scholarly journals Loop amplitudes monodromy relations and color-kinematics duality

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Eduardo Casali ◽  
Sebastian Mizera ◽  
Piotr Tourkine
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Gauge Theory ◽  
Tree Level ◽  
First Principle ◽  
Loop Momentum ◽  
New Developments ◽  
Feynman Graphs ◽  
Definition Of ◽  
Double Copy

Abstract Color-kinematics duality is a remarkable conjectured property of gauge theory which, together with double copy, is at the heart of a wealth of new developments in scattering amplitudes. So far, its validity has been verified in most cases only empirically, with limited ab initio understanding beyond tree-level. In this paper we provide initial steps in a first-principle understanding of color-kinematics duality and double-copy at loop level, through a detailed analysis of the field-theory limit of the monodromy relations of string theory at one loop. In this limit, we dissect the type of Feynman graphs generated and the relations they obey. We find that graphs with contact-terms are unavoidable and are generated in the field theory limit of “bulk” contours which do not have a standard physical interpretation in string perturbation theory. We show how they are related to ambiguities in the definition of the loop momentum and that their role is precisely to cancel those ambiguities.

scholarly journals Construction of lattice Möbius domain wall fermions in the Schrödinger functional scheme

2018 ◽  
Vol 33 (01) ◽  
pp. 1850012
Author(s):  
Yuko Murakami ◽  
Ken-Ichi Ishikawa
Keyword(s):  
Perturbation Theory ◽  
Gauge Theory ◽  
Domain Wall ◽  
Beta Function ◽  
Boundary Operator ◽  
Tree Level ◽  
Domain Wall Fermions ◽  
Functional Scheme ◽  
Temporal Boundary ◽  
Optimal Type

In this paper, we construct the Möbius domain wall fermions (MDWFs) in the Schrödinger functional (SF) scheme for the SU(3) gauge theory by adding a boundary operator at the temporal boundary of the SF scheme setup. Using perturbation theory, we investigate the properties of several constructed MDWFs, including the optimal type domain wall, overlap, truncated domain wall, and truncated overlap fermions. We observe the universality of the spectrum of the effective four-dimensional operator at the tree-level, and fermionic contribution to the universal one-loop beta function is reproduced for MDWFs with a sufficiently large fifth-dimensional extent.

scholarly journals Composing effective prediction at five points

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
John Joseph M. Carrasco ◽  
Laurentiu Rodina ◽  
Suna Zekioğlu
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitude ◽  
Building Blocks ◽  
Tree Level ◽  
Critical Aspect ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Single Trace ◽  
The Relationship ◽  
Double Copy

Abstract Color-kinematics duality in the adjoint has proven key to the relationship between gauge and gravity theory scattering amplitude predictions. In recent work, we demonstrated that at four-point tree-level, a small number of color-dual EFT building blocks could encode all higher-derivative single-trace massless corrections to gauge and gravity theories compatible with adjoint double-copy. One critical aspect was the trivialization of building higher-derivative color-weights — indeed, it is the mixing of kinematics with non-adjoint-type color-weights (like the permutation-invariant d4) which permits description via adjoint double-copy. Here we find that such ideas clarify the predictions of local five-point higher-dimensional operators as well. We demonstrate how a single scalar building block can be combined with color structures to build higher-derivative color factors that generate, through double copy, the amplitudes associated with higher-derivative gauge-theory operators. These may then be suitably mapped, through another double-copy, to higher-derivative corrections in gravity.

scholarly journals Mellin amplitudes for 1d CFT

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Lorenzo Bianchi ◽  
Gabriel Bliard ◽  
Valentina Forini ◽  
Giulia Peveri
Keyword(s):  
Field Theory ◽  
Mellin Transform ◽  
Free Field ◽  
Closed Form Expression ◽  
Tree Level ◽  
Analytical Properties ◽  
Single Complex ◽  
Definition Of ◽  
Infinite Set ◽  
Scaling Dimension

Abstract We define a Mellin amplitude for CFT1 four-point functions. Its analytical properties are inferred from physical requirements on the correlator. We discuss the analytic continuation that is necessary for a fully nonperturbative definition of the Mellin transform. The resulting bounded, meromorphic function of a single complex variable is used to derive an infinite set of nonperturbative sum rules for CFT data of exchanged operators, which we test on known examples. We then consider the perturbative setup produced by quartic interactions with an arbitrary number of derivatives in a bulk AdS2 field theory. With our formalism, we obtain a closed-form expression for the Mellin transform of tree-level contact interactions and for the first correction to the scaling dimension of “two-particle” operators exchanged in the generalized free field theory correlator.

scholarly journals Classical and quantum double copy of back-reaction

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Tim Adamo ◽  
Anton Ilderton
Keyword(s):  
Quantum Theory ◽  
Gauge Theory ◽  
Plane Wave ◽  
Tree Level ◽  
Back Reaction ◽  
Quantum Double ◽  
Four Dimensions ◽  
Helicity Formalism ◽  
Massive Spinor ◽  
Double Copy

Abstract We consider radiation emitted by colour-charged and massive particles crossing strong plane wave backgrounds in gauge theory and gravity. These backgrounds are treated exactly and non-perturbatively throughout. We compute the back-reaction on these fields from the radiation emitted by the probe particles: classically through background-coupled worldline theories, and at tree-level in the quantum theory through three-point amplitudes. Consistency of these two methods is established explicitly. We show that the gauge theory and gravity amplitudes are related by the double copy for amplitudes on plane wave backgrounds. Finally, we demonstrate that in four-dimensions these calculations can be carried out with a background-dressed version of the massive spinor-helicity formalism.

scholarly journals UTILITY OF GALILEAN SYMMETRY IN LIGHT-FRONT PERTURBATION THEORY: A NONTRIVIAL EXAMPLE IN QCD

1998 ◽  
Vol 13 (26) ◽  
pp. 4591-4604 ◽  
Author(s):  
A. HARINDRANATH ◽  
RAJEN KUNDU
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Complex Structure ◽  
Light Front ◽  
Tree Level ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Two Component ◽  
Covariant Field ◽  
Galilean Symmetry

Investigations have revealed a very complex structure for the coefficient functions accompanying the divergences for individual time(x+)-ordered diagrams in light-front perturbation theory. No guidelines seem to be available to look for possible mistakes in the structure of these coefficient functions emerging at the end of a long and tedious calculation, in contrast to covariant field theory. Since, in light-front field theory, the transverse boost generator is a kinematical operator which acts just like the two-dimensional Galilean boost generator in nonrelativistic dynamics, it may provide some constraint on the resulting structures. In this work we investigate the utility of Galilean symmetry beyond tree level in the context of coupling constant renormalization in light-front QCD using the two-component formalism. We show that for each x+-ordered diagram separately, the underlying transverse boost symmetry fixes relative signs of terms in the coefficient functions accompanying the diverging logarithms. We also summarize the results leading to coupling constant renormalization for the most general kinematics.

scholarly journals Perturbative Gravity and Gauge Theory Relations: A Review

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Thomas Søndergaard
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
String Theory ◽  
Gauge Theories ◽  
Point Of View ◽  
Tree Level ◽  
General Properties ◽  
Recent Developments ◽  
Theory Point

This paper is dedicated to the amazing Kawai-Lewellen-Tye relations, connecting perturbative gravity and gauge theories at tree level. The main focus is onn-point derivations and general properties both from a string theory and pure field theory point of view. In particular, the field theory part is based on some very recent developments.

scholarly journals ASPECTS OF ANOMALIES IN FIELD THEORY

2001 ◽  
Vol 16 (03) ◽  
pp. 331-345 ◽  
Author(s):  
KAZUO FUJIKAWA
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Path Integral Formulation ◽  
Lattice Gauge ◽  
Soft Pion ◽  
Quantum Anomaly ◽  
Quantum Anomalies ◽  
True Quantum

We discuss some formal aspects of quantum anomalies with an emphasis on the regularization of field theory. We briefly review how ambiguities in perturbation theory have been resolved by various regularization schemes. To single out the true quantum anomaly among ambiguities, the combined ideas of PCAC, soft pion limit and renormalizability were essential. As for the formal treatment of quantum anomalies, we mainly discuss the path integral formulation both in continuum and lattice theories. In particular, we discuss in some detail the recent development in the treatment of chiral anomalies in lattice gauge theory.

scholarly journals The causal approach proof for the equivalence of SDKP4 and SQED4 at tree-level

2020 ◽  
Vol 35 (09) ◽  
pp. 2050042
Author(s):  
J. Beltrán ◽  
B. M. Pimentel ◽  
D. E. Soto
Keyword(s):  
Perturbation Theory ◽  
Gauge Theory ◽  
Cross Section ◽  
Quantum Electrodynamics ◽  
Electromagnetic Interaction ◽  
Tree Level ◽  
Alternative Formulation ◽  
Complete Proof ◽  
Scalar Quantum ◽  
Causal Approach

The description of the electromagnetic interaction of charged spinless particles is usually formulated by the Scalar Quantum Electrodynamics. However, there is an alternative formulation given by the Duffin–Kemmer–Petiau theory: the Scalar DKP gauge theory. The proof of the equivalence between these two formulations has been discussed in many researches, but there is not yet a conclusive proof. In this paper, we initiate a complete proof in the framework of the Causal Perturbation theory, showing that both scalar formulations provide the same results for the differential cross-section at tree level.

scholarly journals Nonlocal quantum field theory without acausality and nonunitarity at quantum level: Is SUSY the key?

2015 ◽  
Vol 30 (15) ◽  
pp. 1550103 ◽  
Author(s):  
Andrea Addazi ◽  
Giampiero Esposito
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
The Other ◽  
Tree Level ◽  
Quantum Field ◽  
Quantum Level ◽  
Fermionic Sector ◽  
Nonlocal Quantum ◽  
The One

The realization of a nonlocal quantum field theory without losing unitarity, gauge invariance and causality is investigated. It is commonly retained that such a formulation is possible at tree level, but at quantum level acausality is expected to reappear at one loop. We suggest that the problem of acausality is, in a broad sense, similar to the one about anomalies in quantum field theory. By virtue of this analogy, we suggest that acausal diagrams resulting from the fermionic sector and the bosonic one might cancel each other, with a suitable content of fields and suitable symmetries. As a simple example, we show how supersymmetry can alleviate this problem in a simple and elegant way, i.e. by leading to exact cancellations of harmful diagrams, to all orders of perturbation theory. An infinite number of divergent diagrams cancel each other by virtue of the nonrenormalization theorem of supersymmetry. However, supersymmetry is not enough to protect a theory from all acausal divergences. For instance, acausal contributions to supersymmetric corrections to D-terms are not protected by supersymmetry. On the other hand, we show in detail how supersymmetry also helps in dealing with D-terms: divergences are not canceled but they become softer than in the nonsupersymmetric case. The supergraphs' formalism turns out to be a powerful tool to reduce the complexity of perturbative calculations.

scholarly journals Propagators, BCFW recursion and new scattering equations at one loop

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Joseph A. Farrow ◽  
Yvonne Geyer ◽  
Arthur E. Lipstein ◽  
Ricardo Monteiro ◽  
Ricardo Stark-Muchão
Keyword(s):  
Gauge Theory ◽  
Tree Level ◽  
Loop Momentum ◽  
Planar Case ◽  
Linear Type ◽  
Recursion Relations ◽  
Loop Level ◽  
Alternative Approach ◽  
Forward Limit ◽  
Limit Procedure

Abstract We investigate how loop-level propagators arise from tree level via a forward-limit procedure in two modern approaches to scattering amplitudes, namely the BCFW recursion relations and the scattering equations formalism. In the first part of the paper, we revisit the BCFW construction of one-loop integrands in momentum space, using a convenient parametrisation of the D-dimensional loop momentum. We work out explicit examples with and without supersymmetry, and discuss the non-planar case in both gauge theory and gravity. In the second part of the paper, we study an alternative approach to one-loop integrands, where these are written as worldsheet formulas based on new one-loop scattering equations. These equations, which are inspired by BCFW, lead to standard Feynman-type propagators, instead of the ‘linear’-type loop-level propagators that first arose from the formalism of ambitwistor strings. We exploit the analogies between the two approaches, and present a proof of an all-multiplicity worldsheet formula using the BCFW recursion.

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