scholarly journals Twistor theory at fifty: from contour integrals to twistor strings

2017 ◽  
Vol 473 (2206) ◽  
pp. 20170530 ◽  
Author(s):  
Michael Atiyah ◽  
Maciej Dunajski ◽  
Lionel J. Mason
Keyword(s):  
Holomorphic Curves ◽  
Twistor Theory ◽  
Gravitational Instantons ◽  
Yang Mills ◽  
Conformal Curvature ◽  
Twistor Strings ◽  
Equations Of Mathematical Physics ◽  
Elementary Construction ◽  
Dispersionless Systems

We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold—the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics—anti-self-duality equations on Yang–Mills or conformal curvature—can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang–Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang–Mills equations, and Einstein–Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose’s proposal for a role of gravity in quantum collapse of a wave function.

scholarly journals Celestial superamplitude in $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hongliang Jiang
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Momentum Space ◽  
Ward Identity ◽  
Yang Mills ◽  
Conformal Field ◽  
New Perspective ◽  
Celestial Sphere

Abstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $$ \mathcal{N} $$ N = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $$ \mathcal{N} $$ N = 4 SYM amplitudes via 2D celestial conformal field theory.

scholarly journals Exact expressions for n-point maximal U(1)Y-violating integrated correlators in SU(N) $$ \mathcal{N} $$ = 4 SYM

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Daniele Dorigoni ◽  
Michael B. Green ◽  
Congkao Wen
Keyword(s):  
Modular Forms ◽  
Free Field ◽  
Perturbation Expansion ◽  
Flat Space ◽  
Low Energy ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Infinite Sums

Abstract The exact expressions for integrated maximal U(1)Y violating (MUV) n-point correlators in SU(N) $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory are determined. The analysis generalises previous results on the integrated correlator of four superconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of N and τ = θ/(2π) + 4πi/$$ {g}_{YM}^2 $$ g YM 2 , and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights (w, −w) where w = n − 4. The correlators satisfy Laplace-difference equations that relate the SU(N+1), SU(N) and SU(N−1) expressions and generalise the equations previously found in the w = 0 case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight (w, −w). For any fixed value of N the perturbation expansion of this correlator is found to start at order ($$ {g}_{YM}^2 $$ g YM 2 N)w. The contributions of Yang-Mills instantons of charge k > 0 are of the form qkf(gYM), where q = e2πiτ and f(gYM) = O($$ {g}_{YM}^{-2w} $$ g YM − 2 w ) when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form $$ {\overline{q}}^{\left|k\right|}\hat{f}\left({g}_{YM}\right) $$ q ¯ k f ̂ g YM , where $$ \hat{f}\left({g}_{YM}\right)=O\left({g}_{YM}^{2w}\right) $$ f ̂ g YM = O g YM 2 w when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Properties of the large-N expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the identification of n-point free-field MUV correlators with the integrands of (n − 4)-loop perturbative contributions to the four-point correlator. In particular, we emphasise the important rôle of SL(2, ℤ)-covariance in the construction.

Yang-Mills instantons on ALE gravitational instantons

1990 ◽  
Vol 288 (1) ◽  
pp. 263-307 ◽  
Author(s):  
Peter B. Kronheimer ◽  
Hiraku Nakajima
Keyword(s):  
Gravitational Instantons ◽  
Yang Mills

scholarly journals twistors and gauge fields

1986 ◽  
Vol 9 (2) ◽  
pp. 209-221
Author(s):  
A. G. Sergeev
Keyword(s):  
Gauge Fields ◽  
Twistor Theory ◽  
Yang Mills ◽  
Geometrical Properties ◽  
Minkowsky Space ◽  
Basic Ideas ◽  
Massless Fields

We describe briefly the basic ideas and results of the twistor theory. The main points: twistor representation of Minkowsky space, Penrose correspondence and its geometrical properties, twistor interpretation of linear massless fields, Yang-Mills fields (including instantons and monopoles) and Einstein-Hilbert equations.

GEOMETRICAL DERIVATION OF THE FADDEEV-POPOV ANSATZ

1989 ◽  
Vol 04 (24) ◽  
pp. 2397-2407 ◽  
Author(s):  
P. ELLICOTT ◽  
G. KUNSTATTER ◽  
D.J. TOMS
Keyword(s):  
Invariant Measure ◽  
Sigma Models ◽  
Configuration Space ◽  
Effective Action ◽  
General Class ◽  
Gauge Theories ◽  
Yang Mills ◽  
Linear Sigma Models ◽  
Supersymmetric Theories

A geometrical derivation of the Faddeev-Popov measure is presented. This derivation is valid in any gauge for a general class of gauge theories, including Yang-Mills theory, gravitation and non-linear sigma models, and can easily be generalized to include supersymmetric theories. We stress the role of a non-trivial, finite contribution to the effective action from the invariant measure on the orbit over each point in the physical configuration space.

TWISTORS, YANG-MILLS AMPLITUDES AND LANDAU LEVELS

2005 ◽  
Vol 20 (27) ◽  
pp. 6107-6121
Author(s):  
V. P. NAIR
Keyword(s):  
Twistor Space ◽  
Point Of View ◽  
Wave Functions ◽  
Landau Levels ◽  
Holomorphic Curves ◽  
Short Discussion ◽  
Yang Mills ◽  
Lowest Landau Level ◽  
Recent Developments ◽  
Discussion Review

We give a short discussion/review of the recent developments expressing the perturbative scattering amplitudes in Yang-Mills theory, specifically for the [Formula: see text] theory, in terms of holomorphic curves in a supersymmetric twistor space. Holomorphic curves, which are maps of CP1 to the supertwistor space, can also be interpreted as the lowest Landau level wave functions; this point of view is also briefly explained.

scholarly journals VORTEX SOLUTION IN (2+1)-DIMENSIONAL PURE YANG–MILLS THEORY AT HIGH TEMPERATURES

1999 ◽  
Vol 14 (27) ◽  
pp. 1909-1916 ◽  
Author(s):  
DMITRI DIAKONOV
Keyword(s):  
High Temperatures ◽  
Higgs Field ◽  
Higgs Potential ◽  
Yang Mills ◽  
Vortex Solution ◽  
The One ◽  
Mills Field ◽  
Stable Vortex

At high temperatures the A0 component of the Yang–Mills field plays the role of the Higgs field, and the one-loop potential V(A0) plays the role of the Higgs potential. We find a new stable vortex solution of the Abrikosov–Nielsen–Olesen type, and discuss its properties and possible implications.

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