scholarly journals A double copy for asymptotic symmetries in the self-dual sector

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Miguel Campiglia ◽  
Silvia Nagy
Keyword(s):  
Light Cone ◽  
Single Copy ◽  
The Self ◽  
Null Infinity ◽  
Yang Mills ◽  
Self Duality ◽  
Duality Condition ◽  
Infinite Set ◽  
Double Copy ◽  
Asymptotic Symmetries

Abstract We give a double copy construction for the symmetries of the self-dual sectors of Yang-Mills (YM) and gravity, in the light-cone formulation. We find an infinite set of double copy constructible symmetries. We focus on two families which correspond to the residual diffeomorphisms on the gravitational side. For the first one, we find novel non-perturbative double copy rules in the bulk. The second family has a more striking structure, as a non-perturbative gravitational symmetry is obtained from a perturbatively defined symmetry on the YM side.At null infinity, we find the YM origin of the subset of extended Bondi-Metzner-Sachs (BMS) symmetries that preserve the self-duality condition. In particular, holomorphic large gauge YM symmetries are double copied to holomorphic supertranslations. We also identify the single copy of superrotations with certain non-gauge YM transformations that to our knowledge have not been previously presented in the literature.

scholarly journals Flat self-dual gravity

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Kirill Krasnov ◽  
Evgeny Skvortsov
Keyword(s):  
Light Cone ◽  
Space Time ◽  
Kinetic Term ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Covariant Action ◽  
Chiral Interaction ◽  
Double Copy

Abstract We construct a new covariant action for “flat” self-dual gravity in four space-time dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon imposing the light-cone gauge, the action reproduces the expected chiral interaction of Siegel. The new action is in many ways analogous to the known covariant action for self-dual Yang-Mills theory. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure.

Self-duality in four-dimensional Riemannian geometry

1978 ◽  
Vol 362 (1711) ◽  
pp. 425-461 ◽  
Keyword(s):  
Gauge Group ◽  
Riemannian Geometry ◽  
Complex Analysis ◽  
Three Dimensional ◽  
The Self ◽  
Full Detail ◽  
Yang Mills ◽  
Self Duality ◽  
Compact Gauge Group

We present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis. In particular we apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group. Results previously announced are treated with full detail and extended in a number of directions.

SELF-DUAL SUPERGRAVITY AND SUPERSYMMETRIC YANG-MILLS THEORY COUPLED TO GREEN-SCHWARZ SUPERSTRING

1994 ◽  
Vol 09 (17) ◽  
pp. 3077-3101 ◽  
Author(s):  
HITOSHI NISHINO
Keyword(s):  
Shell Structure ◽  
Riemann Tensor ◽  
The Self ◽  
Special Significance ◽  
Yang Mills ◽  
Gravitational Instanton ◽  
Self Duality ◽  
Tensor Multiplet ◽  
Kappa Symmetry ◽  
Previous Series

We present the canonical set of superspace constraints for self-dual supergravity, a “self-dual” tensor multiplet and a self-dual Yang-Mills multiplet with N=1 supersymmetry in the space-time with signature (+,+, −, −). For this set of constraints, the consistency of the self-duality conditions on these multiplets with supersymmetry is manifest. The energy-momentum tensors of all the self-dual “matter” multiplets vanish, to be consistent with the self-duality of the Riemann tensor. In particular, the special significance of the “self-dual” tensor multiplet is noted. This result fills the gap left over in our previous series of papers, with respect to the consistent couplings among the self-dual matter multiplets. We also couple these nontrivial backgrounds to a Green-Schwarz superstring σ model, under the requirement of invariance under fermionic (kappa) symmetry. The finiteness of the self-dual supergravity is discussed, based on its “off-shell” structure. A set of exact solutions for the “self-dual” tensor and self-dual Yang-Mills multiplets for the gauge group SL(2) on a self-dual gravitational instanton background is given, and its consistency with the Green-Schwarz string σ model is demonstrated.

scholarly journals NONCOMMUTATIVE EXTENDED WAVES AND SOLITON-LIKE CONFIGURATIONS IN N = 2 STRING THEORY

2003 ◽  
Vol 18 (26) ◽  
pp. 4889-4931 ◽  
Author(s):  
MATTHIAS IHL ◽  
SEBASTIAN UHLMANN
Keyword(s):  
Field Theory ◽  
String Theory ◽  
String Field Theory ◽  
Plane Waves ◽  
Equation Of Motion ◽  
Lax Pair ◽  
The Self ◽  
Yang Mills ◽  
Self Duality ◽  
Wave Solutions

The Seiberg–Witten limit of fermionic N = 2 string theory with nonvanishing B-field is governed by noncommutative self-dual Yang–Mills theory (ncSDYM) in 2+2 dimensions. Conversely, the self-duality equations are contained in the equation of motion of N = 2 string field theory in a B-field background. Therefore finding solutions to noncommutative self-dual Yang–Mills theory on ℝ2,2 might help to improve our understanding of nonperturbative properties of string (field) theory. In this paper, we construct nonlinear soliton-like and multi-plane wave solutions of the ncSDYM equations corresponding to certain D-brane configurations by employing a solution generating technique, an extension of the so-called dressing approach. The underlying Lax pair is discussed in two different gauges, the unitary and the Hermitian gauge. Several examples and applications for both situations are considered, including Abelian solutions constructed from GMS-like projectors, noncommutative U(2) soliton-like configurations and interacting plane waves. We display a correspondence to earlier work on string field theory and argue that the solutions found here can serve as a guideline in the search for nonperturbative solutions of nonpolynomial string field theory.

scholarly journals Asymptotic Weyl double copy

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Hadi Godazgar ◽  
Mahdi Godazgar ◽  
Ricardo Monteiro ◽  
David Peinador Veiga ◽  
C. N. Pope
Keyword(s):  
Black Holes ◽  
Gauge Transformation ◽  
Single Copy ◽  
Characteristic Value ◽  
Full Solution ◽  
Double Copy ◽  
Asymptotic Formulation ◽  
Large Gauge Transformation ◽  
Asymptotic Symmetries

Abstract A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that the Weyl double copy holds asymptotically in cases where the full solution is algebraically general, using rotating STU supergravity black holes as an example. The asymptotic formulation provides clues regarding the relation between asymptotic symmetries that follows from the double copy. Using the C-metric as an example, we show that a previous interpretation of this gravity solution as a superrotation has a single copy analogue relating the appropriate Liénard-Wiechert potential to a large gauge transformation.

scholarly journals GRAVITATIONAL INSTANTONS IN ASHTEKAR’S FORMALISM

1996 ◽  
Vol 11 (15) ◽  
pp. 2707-2720
Author(s):  
HIDEKI ISHIHARA ◽  
HIROTO KUBOTANI ◽  
TAKESHI FUKUYAMA
Keyword(s):  
Cosmological Constant ◽  
Bianchi Type ◽  
Canonical Formalism ◽  
Coupled System ◽  
The Self ◽  
Initial Surface ◽  
Gravitational Instantons ◽  
Hamiltonian Equations ◽  
Self Duality ◽  
Duality Condition

Gravitational instantons of Bianchi type IX space are constructed in Ashtekar’s canonical formalism. Instead of solving the self-duality condition, we fully solve the constraint on the “initial surface” and “Hamiltonian equations.” This formalism is applicable to the matter coupled system with cosmological constant.

scholarly journals On the self-duality condition in Chern-Simons systems

1991 ◽  
Vol 256 (3-4) ◽  
pp. 427-430 ◽  
Author(s):  
Prem P. Srivastava ◽  
K. Tanaka
Keyword(s):  
The Self ◽  
Self Duality ◽  
Duality Condition ◽  
Chern Simons

scholarly journals On the self-duality of solutions of the Yang-Mills equations

1978 ◽  
Vol 73 (4-5) ◽  
pp. 468-470 ◽  
Author(s):  
G. Girardi ◽  
C. Meyers ◽  
M. de Roo
Keyword(s):  
The Self ◽  
Yang Mills ◽  
Self Duality

NOTE ON SELF-DUALITY CONDITION IN THE CHIRAL BOSON THEORY

1993 ◽  
Vol 08 (05) ◽  
pp. 417-419
Author(s):  
MU-IN PARK ◽  
YOUNG-JAI PARK ◽  
YONGDUK KIM
Keyword(s):  
Boundary Condition ◽  
Equation Of Motion ◽  
The Self ◽  
Theoretical Equation ◽  
Self Duality ◽  
Duality Condition ◽  
Boson Theory

We demonstrate that the self-duality condition for the field itself can naturally be obtained without requiring any boundary condition in Floreanini and Jackiw’s chiral boson theory if we treat carefully the quantum theoretical equation of motion for the theory.

Sign in / Sign up

Export Citation Format

Share Document