Fetching the paper…

Reading the bibliography…

2019

On-shell Methods for Form Factors in N=4 SYM and Their Applications

Yang, Gang

Original
PDF
Post on X

Understand

Form factors are quantities that involve both asymptotic on-shell states and gauge invariant operators.

They provide a natural bridge between on-shell amplitudes and off-shell correlation functions of operators, thus allowing us to use modern on-shell amplitude techniques to probe into the off-shell side of quantum field theory.
In particular, form factors have been successfully used in computing the cusp (soft) anomalous dimensions and anomalous dimensions of general local operators.
This review is intended to provide a pedagogical introduction to some of these developments.

On-shell Methods for Form Factors in N=4 SYM and Their Applications · Around

Built on

T. Ahmed and P. K. Dhani, “Two-loop Doubly Massive Four-Point Amplitude Involving a half-BPS and Konishi Operator,” JHEP
Original
1901
Earlier work this paper cites.
J. M. Henn, T. Peraro, M. Stahlhofen, and P. Wasser, “Matter dependence of the four-loop cusp anomalous dimension,” Phys. Rev. Lett
Original
1901
Earlier work this paper cites.
R. N. Lee, A. V. Smirnov, V. A. Smirnov, and M. Steinhauser, “Four-loop quark form factor with quartic fundamental colour factor,” JHEP
Original
1901
Earlier work this paper cites.
A. von Manteuffel and R. M. Schabinger, “Quark and gluon form factors in four loop QCD: The N f 2 N_{f}^{2} and N q γ N f N_{q\gamma}N_{f} contributions,” Phys. Rev
Original
1902
Earlier work this paper cites.
R. Brüser, A. Grozin, J. M. Henn, and M. Stahlhofen, “Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles,” JHEP
Original
1902
Earlier work this paper cites.
F. Cachazo, M. Spradlin, and A. Volovich, “Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory,” Phys. Rev
Original
1903
Earlier work this paper cites.
A. von Manteuffel and R. M. Schabinger, “Planar master integrals for four-loop form factors,” JHEP
Original
1903
Earlier work this paper cites.
Q. Jin and G. Yang, “Hidden Analytic Relations for Two-Loop Higgs Amplitudes in QCD,” arXiv:1904.07260 [hep-th]
Original
1904
Earlier work this paper cites.
Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, “The Duality Between Color and Kinematics and its Applications,” arXiv:1909.01358 [hep-th]
Original
1909
Earlier work this paper cites.
Q. Jin and G. Yang, “Two-Loop QCD Corrections to the Higgs plus three-parton amplitudes with Top Mass Correction,” arXiv:1910.09384 [hep-ph]
Original
1910
Earlier work this paper cites.
M. A. Huber, A. Brandhuber, S. De Angelis, and G. Travaglini, “Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions,” arXiv:1910.04772 [hep-th]
Original
1910
Earlier work this paper cites.
T. Ahmed, P. Banerjee, A. Chakraborty, P. K. Dhani, and V. Ravindran, “Form factors with two-operator insertion and violation of transcendentality principles,” arXiv:1911.11886 [hep-th]
Original
1911
Earlier work this paper cites.
J. M. Henn, G. P. Korchemsky, and B. Mistlberger, “The full four-loop cusp anomalous dimension in 𝒩 = 4 \mathcal{N}=4 super Yang-Mills and QCD,” arXiv:1911.10174 [hep-th]
Original
1911
Earlier work this paper cites.
T. Huber, A. von Manteuffel, E. Panzer, R. M. Schabinger, and G. Yang, “The Four-Loop Cusp Anomalous Dimension from the 𝒩 = 4 \mathcal{N}=4 Sudakov Form Factor,” arXiv:1912.13459 [hep-th]
Original
1912
Earlier work this paper cites.
G. ’t Hooft, “A planar diagram theory for strong interactions,” Nucl.Phys
1974
Earlier work this paper cites.
L. Brink, J. H. Schwarz, and J. Scherk, “Supersymmetric Yang-Mills Theories,” Nucl. Phys
1977
Earlier work this paper cites.
J. C. Collins, “Algorithm to Compute Corrections to the Sudakov Form-factor,” Phys.Rev
1980
Earlier work this paper cites.
F. A. Berends, R. Kleiss, P. De Causmaecker, R. Gastmans, and T. T. Wu, “Single Bremsstrahlung Processes in Gauge Theories,” Phys. Lett
1981
Earlier work this paper cites.
M. F. Sohnius and P. C. West, “Conformal Invariance in N=4 Supersymmetric Yang-Mills Theory,” Phys. Lett
1981
Earlier work this paper cites.
A. Sen, “Asymptotic Behavior of the Sudakov Form-Factor in QCD,” Phys.Rev
1981
Earlier work this paper cites.
P. De Causmaecker, R. Gastmans, W. Troost, and T. T. Wu, “Multiple Bremsstrahlung in Gauge Theories at High-Energies. 1. General Formalism for Quantum Electrodynamics,” Nucl. Phys
1982
Earlier work this paper cites.
M. B. Green, J. H. Schwarz, and L. Brink, “N=4 Yang-Mills and N=8 Supergravity as Limits of String Theories,” Nucl. Phys
1982
Earlier work this paper cites.
S. Mandelstam, “Light Cone Superspace and the Ultraviolet Finiteness of the N=4 Model,” Nucl. Phys
1983
Earlier work this paper cites.
L. Brink, O. Lindgren, and B. E. W. Nilsson, “The Ultraviolet Finiteness of the N=4 Yang-Mills Theory,” Phys. Lett
1983
Earlier work this paper cites.
R. Kleiss and W. J. Stirling, “Spinor Techniques for Calculating p anti-p → \rightarrow W + ⁣ − / Z 0 W^{+-}/Z^{0} + Jets,” Nucl. Phys
1985
Earlier work this paper cites.
W. van Neerven, “Infrared Behavior of On-shell Form-factors in a 𝒩 = 4 {\cal N}=4 Supersymmetric Yang-Mills Field Theory,” Z.Phys
1986
Earlier work this paper cites.
H. Kawai, D. C. Lewellen, and S. H. H. Tye, “A Relation Between Tree Amplitudes of Closed and Open Strings,” Nucl. Phys
1986
Earlier work this paper cites.
S. J. Parke and T. R. Taylor, “An Amplitude for n n Gluon Scattering,” Phys. Rev. Lett
1986
Earlier work this paper cites.
Z. Xu, D.-H. Zhang, and L. Chang, “Helicity Amplitudes for Multiple Bremsstrahlung in Massless Nonabelian Gauge Theories,” Nucl. Phys
1987
Earlier work this paper cites.
V. Nair, “A Current Algebra for Some Gauge Theory Amplitudes,” Phys.Lett
1988
Earlier work this paper cites.
G. P. Korchemsky, “Asymptotics of the Altarelli-Parisi-Lipatov Evolution Kernels of Parton Distributions,” Mod. Phys. Lett
1989
Earlier work this paper cites.
L. Magnea and G. F. Sterman, “Analytic continuation of the Sudakov form-factor in QCD,” Phys.Rev
1990
Earlier work this paper cites.
M. L. Mangano and S. J. Parke, “Multiparton amplitudes in gauge theories,” Phys. Rept
1991
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, “One-loop n n -point gauge theory amplitudes, unitarity and collinear limits,” Nucl.Phys
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, “Fusing gauge theory tree amplitudes into loop amplitudes,” Nucl.Phys
1995
Earlier work this paper cites.
J. M. Maldacena, “The large n n limit of superconformal field theories and supergravity,” Adv.Theor.Math.Phys
1998
Earlier work this paper cites.
S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys.Lett
1998
Earlier work this paper cites.
E. Witten, “Anti-de Sitter space and holography,” Adv.Theor.Math.Phys
1998
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, M. Perelstein, and J. S. Rozowsky, “On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences,” Nucl. Phys
1998
Earlier work this paper cites.
J. Minahan and K. Zarembo, “The Bethe ansatz for 𝒩 = 4 {\cal N}=4 superYang-Mills,” JHEP
2003
Earlier work this paper cites.
E. Witten, “Perturbative gauge theory as a string theory in twistor space,” Commun.Math.Phys
2004
Earlier work this paper cites.
F. Cachazo, P. Svrcek, and E. Witten, “MHV vertices and tree amplitudes in gauge theory,” JHEP
2004
Earlier work this paper cites.
R. Roiban, M. Spradlin, and A. Volovich, “On the tree level S matrix of Yang-Mills theory,” Phys. Rev
2004
Earlier work this paper cites.
L. J. Dixon, E. W. N. Glover, and V. V. Khoze, “MHV rules for Higgs plus multi-gluon amplitudes,” JHEP
2004
Earlier work this paper cites.
N. Beisert, “The complete one-loop dilatation operator of 𝒩 = 4 {\cal N}=4 superYang-Mills theory,” Nucl.Phys
2004
Earlier work this paper cites.
R. Britto, F. Cachazo, and B. Feng, “New recursion relations for tree amplitudes of gluons,” Nucl.Phys
2005
Earlier work this paper cites.
R. Britto, F. Cachazo, B. Feng, and E. Witten, “Direct proof of tree-level recursion relation in Yang-Mills theory,” Phys.Rev.Lett
2005
Earlier work this paper cites.
R. Britto, F. Cachazo, and B. Feng, “Generalized unitarity and one-loop amplitudes in 𝒩 = 4 {\cal N}=4 super-Yang-Mills,” Nucl.Phys
2005
Earlier work this paper cites.
Z. Bern, L. J. Dixon, and V. A. Smirnov, “Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond,” Phys.Rev
2005
Earlier work this paper cites.
Z. Bern, L. J. Dixon, and D. A. Kosower, “On-Shell Methods in Perturbative QCD,” Annals Phys
Original
2007
Earlier work this paper cites.
L. F. Alday and J. M. Maldacena, “Gluon scattering amplitudes at strong coupling,” JHEP
Original
2007
Earlier work this paper cites.
J. M. Drummond, J. Henn, V. A. Smirnov, and E. Sokatchev, “Magic identities for conformal four-point integrals,” JHEP
2007
Earlier work this paper cites.
L. F. Alday and J. Maldacena, “Comments on gluon scattering amplitudes via AdS/CFT,” JHEP
Original
2007
Earlier work this paper cites.
Cambridge Monographs on Mathematical Physics. Cambridge University Press, 2007
V. N. Gribov, The theory of complex angular momenta: Gribov lectures on theoretical physics · 2007
Earlier work this paper cites.

Similar

N. Beisert, B. Eden, and M. Staudacher, “Transcendentality and Crossing,” J.Stat.Mech
2007
Cited alongside, same era.
L. F. Alday and R. Roiban, “Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence,” Phys. Rept
Original
2008
Cited alongside, same era.
J. M. Drummond, G. P. Korchemsky, and E. Sokatchev, “Conformal properties of four-gluon planar amplitudes and Wilson loops,” Nucl. Phys
Original
2008
Cited alongside, same era.
A. Brandhuber, P. Heslop, and G. Travaglini, “MHV amplitudes in N=4 super Yang-Mills and Wilson loops,” Nucl. Phys
Original
2008
Cited alongside, same era.
Z. Bern, J. Carrasco, and H. Johansson, “New Relations for Gauge-Theory Amplitudes,” Phys.Rev
Original

Then

F. Cachazo, S. He, and E. Y. Yuan, “Scattering of Massless Particles in Arbitrary Dimensions,” Phys. Rev. Lett
Original
2014
Later among the works it cites.
F. Cachazo, S. He, and E. Y. Yuan, “Scattering of Massless Particles: Scalars, Gluons and Gravitons,” JHEP
Original
2014
Later among the works it cites.
Z. Bern, S. Davies, and T. Dennen, “Enhanced ultraviolet cancellations in 𝒩 = 5 \mathcal{N}=5 supergravity at four loops,” Phys. Rev
Original
2014
Later among the works it cites.
L. Bianchi and M. S. Bianchi, “Nonplanarity through unitarity in the ABJM theory,” Phys. Rev
Original
2014
Later among the works it cites.
M. Wilhelm, “Amplitudes, Form Factors and the Dilatation Operator in 𝒩 = 4 \mathcal{N}=4 SYM Theory,” JHEP

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2008

Cited alongside, same era.

L. J. Mason and D. Skinner, “Dual Superconformal Invariance, Momentum Twistors and Grassmannians,” JHEP

2009

Cited alongside, same era.

N. E. J. Bjerrum-Bohr, P. H. Damgaard, and P. Vanhove, “Minimal Basis for Gauge Theory Amplitudes,” Phys. Rev. Lett

2009

Cited alongside, same era.

E. Gardi and L. Magnea, “Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes,” JHEP

2009

Cited alongside, same era.

J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, “Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes,” Nucl. Phys

2010

Cited alongside, same era.

N. Arkani-Hamed, F. Cachazo, C. Cheung, and J. Kaplan, “A Duality For The S Matrix,” JHEP

2010

Cited alongside, same era.

N. Arkani-Hamed, F. Cachazo, and C. Cheung, “The Grassmannian Origin Of Dual Superconformal Invariance,” JHEP

2010

Cited alongside, same era.

Z. Bern, J. J. M. Carrasco, and H. Johansson, “Perturbative Quantum Gravity as a Double Copy of Gauge Theory,” Phys.Rev.Lett

2010

Cited alongside, same era.

Original

2015

Later among the works it cites.

D. Nandan, C. Sieg, M. Wilhelm, and G. Yang, “Cutting through form factors and cross sections of non-protected operators in 𝒩 = 4 \mathcal{N}=4 SYM,” JHEP

2015

Later among the works it cites.

F. Loebbert, D. Nandan, C. Sieg, M. Wilhelm, and G. Yang, “On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders,” JHEP

Original

2015

Later among the works it cites.

Z. Bern, S. Davies, T. Dennen, Y.-t. Huang, and J. Nohle, “Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops,” Phys. Rev

2015

Later among the works it cites.

G. Mogull and D. O’Connell, “Overcoming Obstacles to Colour-Kinematics Duality at Two Loops,” JHEP

2015

Later among the works it cites.

J. J. M. Carrasco, “Gauge and Gravity Amplitude Relations,” in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: Journeys Through the Precision Frontier: Amplitudes for Colliders (TASI 2014): Boulder, Colorado, June 2-27, 2014 · 2015

Later among the works it cites.

G. Yang, “Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory,” Phys. Rev. Lett

2016

Later among the works it cites.

R. Frassek, D. Meidinger, D. Nandan, and M. Wilhelm, “On-shell diagrams, Graßmannians and integrability for form factors,” JHEP

2016

Later among the works it cites.

L. V. Bork and A. I. Onishchenko, “Grassmannians and form factors with q 2

2016

Later among the works it cites.

L. Koster, V. Mitev, M. Staudacher, and M. Wilhelm, “Composite Operators in the Twistor Formulation of 𝒩 = 4 \mathcal{N}=4 Supersymmetric Yang-Mills Theory,” Phys. Rev. Lett

2016

Later among the works it cites.

L. Koster, V. Mitev, M. Staudacher, and M. Wilhelm, “All Tree-Level MHV Form Factors in 𝒩 = 4 \mathcal{N}=4 SYM from Twistor Space,” JHEP

2016

Later among the works it cites.

A. Brandhuber, E. Hughes, R. Panerai, B. Spence, and G. Travaglini, “The connected prescription for form factors in twistor space,” JHEP

2016

Later among the works it cites.

S. He and Z. Liu, “A note on connected formula for form factors,” JHEP

2016

Later among the works it cites.

A. Brandhuber, M. Kostacinska, B. Penante, G. Travaglini, and D. Young, “The SU(2 | | 3) dynamic two-loop form factors,” JHEP

2016

Later among the works it cites.

F. Loebbert, C. Sieg, M. Wilhelm, and G. Yang, “Two-Loop SL(2) Form Factors and Maximal Transcendentality,” JHEP

2016

Later among the works it cites.

S. Caron-Huot and M. Wilhelm, “Renormalization group coefficients and the S-matrix,” JHEP

2016

Later among the works it cites.

R. Huang, Q. Jin, and B. Feng, “Form Factor and Boundary Contribution of Amplitude,” JHEP

2016

Later among the works it cites.

PhD thesis, Humboldt U., Berlin, 2016

M. Wilhelm, Form factors and the dilatation operator in 𝒩 = 4 \mathcal{N}=4 super Yang-Mills theory and its deformations · 2016

Later among the works it cites.

PhD thesis, Queen Mary, U. of London, 2016

B. Penante, On-shell methods for off-shell quantities in 𝒩 = 4 \mathcal{N}=4 Super Yang-Mills: from scattering amplitudes to form factors and the dilatation operator · 2016

Later among the works it cites.

R. Boels, B. A. Kniehl, and G. Yang, “Master integrals for the four-loop Sudakov form factor,” Nucl. Phys

2016

Later among the works it cites.

J. M. Henn, A. V. Smirnov, V. A. Smirnov, and M. Steinhauser, “A planar four-loop form factor and cusp anomalous dimension in QCD,” JHEP

2016

Later among the works it cites.

S. Weinzierl, “Tales of 1001 Gluons,” Phys. Rept

2017

Later among the works it cites.

L. V. Bork and A. I. Onishchenko, “Wilson lines, Grassmannians and gauge invariant off-shell amplitudes in 𝒩 = 4 \mathcal{N}=4 SYM,” JHEP

2017

Later among the works it cites.

L. Koster, V. Mitev, M. Staudacher, and M. Wilhelm, “On Form Factors and Correlation Functions in Twistor Space,” JHEP

2017

Later among the works it cites.

S. He and Y. Zhang, “Connected formulas for amplitudes in standard model,” JHEP

2017

Later among the works it cites.

T. Ahmed, P. Banerjee, P. K. Dhani, N. Rana, V. Ravindran, and S. Seth, “Konishi form factor at three loops in 𝒩 = \cal N= 4 supersymmetric Yang-Mills theory,” Phys. Rev

2017

Later among the works it cites.

PhD thesis, Humboldt U., Berlin, Inst. Math., 2017

L. Koster, Form factors and correlation functions in N = 4 super Yang-Mills theory from twistor space · 2017

Later among the works it cites.

Z. Bern, J. J. Carrasco, W.-M. Chen, H. Johansson, and R. Roiban, “Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes,” Phys. Rev. Lett

2017

Later among the works it cites.

H. Johansson, G. Kälin, and G. Mogull, “Two-loop supersymmetric QCD and half-maximal supergravity amplitudes,” JHEP

2017

Later among the works it cites.

Z. Bern, J. J. M. Carrasco, W.-M. Chen, H. Johansson, R. Roiban, and M. Zeng, “Five-loop four-point integrand of N = 8 N=8 supergravity as a generalized double copy,” Phys. Rev

2017

Later among the works it cites.

R. H. Boels, T. Huber, and G. Yang, “Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory,” Phys. Rev. Lett

2017

Later among the works it cites.

A. von Manteuffel and R. M. Schabinger, “Quark and gluon form factors to four-loop order in QCD: the N f 3 N_{f}^{3} contributions,” Phys. Rev

2017

Later among the works it cites.

J. Henn, A. V. Smirnov, V. A. Smirnov, M. Steinhauser, and R. N. Lee, “Four-loop photon quark form factor and cusp anomalous dimension in the large- N c N_{c} limit of QCD,” JHEP

2017

Later among the works it cites.

R. N. Lee, A. V. Smirnov, V. A. Smirnov, and M. Steinhauser, “The n f 2 n_{f}^{2} contributions to fermionic four-loop form factors,” Phys. Rev

2017

Later among the works it cites.

S. Moch, B. Ruijl, T. Ueda, J. A. M. Vermaseren, and A. Vogt, “Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond,” JHEP

2017

Later among the works it cites.

A. Grozin, J. Henn, and M. Stahlhofen, “On the Casimir scaling violation in the cusp anomalous dimension at small angle,” JHEP

2017

Later among the works it cites.

A. Brandhuber, M. Kostacinska, B. Penante, and G. Travaglini, “Higgs amplitudes from 𝒩 = 4 \mathcal{N}=4 super Yang-Mills theory,” Phys. Rev. Lett

2017

Later among the works it cites.

L. V. Bork and A. I. Onishchenko, “Four dimensional ambitwistor strings and form factors of local and Wilson line operators,” Phys. Rev

2018

Later among the works it cites.

A. E. Bolshov, L. V. Bork, and A. I. Onishchenko, “The all-loop conjecture for integrands of reggeon amplitudes in 𝒩 = 4 \mathcal{N}=4 SYM,” JHEP

2018

Later among the works it cites.

PhD thesis, Humboldt U., Berlin (main), 2018

D. Meidinger, Integrability in weakly coupled super Yang-Mills theory: form factors, on-shell methods and Q-operators · 2018

Later among the works it cites.

L. J. Dixon, “The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension,” JHEP

2018

Later among the works it cites.

R. H. Boels, T. Huber, and G. Yang, “The Sudakov form factor at four loops in maximal super Yang-Mills theory,” JHEP

2018

Later among the works it cites.

S. Moch, B. Ruijl, T. Ueda, J. A. M. Vermaseren, and A. Vogt, “On quartic colour factors in splitting functions and the gluon cusp anomalous dimension,” Phys. Lett

2018

Later among the works it cites.

Q. Jin and G. Yang, “Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle,” Phys. Rev. Lett

2018

Later among the works it cites.

A. Brandhuber, M. Kostacinska, B. Penante, and G. Travaglini, “ Tr ( F 3 ) \text{Tr}(F^{3}) supersymmetric form factors and maximal transcendentality Part I: 𝒩 = 4 \mathcal{N}=4 super Yang-Mills,” JHEP

2018

Later among the works it cites.

A. Brandhuber, M. Kostacinska, B. Penante, and G. Travaglini, “ Tr ( F 3 ) \text{Tr}(F^{3}) supersymmetric form factors and maximal transcendentality Part II: 0 < 𝒩 < 4 0<\mathcal{N}<4 super Yang-Mills,” JHEP

2018

Later among the works it cites.

L. Bianchi, A. Brandhuber, R. Panerai, and G. Travaglini, “Dual conformal invariance for form factors,” JHEP

2019

Closest in time.

L. Bianchi, A. Brandhuber, R. Panerai, and G. Travaglini, “Form factor recursion relations at loop level,” JHEP

2019

Closest in time.

G. Kälin, G. Mogull, and A. Ochirov, “Two-loop 𝒩 \mathcal{N} = 2 SQCD amplitudes with external matter from iterated cuts,” JHEP

2019

Closest in time.

A. H. Mueller, “On the Asymptotic Behavior of the Sudakov Form-factor,” Phys.Rev

2037

Closest in time.