Hidden structure in the form factors of N = 4 SYM
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Dhritiman Nandan
Abstract
On-shell techniques have been the cornerstone of tremendous progress in our understanding of quantum field theory over the last couple of decades. Initially such ideas were only applied to computing scattering amplitudes but in recent years they have also been extended in computing and finding novel structure in off-shell quantities like form factors. As a close cousin of quantum chromodynamics (QCD), N = 4 super Yang-Mills (SYM) theory has been at the center of much of the activity in the above-mentioned on-shell-based approach. On the other hand, in recent years various other aspects of this theory has also been subject to intense investigation, particularly in the framework of the gauge/string duality. Notably, the one-loop dilatation operator of this theory was identified with the Hamiltonian of an integrable spin chain which has lead to non-perturbative solutions of anomalous dimensions based on the conjectured full integrability in the planar limit. In this note, we will focus on the form factors of general gauge invariant operators in N = 4 SYM. Using the on-shell techniques we present novel methods to compute the dilatation operator of this theory.We also present new on-shell diagrams and Grassmannian formulation of form factors, as well as study finite physical observables from form factors.
Abstract
On-shell techniques have been the cornerstone of tremendous progress in our understanding of quantum field theory over the last couple of decades. Initially such ideas were only applied to computing scattering amplitudes but in recent years they have also been extended in computing and finding novel structure in off-shell quantities like form factors. As a close cousin of quantum chromodynamics (QCD), N = 4 super Yang-Mills (SYM) theory has been at the center of much of the activity in the above-mentioned on-shell-based approach. On the other hand, in recent years various other aspects of this theory has also been subject to intense investigation, particularly in the framework of the gauge/string duality. Notably, the one-loop dilatation operator of this theory was identified with the Hamiltonian of an integrable spin chain which has lead to non-perturbative solutions of anomalous dimensions based on the conjectured full integrability in the planar limit. In this note, we will focus on the form factors of general gauge invariant operators in N = 4 SYM. Using the on-shell techniques we present novel methods to compute the dilatation operator of this theory.We also present new on-shell diagrams and Grassmannian formulation of form factors, as well as study finite physical observables from form factors.
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Introduction VII
- Algebraic K-theory, assembly maps, controlled algebra, and trace methods 1
- Lorentzian manifolds with special holonomy – Constructions and global properties 51
- Contributions to the spectral geometry of locally homogeneous spaces 69
- On conformally covariant differential operators and spectral theory of the holographic Laplacian 90
- Moduli and deformations 116
- Vector bundles in algebraic geometry and mathematical physics 150
- Dyson–Schwinger equations: Fix-point equations for quantum fields 186
- Hidden structure in the form factors of N = 4 SYM 197
- On regulating the AdS superstring 221
- Constraints on CFT observables from the bootstrap program 245
- Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities 266
- Yangian symmetry inmaximally supersymmetric Yang-Mills theory 288
- Wave and Dirac equations on manifolds 324
- Geometric analysis on singular spaces 349
- Singularities and long-time behavior in nonlinear evolution equations and general relativity 417
- Index 491
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Introduction VII
- Algebraic K-theory, assembly maps, controlled algebra, and trace methods 1
- Lorentzian manifolds with special holonomy – Constructions and global properties 51
- Contributions to the spectral geometry of locally homogeneous spaces 69
- On conformally covariant differential operators and spectral theory of the holographic Laplacian 90
- Moduli and deformations 116
- Vector bundles in algebraic geometry and mathematical physics 150
- Dyson–Schwinger equations: Fix-point equations for quantum fields 186
- Hidden structure in the form factors of N = 4 SYM 197
- On regulating the AdS superstring 221
- Constraints on CFT observables from the bootstrap program 245
- Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities 266
- Yangian symmetry inmaximally supersymmetric Yang-Mills theory 288
- Wave and Dirac equations on manifolds 324
- Geometric analysis on singular spaces 349
- Singularities and long-time behavior in nonlinear evolution equations and general relativity 417
- Index 491
