Asymptotic dynamics on the worldline for spinning particles

Abstract There has been a renewed interest in the description of dressed asymptotic states à la Faddeev-Kulish. In this regard, a worldline representation for asymptotic states dressed by radiation at subleading power in the soft expansion, known as the Generalized Wilson Line (GWL) in the literature, has been available for some time, and it recently found applications in the derivation of factorization theorems for scattering processes of phenomenological relevance. In this paper we revisit the derivation of the GWL in the light of the well-known supersymmetric wordline formalism for the relativistic spinning particle. In particular, we discuss the importance of wordline supersymmetry to understand the contribution of the soft background field to the asymptotic dynamics. We also provide a derivation of the GWL for the gluon case, which was not previously available in the literature, thus extending the exponentiation of next-to-soft gauge boson corrections to Yang-Mills theory. Finally, we comment about possible applications in the current research about asymptotic states in scattering amplitudes for gauge and gravity theories and their classical limit.

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Yang-Mills observables: from KMOC to eikonal through EFT

Journal of High Energy Physics ◽

10.1007/jhep01(2022)045 ◽

2022 ◽

Vol 2022 (1) ◽

Author(s):

Leonardo de la Cruz ◽

Andres Luna ◽

Trevor Scheopner

Keyword(s):

Field Theory ◽

Scattering Amplitudes ◽

Effective Field Theory ◽

Effective Field ◽

Direct Integration ◽

Spinning Particles ◽

Yang Mills ◽

Domain Of Applicability

Abstract We obtain a conservative Hamiltonian describing the interactions of two charged bodies in Yang-Mills through $$ \mathcal{O}\left({\alpha}^2\right) $$ O α 2 and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory (EFT) to consider color-charged objects. These results are checked against the direct integration of the observables in the Kosower-Maybee-O’Connell (KMOC) formalism. At the order we consider we find that the linear and color impulses in a scattering event can be concisely described in terms of the eikonal phase, thus extending the domain of applicability of a formula originally proposed in the context of spinning particles.

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Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

Canadian Journal of Physics ◽

10.1139/p95-048 ◽

1995 ◽

Vol 73 (5-6) ◽

pp. 344-348 ◽

Cited By ~ 2

Author(s):

Yeong-Chuan Kao ◽

Hsiang-Nan Li

Keyword(s):

Effective Action ◽

Background Field ◽

Landau Gauge ◽

Quantum Corrections ◽

Simons Theory ◽

Loop Correction ◽

Loop Contribution ◽

Yang Mills ◽

Chern Simons ◽

Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

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Algebraic singularities of scattering amplitudes from tropical geometry

Journal of High Energy Physics ◽

10.1007/jhep04(2021)002 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

James Drummond ◽

Jack Foster ◽

Ömer Gürdoğan ◽

Chrysostomos Kalousios

Keyword(s):

Scattering Amplitudes ◽

Natural Language ◽

Tropical Geometry ◽

Cluster Algebras ◽

Finite Alphabet ◽

Square Root ◽

Finite Sets ◽

Yang Mills ◽

Square Roots ◽

Algebraic Singularities

Abstract We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

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Nonrelativistic near-BPS corners of $$ \mathcal{N} $$ = 4 super-Yang-Mills with SU(1, 1) symmetry

Journal of High Energy Physics ◽

10.1007/jhep02(2021)188 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Stefano Baiguera ◽

Troels Harmark ◽

Nico Wintergerst

Keyword(s):

Classical Limit ◽

Particle Number ◽

Matrix Theory ◽

Companion Paper ◽

Positive Definite ◽

Normal Ordering ◽

Yang Mills ◽

Three Sphere ◽

Dilatation Operator ◽

Definite Expressions

Abstract We consider limits of $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM) theory that approach BPS bounds and for which an SU(1,1) structure is preserved. The resulting near-BPS theories become non-relativistic, with a U(1) symmetry emerging in the limit that implies the conservation of particle number. They are obtained by reducing $$ \mathcal{N} $$ N = 4 SYM on a three-sphere and subsequently integrating out fields that become non-dynamical as the bounds are approached. Upon quantization, and taking into account normal-ordering, they are consistent with taking the appropriate limits of the dilatation operator directly, thereby corresponding to Spin Matrix theories, found previously in the literature. In the particular case of the SU(1,1—1) near-BPS/Spin Matrix theory, we find a superfield formulation that applies to the full interacting theory. Moreover, for all the theories we find tantalizingly simple semi-local formulations as theories living on a circle. Finally, we find positive-definite expressions for the interactions in the classical limit for all the theories, which can be used to explore their strong coupling limits. This paper will have a companion paper in which we explore BPS bounds for which a SU(2,1) structure is preserved.

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Holographic entanglement entropy of the Coulomb branch

Journal of High Energy Physics ◽

10.1007/jhep04(2021)153 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Adam Chalabi ◽

S. Prem Kumar ◽

Andy O’Bannon ◽

Anton Pribytok ◽

Ronnie Rodgers ◽

...

Keyword(s):

W Boson ◽

Wilson Line ◽

Entanglement Entropy ◽

Physical Principle ◽

Boson Mass ◽

Extremal Black Hole ◽

Energy Tensor ◽

Large Radius ◽

Coulomb Branch ◽

Yang Mills

Abstract We compute entanglement entropy (EE) of a spherical region in (3 + 1)-dimensional $$ \mathcal{N} $$ N = 4 supersymmetric SU(N) Yang-Mills theory in states described holographically by probe D3-branes in AdS5 × S5. We do so by generalising methods for computing EE from a probe brane action without having to determine the probe’s backreaction. On the Coulomb branch with SU(N) broken to SU(N − 1) × U(1), we find the EE monotonically decreases as the sphere’s radius increases, consistent with the a-theorem. The EE of a symmetric-representation Wilson line screened in SU(N − 1) also monotonically decreases, although no known physical principle requires this. A spherical soliton separating SU(N) inside from SU(N − 1) × U(1) outside had been proposed to model an extremal black hole. However, we find the EE of a sphere at the soliton’s radius does not scale with the surface area. For both the screened Wilson line and soliton, the EE at large radius is described by a position-dependent W-boson mass as a short-distance cutoff. Our holographic results for EE and one-point functions of the Lagrangian and stress-energy tensor show that at large distance the soliton looks like a Wilson line in a direct product of fundamental representations.

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Two-loop rational terms in Yang-Mills theories

Journal of High Energy Physics ◽

10.1007/jhep10(2020)016 ◽

2020 ◽

Vol 2020 (10) ◽

Author(s):

Jean-Nicolas Lang ◽

Stefano Pozzorini ◽

Hantian Zhang ◽

Max F. Zoller

Keyword(s):

Scattering Amplitudes ◽

Gauge Theories ◽

A Posteriori ◽

Four Dimensions ◽

Yang Mills ◽

General Properties ◽

Finite Set ◽

Numerical Tools ◽

Loop Amplitudes

Abstract Scattering amplitudes in D dimensions involve particular terms that originate from the interplay of UV poles with the (D − 4)-dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [1] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the (D−4)-dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to nf fermions with arbitrary masses.

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Celestial superamplitude in $$ \mathcal{N} $$ = 4 SYM theory

Journal of High Energy Physics ◽

10.1007/jhep08(2021)031 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Hongliang Jiang

Keyword(s):

Field Theory ◽

Conformal Field Theory ◽

Scattering Amplitudes ◽

Momentum Space ◽

Ward Identity ◽

Yang Mills ◽

Conformal Field ◽

New Perspective ◽

Celestial Sphere

Abstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $$ \mathcal{N} $$ N = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $$ \mathcal{N} $$ N = 4 SYM amplitudes via 2D celestial conformal field theory.

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SPINNING PARTICLES ON SPACELIKE HYPERSURFACES AND THEIR REST FRAME DESCRIPTION

International Journal of Modern Physics A ◽

10.1142/s0217751x99000749 ◽

1999 ◽

Vol 14 (09) ◽

pp. 1429-1484 ◽

Cited By ~ 16

Author(s):

FRANCESCO BIGAZZI ◽

LUCA LUSANNA

Keyword(s):

Spin Structure ◽

Rest Frame ◽

Negative Energy ◽

Nonrelativistic Limit ◽

Critical Discussion ◽

Positive Energy ◽

Spinning Particle ◽

Spinning Particles ◽

Spacelike Hypersurfaces ◽

Energy Formula

A new spinning particle with a definite sign of the energy is defined on spacelike hypersurfaces after a critical discussion of the standard spinning particles. It is the pseudoclassical basis of the positive energy [Formula: see text] [or negative energy [Formula: see text]] part of the [Formula: see text] solutions of the Dirac equation. The study of the isolated system of N such spinning charged particles plus the electromagnetic field leads to their description in the rest frame Wigner-covariant instant form of dynamics on the Wigner hyperplanes orthogonal to the total four-momentum of the isolated system (when it is timelike). We find that on such hyperplanes these spinning particles have a nonminimal coupling only of the type "spin–magnetic field," like the nonrelativistic Pauli particles to which they tend in the nonrelativistic limit. The Lienard–Wiechert potentials associated with these charged spinning particles are found. Then, a comment is made on how to quantize the spinning particles respecting their fibered structure describing the spin structure.

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