Literature Guide

The following literature is provided to accompany the SAGEX scientific curriculum; links to the materials are provided wherever possible.

Books

Perturbative QCD:

• R. Keith Ellis, W. James Stirling, and B. R. Webber, QCD and collider physics, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol., 8:1–435, 1996.
• John Collins, Foundations of perturbative QCD, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol., 32:1–624, 2011.

On-shell methods:

• Henriette Elvang and Yu-tin Huang, Scattering amplitudes, arXiv:1308.1697, 2013.
• Johannes M. Henn and Jan C. Plefka, Scattering amplitudes in gauge theories, Lect. Notes Phys., 883:pp.1–195, 2014.

String theory:

• Michael B. Green, J. H. Schwarz, and Edward Witten, Superstring Theory. Vol. 1: Introduction, Cambridge Monographs on Mathematical Physics, 1988.
• Michael B. Green, J. H. Schwarz, and Edward Witten, Superstring Theory. Vol. 2: Loop amplitudes, anomalies and phenomenology, 1988.
• J. Polchinski, String Theory. Vol. 1: An introduction to the bosonic string, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 2007.
• J. Polchinski, String Theory. Vol. 2: Superstring Theory and beyond, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 2007.
• Volker Schomerus, A primer on String Theory, Cambridge University Press, 2017.

Reviews/Pedagogical Lectures

General introduction to modern methods for amplitudes:

• Michelangelo L. Mangano and Stephen J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept., 200:301–367, 1991.
• Lance J. Dixon, Calculating scattering amplitudes efficiently. In QCD and beyond, Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics, TASI95, Boulder, USA, June 4-30, 1995, pages 539–584, 1996.
• Lance J. Dixon, Scattering amplitudes: the most perfect microscopic structures in the universe, J. Phys., A44:454001, 2011.

Loop methods:

• Zvi Bern, Lance J. Dixon, and David A. Kosower, On-shell methods in perturbative QCD, Annals Phys., 322:1587–1634, 2007.
• Ruth Britto, Loop amplitudes in gauge theories: modern analytic approaches, J. Phys., A44:454006, 2011.
• R. Keith Ellis, Zoltan Kunszt, Kirill Melnikov, and Giulia Zanderighi, One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts, Phys. Rept., 518:141–250, 2012.
• Johannes Blümlein and Carsten Schneider, Analytic computing methods for precision calculations in quantum field theory, Int. J. Mod. Phys., A33(17):1830015, 2018.

Generalised unitarity:

• Zvi Bern, Lance J. Dixon, and David A. Kosower, Progress in one loop QCD computations, Ann. Rev. Nucl. Part. Sci., 46:109–148, 1996.
• Harald Ita, Susy theories and QCD: numerical approaches, J. Phys., A44:454005, 2011.

Differential equations:

• Johannes M. Henn, Lectures on differential equations for Feynman integrals, J. Phys., A48:153001, 2015.

Mulitple polylogs, symbols, Hopf algebra structure:

• Claude Duhr, Mathematical aspects of scattering amplitudes, 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, pages 419–476, 2015.
• Erik Panzer, Feynman integrals and hyperlogarithms, PhD thesis, Humboldt U., Berlin, Inst. Math., 2015.
• Christian Vergu, Polylogarithms and physical applications, Notes from the summer school ‘Polylogarithms as a bridge between number theory
  and particle physics”, Durham, UK, July 2013.

Twistor methods:

• Freddy Cachazo and Peter Svrcek, Lectures on twistor strings and perturbative Yang Mills theory, PoS, RTN2005:004, 2005.
• Martin Wolf, A first course on twistors, integrability and gluon scattering amplitudes, J. Phys., A43:393001, 2010.
• Tim Adamo, Mathew Bullimore, Lionel Mason, and David Skinner, Scattering amplitudes and Wilson loops in twistor space, J. Phys., A44:454008, 2011.
• Tim Adamo, Twistor actions for gauge theory and gravity, PhD thesis, Cambridge U.,DAMTP, 2013.

Grassmannian geometry:  (original papers)

• Nima Arkani-Hamed, Jacob L. Bourjaily, Freddy Cachazo, Alexander B. Goncharov, Alexander Postnikov, and Jaroslav Trnka, Grassmannian geometry of scattering amplitudes, Cambridge University Press, 2016.
• Nima Arkani-Hamed and Jaroslav Trnka, The amplituhedron, JHEP, 10:030, 2014.

Regge kinematics:

• J. Bartels, L. N. Lipatov, and A. Prygarin, Integrable spin chains and scattering amplitudes, J. Phys., A44:454013, 2011.
• J. Bartels, AdS/CFT: scattering amplitudes in the Regge limit: from weak to strong coupling, Int. J. Mod. Phys. Conf. Ser., 04:26–34, 2011.

Methods for supersymmetric amplitudes:

• Luis F. Alday and Radu Roiban, Scattering amplitudes, Wilson loops and the string/gauge theory correspondence, Phys. Rept., 468:153–211, 2008.
• J. M. Drummond, Hidden simplicity of gauge theory amplitudes, Class. Quant. Grav., 27:214001, 2010.
• John Joseph M. Carrasco and Henrik Johansson, Generic multiloop methods and application to N=4 super-Yang-Mills, J. Phys., A44:454004, 2011.

SUSY Ward identities:

• Henriette Elvang, Daniel Z. Freedman, and Michael Kiermaier, SUSY Ward identities, superamplitudes, and counterterms, J. Phys., A44:454009, 2011.

Dual conformal symmetry and Yangian symmetry:

• J. M. Drummond, Tree-level amplitudes and dual superconformal symmetry, J. Phys., A44:454010, 2011.

Asymptotic symmetries and soft theorems:

• Andrew Strominger, Lectures on the infrared structure of gravity and gauge theory, Harvard, 2016.

Integrability in AdS/CFT:

• Niklas Beisert et al, Review of AdS/CFT integrability: an overview, Lett. Math.
  Phys., 99:3–32, 2012.
• Diego Bombardelli et al, An integrability primer for the gauge-gravity correspondence: an introduction, J. Phys., A49(32):320301, 2016.

Wilson loop/pentagon operator product expansion:

• Luis F. Alday, Davide Gaiotto, Juan Maldacena, Amit Sever, and Pedro Vieira, An operator product expansion for polygonal null Wilson loops, JHEP, 04:088, 2011.
• Benjamin Basso, Amit Sever, and Pedro Vieira, Space-time S-matrix and flux tube S-matrix II. Extracting and matching data, JHEP, 01:008, 2014.

Color-kinematics duality:

• Z. Bern, Colour-kinematics duality, Lecture Notes, Amplitudes 2018 Summer School.
• John Joseph 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, pages 477–557. WSP, WSP, 2015.

CHY: (original papers)

• Freddy Cachazo, Song He, and Ellis Ye Yuan, Scattering of massless particles: scalars, gluons and gravitons, JHEP, 07:033, 2014.
• Freddy Cachazo, Song He, and Ellis Ye Yuan, Scattering of massless particles in arbitrary dimensions, Phys. Rev. Lett., 113(17):171601, 2014.

String theory:

• David Tong, String Theory, Lectures, University of Cambridge, UK.

AdS/CFT:

• Ofer Aharony, Steven S. Gubser, Juan Martin Maldacena, Hirosi Ooguri, and Yaron Oz, Large N field theories, string theory and gravity, Phys. Rept., 323:183–386, 2000.
• Eric D’Hoker and Daniel Z. Freedman, Supersymmetric gauge theories and the AdS / CFT correspondence. In strings, branes and extra dimensions: TASI 2001: Proceedings, pages 3–158, 2002.
• Joao Penedones. TASI lectures on AdS/CFT, In Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: new frontiers in fields and strings (TASI 2015): Boulder, CO, USA, June 1-26, 2015, pages 75–136, 2017.

Classic Papers

• V. Bargmann and Eugene P. Wigner, Group theoretical discussion of relativistic wave equations, Proc. Nat. Acad. Sci., 34:211, 1948.
• R. E. Cutkosky, Singularities and discontinuities of Feynman amplitudes, J. Math. Phys., 1:429–433, 1960.
• Steven Weinberg, Photons and gravitons in S-matrix theory: derivation of charge conservation and equality of gravitational and inertial mass, Phys. Rev., 135:B1049–B1056, 1964.
• Steven Weinberg, Infrared photons and gravitons, Phys. Rev., 140:B516–B524, 1965.
• Gerard ’t Hooft and M. J. G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys., B44:189–213, 1972.
• David J. Gross and Frank Wilczek, Ultraviolet behavior of nonabelian gauge theories, Phys. Rev. Lett., 30:1343–1346, 1973; H. David Politzer, Reliable perturbative results for strong interactions?, Phys. Rev. Lett., 30:1346–1349, 1973.
• Gerard ’t Hooft and M. J. G. Veltman, One loop divergencies in the theory of gravitation, Ann. Inst. H. Poincare Phys. Theor., A20:69–94, 1974.
• J. Wess and B. Zumino, Supergauge transformations in four-dimensions, Nucl. Phys., B70:39–50, 1974.
• Lars Brink, John H. Schwarz, and Joel Scherk, Supersymmetric Yang-Mills theories, Nucl. Phys., B121:77–92, 1977.
• K. G. Chetyrkin and F. V. Tkachov, Integration by parts: the algorithm to calculate beta functions in 4 loops, Nucl. Phys., B192:159–204, 1981.
• Alexander M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett., B103:207– 210, 1981.
• Michael B. Green, John H. Schwarz, and Lars Brink, N=4 Yang-Mills and N=8 supergravity as limits of string theories, Nucl. Phys., B198:474–492, 1982.
• R. Kleiss and W. James Stirling, Spinor techniques for calculating p anti-p —> W+-/Z0 + jets, Nucl. Phys., B262:235–262, 1985; Zhan Xu, Da-Hua Zhang, and Lee Chang, Helicity amplitudes for multiple bremsstrahlung in massless nonabelian gauge theories, Nucl. Phys., B291:392–428, 1987.
• H. Kawai, D. C. Lewellen, and S. H. H. Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys., B269:1–23, 1986.
• Stephen J. Parke and T. R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett., 56:2459, 1986.
• Frits A. Berends and W. T. Giele, Recursive calculations for processes with n gluons, Nucl. Phys., B306:759–808, 1988.
• V. P. Nair, A current algebra for some gauge theory amplitudes, Phys. Lett.,
  B214:215–218, 1988.
• Zvi Bern and David A. Kosower, The computation of loop amplitudes in gauge theories, Nucl. Phys., B379:451–561, 1992; Zvi Bern, Lance J. Dixon, David C. Dunbar, and David A. Kosower, One loop n-point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys., B425:217–260, 1994.
• Juan Martin Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38:1113–1133, 1999. [Adv. Theor. Math. Phys.2,231(1998)].
• Z. Bern, Lance 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., B530:401–456, 1998.
• Stefano Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett., B427:161–171, 1998; George F. Sterman and Maria E. Tejeda-Yeomans, Multiloop amplitudes and resummation, Phys. Lett., B552:48–56, 2003.
• Edward Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys., 252:189–258, 2004.
• Ruth Britto, Freddy Cachazo, and Bo Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys., B715:499–522, 2005; Ruth Britto, Freddy Cachazo, Bo Feng, and Edward Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett., 94:181602, 2005.