scholarly journals Direct evaluation of n-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY formalism

2016 ◽  
Vol 2016 (9) ◽  
Author(s):  
Yi-Jian Du ◽  
Fei Teng ◽  
Yong-Shi Wu
Keyword(s):  
Direct Evaluation ◽  
Yang Mills ◽  
Single Trace

scholarly journals Evaluating EYM amplitudes in four dimensions by refined graphic expansion

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hongxiang Tian ◽  
Enze Gong ◽  
Chongsi Xie ◽  
Yi-Jian Du
Keyword(s):  
Tree Level ◽  
Tree Amplitude ◽  
Four Dimensions ◽  
Yang Mills ◽  
Negative Helicity ◽  
Spanning Forests ◽  
Single Trace

Abstract The recursive expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes induces a refined graphic expansion, by which any tree-level EYM amplitude can be expressed as a summation over all possible refined graphs. Each graph contributes a unique coefficient as well as a proper combination of color-ordered Yang-Mills (YM) amplitudes. This expansion allows one to evaluate EYM amplitudes through YM amplitudes, the latter have much simpler structures in four dimensions than the former. In this paper, we classify the refined graphs for the expansion of EYM amplitudes into N k MHV sectors. Amplitudes in four dimensions, which involve k + 2 negative-helicity particles, at most get non-vanishing contribution from graphs in N k′ (k′ ≤ k) MHV sectors. By the help of this classification, we evaluate the non-vanishing amplitudes with two negative-helicity particles in four dimensions. We establish a correspondence between the refined graphs for single-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − or $$ \left({h}_i^{-},{g}_j^{-}\right) $$ h i − g j − configuration and the spanning forests of the known Hodges determinant form. Inspired by this correspondence, we further propose a symmetric formula of double-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − configuration. By analyzing the cancellation between refined graphs in four dimensions, we prove that any other tree amplitude with two negative-helicity particles has to vanish.

scholarly journals On topological recursion for Wilson loops in $$ \mathcal{N} $$ = 4 SYM at strong coupling

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
M. Beccaria ◽  
A. Hasan
Keyword(s):  
Strong Coupling ◽  
Matrix Model ◽  
Wilson Loops ◽  
Expectation Value ◽  
Yang Mills ◽  
Usual Procedure ◽  
Topological Recursion ◽  
Sample Application ◽  
Single Trace ◽  
Genus Expansion

Abstract We consider U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory and discuss how to extract the strong coupling limit of non-planar corrections to observables involving the $$ \frac{1}{2} $$ 1 2 -BPS Wilson loop. Our approach is based on a suitable saddle point treatment of the Eynard-Orantin topological recursion in the Gaussian matrix model. Working directly at strong coupling we avoid the usual procedure of first computing observables at finite planar coupling λ, order by order in 1/N, and then taking the λ ≫ 1 limit. In the proposed approach, matrix model multi-point resolvents take a simplified form and some structures of the genus expansion, hardly visible at low order, may be identified and rigorously proved. As a sample application, we consider the expectation value of multiple coincident circular supersymmetric Wilson loops as well as their correlator with single trace chiral operators. For these quantities we provide novel results about the structure of their genus expansion at large tension, generalising recent results in arXiv:2011.02885.

scholarly journals Single particle operators and their correlators in free $$ \mathcal{N} $$ = 4 SYM

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
F. Aprile ◽  
J. M. Drummond ◽  
P. Heslop ◽  
H. Paul ◽  
F. Sanfilippo ◽  
...  
Keyword(s):  
Single Particle ◽  
Operator Product ◽  
Point Function ◽  
Superstring Theory ◽  
Yang Mills ◽  
Free Theory ◽  
Explicit Formulae ◽  
Orthogonality Theorem ◽  
Single Trace ◽  
Bps States

Abstract We consider a set of half-BPS operators in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which are appropriate for describing single-particle states of superstring theory on AdS5× S5. These single-particle operators are defined to have vanishing two-point functions with all multi-trace operators and therefore correspond to admixtures of single- and multi-traces. We find explicit formulae for all single-particle operators and for their two-point function normalisation. We show that single-particle U(N) operators belong to the SU(N) subspace, thus for length greater than one they are simply the SU(N) single-particle operators. Then, we point out that at large N, as the length of the operator increases, the single-particle operator naturally interpolates between the single-trace and the S3 giant graviton. At finite N, the multi-particle basis, obtained by taking products of the single-particle operators, gives a new basis for all half-BPS states, and this new basis naturally cuts off when the length of any of the single-particle operators exceeds the number of colours. From the two-point function orthogonality we prove a multipoint orthogonality theorem which implies vanishing of all near-extremal correlators. We then compute all maximally and next-to-maximally extremal free correlators, and we discuss features of the correlators when the extremality is lowered. Finally, we describe a half-BPS projection of the operator product expansion on the multi-particle basis which provides an alternative construction of four- and higher-point functions in the free theory.

scholarly journals Towards the Virasoro-Shapiro amplitude in AdS5×S5

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Theresa Abl ◽  
Paul Heslop ◽  
Arthur E. Lipstein
Keyword(s):  
Effective Field Theory ◽  
Flat Space ◽  
Effective Field ◽  
Tree Level ◽  
Yang Mills ◽  
Additional Information ◽  
Tree Level Amplitude ◽  
Covariant Derivatives ◽  
Type Iib String Theory ◽  
Single Trace

Abstract We propose a systematic procedure for obtaining all single trace 1/2-BPS correlators in $$ \mathcal{N} $$ N = 4 super Yang-Mills corresponding to the four-point tree-level amplitude for type IIB string theory in AdS5 × S5. The underlying idea is to compute generalised contact Witten diagrams coming from a 10d effective field theory on AdS5 × S5 whose coefficients are fixed by the flat space Virasoro-Shapiro amplitude up to ambiguities related to commutators of the 10d covariant derivatives which require additional information such as localisation. We illustrate this procedure by computing stringy corrections to the supergravity prediction for all single trace 1/2-BPS correlators up to $$ \mathcal{O} $$ O (α′7), and spell out a general algorithm for extending this to any order in α′.

scholarly journals The worldsheet dual of free super Yang-Mills in 4D

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Matthias R. Gaberdiel ◽  
Rajesh Gopakumar
Keyword(s):  
String Theory ◽  
Sigma Model ◽  
Twistor Space ◽  
Free Field ◽  
Spectral Flow ◽  
Yang Mills ◽  
Finite Set ◽  
Single Trace ◽  
Covariant Version ◽  
Gauge Conditions

Abstract The worldsheet string theory dual to free 4d $$ \mathcal{N} $$ N = 4 super Yang-Mills theory was recently proposed in [1]. It is described by a free field sigma model on the twistor space of AdS5 × S5, and is a direct generalisation of the corresponding model for tensionless string theory on AdS3 × S3. As in the case of AdS3, the worldsheet theory contains spectrally flowed representations. We proposed in [1] that in each such sector only a finite set of generalised zero modes (‘wedge modes’) are physical. Here we show that after imposing the appropriate residual gauge conditions, this worldsheet description reproduces precisely the spectrum of the planar gauge theory. Specifically, the states in the sector with w units of spectral flow match with single trace operators built out of w super Yang-Mills fields (‘letters’). The resulting physical picture is a covariant version of the BMN light-cone string, now with a finite number of twistorial string bit constituents of an essentially topological worldsheet.

scholarly journals Higher-dimensional invariants in 6D super Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Serafim Buyucli ◽  
Evgeny Ivanov
Keyword(s):  
Loop Order ◽  
Harmonic Superspace ◽  
Gauge Sector ◽  
Yang Mills ◽  
Higher Dimensional ◽  
Dimensional Invariants ◽  
Single Trace ◽  
Canonical Dimension ◽  
Super Yang Mills Theory

Abstract We exploit the 6D,$$ \mathcal{N} $$ N = (1, 0) and $$ \mathcal{N} $$ N = (1, 1) harmonic superspace approaches to construct the full set of the maximally supersymmetric on-shell invariants of the canonical dimension d = 12 in 6D,$$ \mathcal{N} $$ N = (1, 1) supersymmetric Yang-Mills (SYM) theory. Both single- and double-trace invariants are derived. Only four single-trace and two double-trace invariants prove to be independent. The invariants constructed can provide the possible counterterms of $$ \mathcal{N} $$ N = (1, 1) SYM theory at four-loop order, where the first double-trace divergences are expected to appear. We explicitly exhibit the gauge sector of all invariants in terms of $$ \mathcal{N} $$ N = (1, 0) gauge superfields and find the absence of $$ \mathcal{N} $$ N = (1, 1) supercompletion of the F6 term in the abelian limit.

THE VANISHING β-FUNCTION OF N=4 SUPERSYMMETRIC YANG-MILLS THEORY

1982 ◽  
Vol 43 (C3) ◽  
pp. C3-326-C3-327
Author(s):  
K. S. Stelle
Keyword(s):  
Yang Mills ◽  
Β Function

Radiation in electrodynamics and in Yang–Mills theory

1992 ◽  
Vol 162 (2) ◽  
pp. 161 ◽  
Author(s):  
B.P. Kosyakov
Keyword(s):  
Yang Mills

Current uses of intracranial vessel wall imaging for clinical practice: a high-resolution MR technique recently available

2020 ◽  
Vol 78 (10) ◽  
pp. 642-650
Author(s):  
Felipe Torres PACHECO ◽  
Luiz Celso Hygino da CRUZ JUNIOR ◽  
Igor Gomes PADILHA ◽  
Renato Hoffmann NUNES ◽  
Antônio Carlos Martins MAIA JUNIOR ◽  
...  
Keyword(s):  
Clinical Practice ◽  
Vessel Wall ◽  
Vascular Diseases ◽  
Vascular Wall ◽  
Vessel Wall Imaging ◽  
Clinical Settings ◽  
Direct Evaluation ◽  
Intracranial Vessel ◽  
Indirect Evaluation ◽  
Wall Imaging

ABSTRACT Intracranial vessel wall imaging plays an increasing role in diagnosing intracranial vascular diseases. With the growing demand and subsequent increased use of this technique in clinical practice, radiologists and neurologists should be aware of the choices in imaging parameters and how they affect image quality, clinical indications, methods of assessment, and limitations in the interpretation of these images. Due to the improvement of the MRI techniques, the possibility of accurate and direct evaluation of the abnormalities in the arterial vascular wall (vessel wall imaging) has evolved, adding substantial data to diagnosis when compared to the indirect evaluation based on conventional flow analyses. Herein, the authors proposed a comprehensive approach of this technique reinforcing appropriated clinical settings to better use intracranial vessel wall imaging.

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