scholarly journals Cosmological Cutting Rules

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Scott Melville ◽  
Enrico Pajer
Keyword(s):  
Effective Field Theory ◽  
Effective Field ◽  
Field Theories ◽  
Tree Level ◽  
Optical Theorem ◽  
Loop Order ◽  
Founding Principle ◽  
Lower Loop ◽  
Infinite Set ◽  
The Universe

Abstract Primordial perturbations in our universe are believed to have a quantum origin, and can be described by the wavefunction of the universe (or equivalently, cosmological correlators). It follows that these observables must carry the imprint of the founding principle of quantum mechanics: unitary time evolution. Indeed, it was recently discovered that unitarity implies an infinite set of relations among tree-level wavefunction coefficients, dubbed the Cosmological Optical Theorem. Here, we show that unitarity leads to a systematic set of “Cosmological Cutting Rules” which constrain wavefunction coefficients for any number of fields and to any loop order. These rules fix the discontinuity of an n-loop diagram in terms of lower-loop diagrams and the discontinuity of tree-level diagrams in terms of tree-level diagrams with fewer external fields. Our results apply with remarkable generality, namely for arbitrary interactions of fields of any mass and any spin with a Bunch-Davies vacuum around a very general class of FLRW spacetimes. As an application, we show how one-loop corrections in the Effective Field Theory of inflation are fixed by tree-level calculations and discuss related perturbative unitarity bounds. These findings greatly extend the potential of using unitarity to bootstrap cosmological observables and to restrict the space of consistent effective field theories on curved spacetimes.

scholarly journals Optical theorem and indefinite metric in λϕ4 delta-theory

2020 ◽  
Vol 35 (33) ◽  
pp. 2050214
Author(s):  
Ricardo Avila ◽  
Carlos M. Reyes
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Coupling Parameter ◽  
Effective Field ◽  
Optical Theorem ◽  
Indefinite Metric ◽  
Quantum Field ◽  
Scalar Model ◽  
Loop Order ◽  
Interaction Term

A class of effective field theory called delta-theory, which improves ultraviolet divergences in quantum field theory, is considered. We focus on a scalar model with a quartic self-interaction term and construct the delta theory by applying the so-called delta prescription. We quantize the theory using field variables that diagonalize the Lagrangian, which include a standard scalar field and a ghost or negative norm state. As well known, the indefinite metric may lead to the loss of unitary of the [Formula: see text]-matrix. We study the optical theorem and check the validity of the cutting equations for three processes at one-loop order, and found suppressed violations of unitarity in the delta coupling parameter of the order of [Formula: see text].

scholarly journals Towards Feynman rules for conformal blocks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Hoback ◽  
Sarthak Parikh
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Hypergeometric Functions ◽  
Power Series Expansion ◽  
Effective Field ◽  
Conformal Block ◽  
Tree Level ◽  
Conformal Blocks ◽  
Simple Set ◽  
Feynman Rules

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

scholarly journals Cosmological phase transitions: is effective field theory just a toy?

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Marieke Postma ◽  
Graham White
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Phase Transitions ◽  
Effective Field Theory ◽  
New Physics ◽  
Effective Field ◽  
Tree Level ◽  
Dark Sector ◽  
First Order ◽  
First Order Phase

Abstract To obtain a first order phase transition requires large new physics corrections to the Standard Model (SM) Higgs potential. This implies that the scale of new physics is relatively low, raising the question whether an effective field theory (EFT) description can be used to analyse the phase transition in a (nearly) model-independent way. We show analytically and numerically that first order phase transitions in perturbative extensions of the SM cannot be described by the SM-EFT. The exception are Higgs-singlet extension with tree-level matching; but even in this case the SM-EFT can only capture part of the full parameter space, and if truncated at dim-6 operators, the description is at most qualitative. We also comment on the applicability of EFT techniques to dark sector phase transitions.

scholarly journals Effective field theory, past and future

2016 ◽  
Vol 31 (06) ◽  
pp. 1630007 ◽  
Author(s):  
Steven Weinberg
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Effective Field Theories ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Field Theories ◽  
Strong Interactions ◽  
The Standard Model ◽  
Theory Of Gravitation

I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.

scholarly journals Power counting and Wilsonian renormalization in nuclear effective field theory

2016 ◽  
Vol 25 (05) ◽  
pp. 1641007 ◽  
Author(s):  
Manuel Pavón Valderrama
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Nuclear Physics ◽  
High Energy ◽  
Effective Field ◽  
Power Counting ◽  
Low Energy ◽  
Field Theories ◽  
Nuclear Forces

Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.

scholarly journals CLOSED N=2 STRINGS: PICTURE-CHANGING, HIDDEN SYMMETRIES AND SDG HIERARCHY

2000 ◽  
Vol 15 (26) ◽  
pp. 4191-4236 ◽  
Author(s):  
OLAF LECHTENFELD ◽  
ALEXANDER D. POPOV
Keyword(s):  
Effective Field Theory ◽  
Dimensional Space ◽  
Effective Field ◽  
Spectral Flow ◽  
Hidden Symmetries ◽  
Commuting Flows ◽  
Brst Cohomology ◽  
Gravity Equations ◽  
Dimensional Space Time ◽  
Infinite Set

We study the action of picture-changing and spectral flow operators on a ground ring of ghost number zero operators in the chiral BRST cohomology of the closed N=2 string and describe an infinite set of symmetry charges acting on physical states. The transformations of physical string states are compared with symmetries of self-dual gravity which is the effective field theory of the closed N=2 string. We derive all infinitesimal symmetries of the self-dual gravity equations in (2+2)-dimensional space–time and introduce an infinite hierarchy of commuting flows on the moduli space of self-dual metrics. The dependence on moduli parameters can be recovered by solving the equations of the SDG hierarchy associated with an infinite set of Abelian symmetries generated recursively from translations. These nonlocal Abelian symmetries are shown to coincide with the hidden Abelian string symmetries responsible for the vanishing of most scattering amplitudes. Therefore, N=2 string theory "predicts" not only self-dual gravity but also the SDG hierarchy.

From infinities in quantum electrodynamics to the general renormalization group

2019 ◽  
pp. 53-68
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Effective Field Theory ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Essential Role ◽  
Effective Field ◽  
Fine Tuning ◽  
Field Theories ◽  
Higgs Particle ◽  
Renormalization Groups ◽  
Statistical Field

Chapter 4 describes a few important steps which have led from the discovery of infinities in quantum electrodynamics in the calculation of Feynman diagrams (ultraviolet divergences (UV divergences)) to the concept of renormalization and renormalization groups (RG). The constructions of quantum (or statistical) field theories (QFTs) and the deeply related RG have been some of the major theoretical achievements in physics of the last century. RG today plays an essential role in the understanding of the properties of QFT and of continuous macroscopic phase transitions. The existence of RG fixed points makes it possible to understand universality when there is no scale decoupling. In particle physics, it leads to the notion of effective field theory and the fine tuning problem in the Higgs particle sector.

HALO EFFECTIVE FIELD THEORY

2005 ◽  
Vol 14 (01) ◽  
pp. 11-19
Author(s):  
U. VAN KOLCK
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Bound States ◽  
Effective Field ◽  
Field Theories ◽  
Alpha Scattering

I discuss effective field theories for bound states and narrow resonances near two-body thresholds. I illustrate the method in the case of nucleon-alpha scattering.

scholarly journals Effective-field theories for charged lepton flavour violation

2018 ◽  
Vol 179 ◽  
pp. 01019
Author(s):  
Giovanni Marco Pruna
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Parameter Space ◽  
Effective Field Theory ◽  
Charged Lepton ◽  
Effective Field ◽  
Field Theories ◽  
The Status ◽  
Flavour Violation ◽  
Lepton Flavour

These proceedings review the status of present and future bounds on muonic lepton flavour violating transitions in the context of an effective-field theory defined below the electroweak scale. A specific focus is set on the phenomenology of μ → eγ, μ → 3e transitions and coherent μ → e nuclear conversion in the light of current and future experiments. Once the experimental limits are recast into bounds at higher scales, it is shown that the interplay between the various experiments is crucial to cover all corners of the parameter space.

THE HEART OF FACTORIZATION

2014 ◽  
Vol 25 ◽  
pp. 1460014
Author(s):  
MATTHEW D. SCHWARTZ
Keyword(s):  
Effective Field Theory ◽  
Recent Progress ◽  
Gauge Theories ◽  
Effective Field ◽  
Effective Theory ◽  
Tree Level ◽  
Soft Collinear Effective Theory ◽  
Factorization Formula ◽  
The Many ◽  
Traditional Approaches

Factorization is at the heart of nearly any calculation in pertubative QCD. It follows from the universal behavior of gauge theories in soft and collinear limits. This talk gives a summary of recent progress on producing a more transparent understanding of factorization and connecting traditional approaches to those of Soft-Collinear Effective Theory. The main result is the formulation and proof, at tree-level, of a factorization formula in QCD. The proof exploits the many advantages of spinor helicity methods, but does not use any effective field theory tricks. Once the factorization formula is proven, the transition to an effective theory description is effortless.

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