loop results for these processes in the BFM. We emphasize calculational scheme dependence present across these processes, and how the operator and loop expansions are not independent beyond leading order. We illustrate several cross checks of consistency in the results.

scholarly journals The Feynman rules for the SMEFT in the background field gauge

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tyler Corbett
Keyword(s):  
Background Field ◽  
Field Method ◽  
Effective Field ◽  
Ward Identities ◽  
The Standard Model ◽  
Gauge Fixing ◽  
Feynman Rules ◽  
Supplementary Material ◽  
Background Field Method ◽  
Mass Terms

Abstract We present a package for FeynRules which derives the Feynman rules for the Standard Model Effective Field Theory up to dimension-six using the background field method for gauge fixing. The package includes operators which shift the kinetic and mass terms of the Lagrangian up to dimension-eight and including dimension-six squared effects consistently. To the best of the author’s knowledge this is the first publicly available package to include dimension-six squared effects consistently. The package is validated in a partner publication by analyzing the Ward Identities at dimension-six and one-loop order. We also extend the partner work in this article by including the dimension-six squared effects further demonstrating the consistency of their implementation. In doing so we find that failure to consistently include field shifts to dimension-six squared causes a breakdown in the Ward identities implying concerns about many calculations in the literature which do not properly incorporate these effects.The FeynRules files, as well as Mathematica notebooks performing the relevant calculations, can be downloaded from the FeynRules website and are included as supplementary material to this publication.

scholarly journals Topological terms and anomaly matching in effective field theories on ℝ3 × 𝕊1. Part I. Abelian symmetries and intermediate scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Erich Poppitz ◽  
F. David Wandler
Keyword(s):  
Effective Field Theories ◽  
Gauge Theories ◽  
Background Field ◽  
Effective Field ◽  
Field Theories ◽  
Global Symmetry ◽  
Dirac Fermions ◽  
Yang Mills ◽  
Local Background ◽  
Weyl Fermion

Abstract We explicitly calculate the topological terms that arise in IR effective field theories for SU(N) gauge theories on ℝ3 × 𝕊1 by integrating out all but the lightest modes. We then show how these terms match all global-symmetry ’t Hooft anomalies of the UV description. We limit our discussion to theories with abelian 0-form symmetries, namely those with one flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions. While anomaly matching holds as required, it takes a different form than previously thought. For example, cubic- and mixed-U(1) anomalies are matched by local background-field-dependent topological terms (background TQFTs) instead of chirallagrangian Wess-Zumino terms. We also describe the coupling of 0-form and 1-form symmetry backgrounds in the magnetic dual of super-Yang-Mills theory in a novel way, valid throughout the RG flow and consistent with the monopole-instanton ’t Hooft vertices. We use it to discuss the matching of the mixed chiral-center anomaly in the magnetic dual.

scholarly journals THE ULTRAVIOLET PROPERTIES OF SUPERSYMMETRIC FIELD THEORIES

1989 ◽  
Vol 04 (08) ◽  
pp. 1871-1912 ◽  
Author(s):  
P. S. HOWE ◽  
K. S. STELLE
Keyword(s):  
Perturbation Theory ◽  
Higher Dimensions ◽  
Background Field ◽  
Field Method ◽  
Field Theories ◽  
Ultraviolet Divergence ◽  
Two Dimensional ◽  
Yang Mills ◽  
Supersymmetric Field Theories ◽  
Background Field Method

We review the structure of ultraviolet divergence cancellations in supersymmetric field theories. We discuss the various nonrenormalization theorems of superspace perturbation theory, both for extended and for simple supersymmetry. These theorems and the background field method are applied to super Yang-Mills theories in four and higher dimensions, to supergravity theories and to two-dimensional supersymmetric nonlinear σ-models.

scholarly journals Exceptional nonrelativistic effective field theories with enhanced symmetries

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Tomáš Brauner
Keyword(s):  
Effective Field Theories ◽  
Explicit Construction ◽  
Effective Field ◽  
Field Theories ◽  
Relativistic Case ◽  
Starting Point ◽  
Higher Power ◽  
Mere Presence ◽  
Spatial Rotations

Abstract We initiate the classification of nonrelativistic effective field theories (EFTs) for Nambu-Goldstone (NG) bosons, possessing a set of redundant, coordinate-dependent symmetries. Similarly to the relativistic case, such EFTs are natural candidates for “exceptional” theories, whose scattering amplitudes feature an enhanced soft limit, that is, scale with a higher power of momentum at long wavelengths than expected based on the mere presence of Adler’s zero. The starting point of our framework is the assumption of invariance under spacetime translations and spatial rotations. The setup is nevertheless general enough to accommodate a variety of nontrivial kinematical algebras, including the Poincaré, Galilei (or Bargmann) and Carroll algebras. Our main result is an explicit construction of the nonrelativistic versions of two infinite classes of exceptional theories: the multi-Galileon and the multi-flavor Dirac-Born-Infeld (DBI) theories. In both cases, we uncover novel Wess-Zumino terms, not present in their relativistic counterparts, realizing nontrivially the shift symmetries acting on the NG fields. We demonstrate how the symmetries of the Galileon and DBI theories can be made compatible with a nonrelativistic, quadratic dispersion relation of (some of) the NG modes.

scholarly journals Background field method in thermo field dynamics for wave propagation in unmagnetized spinor QED plasmas

2020 ◽  
Vol 27 (11) ◽  
pp. 112104
Author(s):  
Shan Wu ◽  
Ji-ying Zhang
Keyword(s):  
Wave Propagation ◽  
Background Field ◽  
Field Method ◽  
Thermo Field Dynamics ◽  
Background Field Method

scholarly journals The Swampland Conjectures: A Bridge from Quantum Gravity to Particle Physics

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 273
Author(s):  
Mariana Graña ◽  
Alvaro Herráez
Keyword(s):  
Effective Field Theories ◽  
Quantum Gravity ◽  
Particle Physics ◽  
Effective Field ◽  
Low Energy ◽  
Field Theories ◽  
Neutrino Masses ◽  
Higgs Potential ◽  
Photon Mass ◽  
Effective Theories

The swampland is the set of seemingly consistent low-energy effective field theories that cannot be consistently coupled to quantum gravity. In this review we cover some of the conjectural properties that effective theories should possess in order not to fall in the swampland, and we give an overview of their main applications to particle physics. The latter include predictions on neutrino masses, bounds on the cosmological constant, the electroweak and QCD scales, the photon mass, the Higgs potential and some insights about supersymmetry.

scholarly journals A note on gauge anomaly cancellation in effective field theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ferruccio Feruglio
Keyword(s):  
Effective Field Theories ◽  
Effective Field ◽  
Field Theories ◽  
Anomaly Cancellation ◽  
Charge Assignment ◽  
The Standard Model ◽  
Renormalizable Theory ◽  
Complete Set ◽  
Gauge Anomalies ◽  
Gauge Anomaly

Abstract The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.

scholarly journals NONCOMMUTATIVITY AND NON-ANTICOMMUTATIVITY PERTURBATIVE QUANTUM GRAVITY

2012 ◽  
Vol 27 (13) ◽  
pp. 1250075 ◽  
Author(s):  
MIR FAIZAL
Keyword(s):  
Quantum Gravity ◽  
Lagrangian Density ◽  
Background Field ◽  
Field Method ◽  
Gauge Fixing ◽  
Perturbative Quantum ◽  
Background Field Method

In this paper, we will study perturbative quantum gravity on supermanifolds with both noncommutativity and non-anticommutativity of spacetime coordinates. We shall first analyze the BRST and the anti-BRST symmetries of this theory. Then we will also analyze the effect of shifting all the fields of this theory in background field method. We will construct a Lagrangian density which apart from being invariant under the extended BRST transformations is also invariant under on-shell extended anti-BRST transformations. This will be done by using the Batalin–Vilkovisky (BV) formalism. Finally, we will show that the sum of the gauge-fixing term and the ghost term for this theory can be elegantly written down in superspace with a two Grassmann parameter.

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