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-DUALITY AND GENERALIZED KdV FLOWS

1991 ◽  
Vol 06 (05) ◽  
pp. 399-408 ◽  
Author(s):  
IOANNIS BAKAS ◽  
DIDIER A. DEPIREUX
Keyword(s):  
Gauge Group ◽  
Dimensional Reduction ◽  
Vector Fields ◽  
Killing Vector ◽  
The Self ◽  
Killing Vector Fields ◽  
Yang Mills ◽  
Kdv Hierarchy ◽  
Self Duality ◽  
Time Signature

We obtain the (N+1)-th flow of the generalized (N–1)-KdV hierarchy from self-dual Yang-Mills equations with gauge group SL(N) and space-time signature (2, 2). The dimensional reduction is performed by using a pair of orthogonal Killing vector fields (one time-like and one null) and we generalize previous results by Mason and Sparling to N≥2. We illustrate our method with explicit examples and determine the form of the self-dual solutions for N=2, 3, 4. Applications of this formalism and its possible generalizations are also discussed briefly.

scholarly journals Dirac operators with Lorentz scalar shell interactions

2018 ◽  
Vol 30 (05) ◽  
pp. 1850013 ◽  
Author(s):  
Markus Holzmann ◽  
Thomas Ourmières-Bonafos ◽  
Konstantin Pankrashkin
Keyword(s):  
Dirac Operator ◽  
Spectral Properties ◽  
Smooth Surface ◽  
Three Dimensional ◽  
The Self ◽  
Eigenvalue Asymptotics ◽  
Yang Mills ◽  
Lorentz Scalar ◽  
Definition Of ◽  
The Individual

This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions along the surface. After showing the self-adjointness of the resulting operator, we switch to the investigation of its spectral properties, in particular, to the existence and non-existence of eigenvalues. In the case of an attractive coupling, we study the eigenvalue asymptotics as the mass becomes large and show that the behavior of the individual eigenvalues and their total number are governed by an effective Schrödinger operator on the boundary with an external Yang–Mills potential and a curvature-induced potential.

YANG-MILLS FIELD QUANTIZATION WITH NON-COMPACT GAUGE GROUP

1992 ◽  
Vol 07 (29) ◽  
pp. 2747-2752 ◽  
Author(s):  
A. E. MARGOLIN ◽  
V. I. STRAZHEV
Keyword(s):  
State Space ◽  
Gauge Group ◽  
Physical State ◽  
Indefinite Metric ◽  
Yang Mills ◽  
S Matrix ◽  
Field Quantization ◽  
Compact Gauge Group ◽  
Mills Field

Yang-Mills field quantization in BRST-formalism with non-compact semi-simple gauge group is performed. The S-matrix unitarity in the physical state space, having indefinite metric is determined.

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 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

scholarly journals Symmetries of the self-dual Yang-Mills equations

1994 ◽  
Vol 49 (1) ◽  
pp. 151-158
Author(s):  
Rod Halburd
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Gauge Group ◽  
Finite Dimension ◽  
The Self ◽  
Partial Differential ◽  
Yang Mills ◽  
Master System ◽  
Group Of Symmetries ◽  
Conformal Symmetries

It has been conjectured by R. S. Ward that the self-dual Yang-Mills Equations (SDYMEs) form a “master system” in the sense that most known integrable ordinary and partial differential equations are obtainable as reductions. We systematically construct the group of symmetries of the SDYMEs on R4 with semisimple gauge group of finite dimension and show that this yields only the well known gauge and conformal symmetries.

scholarly journals NONSINGULAR COMPLEX INSTANTONS ON EUCLIDEAN SPACETIME

2008 ◽  
Vol 05 (06) ◽  
pp. 963-971 ◽  
Author(s):  
LLOHANN DALLAGNOL ◽  
MARCOS JARDIM
Keyword(s):  
Harmonic Function ◽  
Gauge Group ◽  
Yang Mills ◽  
Self Duality

Building on a variation of 't Hooft's harmonic function ansatz for SU(2) instantons on ℝ4, we provide new explicit nonsingular solutions of the Yang–Mills anti-self-duality equations on Euclidean spacetime with gauge group SL(2, ℂ) and SL(3, ℝ).

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