Conformal kernel for the next-to-leading-order BFKL equation inN=4super Yang-Mills theory

The physics of meron pairs is considered in this series of papers. The first paper presents the motivation for focussing on this particular type of field configuration as an important degree of freedom in the SU(N) Yang–Mills theory. It also outlines the formalism for doing a saddle point expansion of path integrals about configurations which are constrained minima of the action (such as meron pairs) as opposed to local minima (such as instantons). The formalism is illustrated by the treatment of an ordinary integral which is analogous to the meron pair region of the Yang–Mills path integral. It is found that the expansion about constrained minima depends to leading order on the constraints chosen to partition the integral. This means that some criteria must be found for the choice of constraints. This problem is discussed. The actual meron pair calculations are partially described here and done in the second and third papers. Applications are to be considered in any subsequent papers.

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Gauge copies and the fate of background independence in Yang-Mills theories: A leading order analysis

Physical Review D ◽

10.1103/physrevd.102.074029 ◽

2020 ◽

Vol 102 (7) ◽

Author(s):

O. C. Junqueira ◽

I. F. Justo ◽

D. S. Montes ◽

A. D. Pereira ◽

R. F. Sobreiro

Keyword(s):

Leading Order ◽

Yang Mills ◽

Background Independence ◽

Order Analysis

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Holographic baryons and instanton crystals

Modern Physics Letters B ◽

10.1142/s0217984915400527 ◽

2015 ◽

Vol 29 (16) ◽

pp. 1540052 ◽

Cited By ~ 13

Author(s):

Vadim Kaplunovsky ◽

Dmitry Melnikov ◽

Jacob Sonnenschein

Keyword(s):

Gauge Fields ◽

Leading Order ◽

Abelian Gauge ◽

Yang Mills ◽

World Volume ◽

Dense Nuclear Matter ◽

The World ◽

The One ◽

Holographic Description ◽

Matter Phase

In a wide class of holographic models, like the one proposed by Sakai and Sugimoto, baryons can be approximated by instantons of non-Abelian gauge fields that live on the world-volume of flavor D-branes. In the leading order, those are just the Yang–Mills instantons, whose solutions can be constructed from the celebrated Atiyah–Drinfeld–Hitchin–Manin (ADHM) construction. This fact can be used to study various properties of baryons in the holographic limit. In particular, one can attempt to construct a holographic description of the cold dense nuclear matter phase of baryons. It can be argued that holographic baryons in such a regime are necessarily in a solid crystalline phase. In this review, we summarize the known results on the construction and phases of crystals of the holographic baryons.

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Integrability in Yang-Mills Theory on the Light Cone Beyond Leading Order

Physical Review Letters ◽

10.1103/physrevlett.94.151603 ◽

2005 ◽

Vol 94 (15) ◽

Cited By ~ 21

Author(s):

A. V. Belitsky ◽

G. P. Korchemsky ◽

D. Müller

Keyword(s):

Light Cone ◽

Leading Order ◽

Yang Mills

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SOLUTION OF THE NEXT-TO-LEADING ORDER BFKL EQUATION

International Journal of Modern Physics Conference Series ◽

10.1142/s201019451460026x ◽

2014 ◽

Vol 25 ◽

pp. 1460026

Author(s):

GIOVANNI ANTONIO CHIRILLI

Keyword(s):

Perturbative Expansion ◽

Bfkl Equation ◽

Leading Order

The solution of the next-to-leading order BFKL equation is obtained by constructing the eigenfunctions as a perturbative expansion of the conforma leading order conformal eigenfunctions.

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Residues, modularity, and the Cardy limit of the 4d $$ \mathcal{N} $$ = 4 superconformal index

Journal of High Energy Physics ◽

10.1007/jhep04(2021)216 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Kevin Goldstein ◽

Vishnu Jejjala ◽

Yang Lei ◽

Sam van Leuven ◽

Wei Li

Keyword(s):

Black Hole ◽

Chemical Potential ◽

Specific Region ◽

Partition Functions ◽

Potential Space ◽

Leading Order ◽

Yang Mills ◽

Superconformal Index ◽

Chemical Potentials ◽

Entropy Functions

Abstract We compute the superconformal index of the $$ \mathcal{N} $$ N = 4 SU(N) Yang-Mills theory through a residue calculation. The method is similar in spirit to the Bethe Ansatz formalism, except that all poles are explicitly known, and we do not require specialization of any of the chemical potentials. Our expression for the index allows us to revisit the Cardy limit using modular properties of four-dimensional supersymmetric partition functions. We find that all residues contribute at leading order in the Cardy limit. In a specific region of flavour chemical potential space, close to the two unrefined points, in fact all residues contribute universally. These universal residues precisely agree with the entropy functions of the asymptotically AdS5 black hole and its “twin saddle” respectively. Finally, we discuss how our formula is suited to study the implications of four-dimensional modularity for the index beyond the Cardy limit.

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First saturation correction in high energy proton-nucleus collisions. Part I. Time evolution of classical Yang-Mills fields beyond leading order

Journal of High Energy Physics ◽

10.1007/jhep06(2021)140 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Ming Li ◽

Vladimir V. Skokov

Keyword(s):

High Energy ◽

Analytic Solutions ◽

Effective Theory ◽

Color Glass ◽

Leading Order ◽

Color Charge ◽

High Energy Proton ◽

Yang Mills ◽

Energy Proton ◽

Transverse Area

Abstract In high energy proton-nucleus collisions, the single- and double-inclusive soft gluon productions at the leading order have been calculated and phenomenologically studied in various approaches for many years. These studies do not take into account the saturation and multiple rescatterings in the field of the proton. The first saturation correction to these leading order results (the terms that are enhanced by the combination $$ {\alpha}_s^2{\mu}^2 $$ α s 2 μ 2 , where μ2 is the proton’s color charge squared per unit transverse area) has not been completely derived despite recent attempts using a diagrammatic approach. This paper is the first in a series of papers towards analytically completing the first saturation correction to physical observables in high energy proton-nucleus collisions. Our approach is to analytically solve the classical Yang-Mills equations in the dilute-dense regime using the Color Glass Condensate effective theory and compute physical observables constructed from classical gluon fields. In the current paper, the Yang-Mills equations are solved perturbatively in the field of the dilute object (the proton). Next-to-leading order and next-to-next-to-leading order analytic solutions are explicitly constructed. A systematic way to obtain all higher order analytic solutions is outlined.

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Center-symmetric effective theory for two-color quark matter

Open Physics ◽

10.2478/s11534-012-0045-8 ◽

2012 ◽

Vol 10 (6) ◽

Author(s):

Tomáš Brauner

Keyword(s):

Order Parameter ◽

Large Scale ◽

Chemical Potential ◽

Three Dimensional ◽

Polyakov Loop ◽

Effective Theory ◽

Leading Order ◽

Baryon Chemical Potential ◽

Yang Mills ◽

Model Independent

AbstractWe revisit the center-symmetric dimensionally reduced effective theory for two-color Yang-Mills theory at high temperature. This effective theory includes an order parameter for deconfinement and thus allows to broaden the range of validity of the conventional three-dimensional effective theory (EQCD) towards the confining phase transition. We extend the previous results by including the effects of massive quarks with nonzero baryon chemical potential. The parameter space of the theory is constrained by leading-order matching to the Polyakov loop effective potential of two-color QCD. Once all the parameters are fixed, the effective theory can provide model-independent predictions for the physics above the deconfinement transition, thus bridging the gap between large-scale numerical simulations and semi-analytical calculations within phenomenological models.

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Real Valued Functions for the BFKL Eigenvalue

Universe ◽

10.3390/universe7110444 ◽

2021 ◽

Vol 7 (11) ◽

pp. 444

Author(s):

Mohammad Joubat ◽

Alex Prygarin

Keyword(s):

Perturbation Theory ◽

Bfkl Equation ◽

Complex Conjugate ◽

Yang Mills ◽

General Space ◽

Function Of Two Variables ◽

Super Yang Mills Theory

We consider known expressions for the eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in N=4 super Yang-Mills theory as a real valued function of two variables. We define new real valued functions of two complex conjugate variables that have a definite complexity analogous to the weight of the nested harmonic sums. We argue that those functions span a general space of functions for the BFKL eigenvalue at any order of the perturbation theory.

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Classical Yang-Mills observables from amplitudes

Journal of High Energy Physics ◽

10.1007/jhep12(2020)076 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Leonardo de la Cruz ◽

Ben Maybee ◽

Donal O’Connell ◽

Alasdair Ross

Keyword(s):

General Relativity ◽

Body Problem ◽

Equations Of Motion ◽

Colour Change ◽

Classical Dynamics ◽

Particle Scattering ◽

Leading Order ◽

Yang Mills ◽

Two Body Problem ◽

Double Copy

Abstract The double copy suggests that the basis of the dynamics of general relativity is Yang-Mills theory. Motivated by the importance of the relativistic two-body problem, we study the classical dynamics of colour-charged particle scattering from the perspective of amplitudes, rather than equations of motion. We explain how to compute the change of colour, and the radiation of colour, during a classical collision. We apply our formalism at next-to-leading order for the colour change and at leading order for colour radiation.

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