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.

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.

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 Bianchi-IX, Darboux–Halphen and Chazy–Ramanujan

2016 ◽  
Vol 13 (04) ◽  
pp. 1650042 ◽  
Author(s):  
Sumanto Chanda ◽  
Partha Guha ◽  
Raju Roychowdhury
Keyword(s):  
Vacuum Einstein Equation ◽  
Yang Mills ◽  
Gravitational Instanton ◽  
Self Duality ◽  
Bianchi Ix ◽  
Euler Top ◽  
Integrable Dynamical Systems ◽  
Halphen System ◽  
Special Case ◽  
Dual Case

Bianchi-IX four metrics are SU(2) invariant solutions of vacuum Einstein equation, for which the connection-wise self-dual case describes the Euler top, while the curvature-wise self-dual case yields the Ricci flat classical Darboux–Halphen system. It is possible to see such a solution exhibiting Ricci flow. The classical Darboux–Halphen system is a special case of the generalized one that arises from a reduction of the self-dual Yang–Mills equation and the solutions to the related homogeneous quadratic differential equations provide the desired metric. A few integrable and near-integrable dynamical systems related to the Darboux–Halphen system and occurring in the study of Bianchi-IX gravitational instanton have been listed as well. We explore in details whether self-duality implies integrability.

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 Lectures on Classical Integrable Systems and Gauge Field Theories

10.14311/951 ◽  
2008 ◽  
Vol 48 (2) ◽  
Author(s):  
M. Olshanetsky
Keyword(s):  
Integrable Systems ◽  
Gauge Field Theories ◽  
The Self ◽  
Field Theories ◽  
Coadjoint Orbits ◽  
Yang Mills ◽  
Self Duality ◽  
Hecke Correspondence ◽  
Classical Integrable ◽  
Moser System

In these lectures we consider Hitchin integrable systems and their relations with the self-duality equations and twisted super-symmetric Yang-Mills theory in four dimension. We define the Symplectic Hecke correspondence between different integrable systems. As an example we consider Elliptic Calogero-Moser system and integrable Euler-Arnold top on coadjoint orbits of the group GL(N, C) and explain the Symplectic Hecke correspondence for these systems. 

scholarly journals ON GENERALIZED SELF-DUALITY EQUATIONS TOWARDS SUPERSYMMETRIC QUANTUM FIELD THEORIES OF FORMS

1998 ◽  
Vol 13 (14) ◽  
pp. 1115-1132 ◽  
Author(s):  
LAURENT BAULIEU ◽  
CÉLINE LAROCHE
Keyword(s):  
The Self ◽  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Time Dimension ◽  
Yang Mills ◽  
Self Duality ◽  
Topological Quantum ◽  
Gauge Functions

We classify possible "self-duality" equations for p-form gauge fields in space–time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang–Mills fields (p=1) in 4<D≤8. We impose two crucial requirements. First, there should exist a 2(p+1)-form T-invariant under a subgroup H of SO D. Second, the representation for the SO D curvature of the gauge field must decompose under H in a relevant way. When these criteria are fulfilled, the "self-duality" equations can be candidates of gauge functions for SO D-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for D≥10 for various p-form gauge fields.

New Representation of the Self-Duality and Exact Solutions for Yang–Mills Equations

2006 ◽  
Vol 45 (6) ◽  
pp. 1021-1028 ◽  
Author(s):  
A. H. Khater ◽  
D. K. Callebaut ◽  
S. M. Sayed
Keyword(s):  
Exact Solutions ◽  
The Self ◽  
Yang Mills ◽  
Self Duality

scholarly journals SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Jean Thierry-Mieg ◽  
Peter Jarvis
Keyword(s):  
Lie Algebras ◽  
The Self ◽  
Quantum Field ◽  
Yang Mills ◽  
Self Duality ◽  
Simple Superalgebra ◽  
Charge Parity ◽  
Structure Constants ◽  
Definition Of ◽  
Exterior Forms

Abstract We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form A, by a superalgebra-valued polyform $$ \tilde{A} $$ A ˜ mixing exterior-forms of all degrees and satisfying the chiral self-duality condition $$ \tilde{A} =^{\ast }{\tilde{A}}_{\chi } $$ A ˜ = ∗ A ˜ χ , where χ denotes the superalgebra grading operator. This superconnection contains Yang-Mills vectors valued in the even Lie subalgebra, together with scalars and self-dual tensors valued in the odd module, all coupling only to the charge parity CP-positive Fermions. The Fermion quantum loops then induce the usual Yang-Mills-scalar Lagrangian, the self-dual Avdeev-Chizhov propagator of the tensors, plus a new vector-scalar-tensor vertex and several quartic terms which match the geometric definition of the supercurvature. Applied to the SU(2/1) Lie-Kac simple superalgebra, which naturally classifies all the elementary particles, the resulting quantum field theory is anomaly-free and the interactions are governed by the super-Killing metric and by the structure constants of the superalgebra.

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 THE d = 6, (2, 0)-TENSOR MULTIPLET COUPLED TO SELF-DUAL STRINGS

2002 ◽  
Vol 17 (15) ◽  
pp. 2051-2072 ◽  
Author(s):  
ANDREAS GUSTAVSSON
Keyword(s):  
Field Strength ◽  
Quantization Condition ◽  
The Self ◽  
Coupling Constants ◽  
Coupling Constant ◽  
Self Duality ◽  
Charge Quantization ◽  
Form Field ◽  
Tensor Multiplet ◽  
A Charge

We show that the central charges that group theory allows in the (2, 0)-supersymmetry translations algebra arise from a string and a three-brane by commuting two supercharges. We show that the net force between two such parallel strings vanishes. We show that all the coupling constants are fixed numbers, due to supersymmetry, and self-duality of the three-form field strength. We obtain a charge quantization for the self-dual field strength, and show that when compactifying on a two-torus, it reduces to the usual quantization condition of N = 4 SYM with gauge group SU(2), and with coupling constant and theta angle given by the τ-parameter of the two-torus, provided that we pick that chiral theory which corresponds to a theta function with zero characteristics, as expected on manifolds of this form.

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