scholarly journals SELF-DUALITY AND THE KdV HIERARCHY

1993 ◽  
Vol 08 (07) ◽  
pp. 661-665
Author(s):  
ASHOK DAS ◽  
C.A.P. GALVĀO
Keyword(s):  
The Self ◽  
Gauge Fields ◽  
Recursion Relations ◽  
Four Dimensions ◽  
Kdv Hierarchy ◽  
Self Duality ◽  
Duality Condition

We derive the entire KdV hierarchy as well as the recursion relations from the self-duality condition on gauge fields in four dimensions.

scholarly journals SELF-DUALITY AND THE SUPERSYMMETRIC KdV HIERARCHY

1993 ◽  
Vol 08 (15) ◽  
pp. 1399-1406 ◽  
Author(s):  
ASHOK DAS ◽  
C. A. P. GALVÃO
Keyword(s):  
Kdv Equation ◽  
Curvature Condition ◽  
Four Dimensions ◽  
Yang Mills ◽  
Kdv Hierarchy ◽  
Self Duality ◽  
Kdv Equations ◽  
Duality Condition ◽  
Graded Lie Algebra ◽  
Supersymmetric Kdv Equation

We show how the supersymmetric KdV equation can be obtained from the self-duality condition on Yang-Mills fields in four dimensions associated with the graded Lie algebra OSp(2/1). We also obtain the hierarchy of SUSY KdV equations as well as the s-KdV equations from such a condition. We formulate the SUSY KdV hierarchy as a vanishing curvature condition associated with the U(1) group and show how an Abelian self-duality condition in four dimensions can also lead to these equations.

scholarly journals TWO-LOOP VACUUM DIAGRAMS IN BACKGROUND FIELD AND THE HEISENBERG–EULER EFFECTIVE ACTION

2008 ◽  
Vol 23 (32) ◽  
pp. 5201-5215 ◽  
Author(s):  
MAREK KRASŇANSKÝ
Keyword(s):  
Explicit Form ◽  
Effective Action ◽  
Background Field ◽  
Two Dimensions ◽  
Recursion Relations ◽  
Four Dimensions ◽  
Self Duality

We show that in arbitrary even dimensions, the two-loop scalar QED Heisenberg–Euler effective action can be reduced to simple one-loop quantities, using just algebraic manipulations, when the constant background field satisfies F2 = -f2𝟙, which in four dimensions coincides with the condition for self-duality, or definite helicity. This result relies on new recursion relations between two-loop and one-loop diagrams, with background field propagators. It also yields an explicit form of the renormalized two-loop effective action in a general constant background field in two dimensions.

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

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.

EXACT SOLUTIONS OF THE SELF-DUALITY EQUATIONS ON THE MINKOWSKI SPACE-TIME

2001 ◽  
Vol 12 (06) ◽  
pp. 801-806 ◽  
Author(s):  
V. MANTA ◽  
G. ZET
Keyword(s):  
Gauge Theory ◽  
Exact Solutions ◽  
Minkowski Space ◽  
Space Time ◽  
The Self ◽  
Gauge Fields ◽  
Self Duality ◽  
Minkowski Space Time ◽  
Dynamical Type ◽  
Analytical Program

A SU(2) Gauge Theory with spherical symmetry over the Minkowski space-time is considered. The self-duality equation of the gauge fields are written and their solutions are obtained. Two exact solutions, one of which is statical and another of dynamical type are given. All the calculations are performed using an analytical program written in GRTensor computer algebra package, which runs on the MapleV platform.

scholarly journals ALTERNATIVE FORMULATION FOR DUALITY-SYMMETRIC 11-DIMENSIONAL SUPERGRAVITY COUPLED TO SUPER M-5-BRANE

1999 ◽  
Vol 14 (15) ◽  
pp. 977-992 ◽  
Author(s):  
HITOSHI NISHINO
Keyword(s):  
Field Strength ◽  
Tensor Field ◽  
The Self ◽  
Gauge Fields ◽  
Necessary Condition ◽  
Alternative Formulation ◽  
Field Equations ◽  
Self Duality ◽  
Form Field ◽  
Brane Action

We present an alternative formulation of duality-symmetric 11-dimensional supergravity with both three-form and six-form gauge fields. Instead of the recently-proposed scalar auxiliary field, we use a simpler Lagrangian with a non-propagating auxiliary multiplier tensor field with eight-indices. We also complete the superspace formulation in a duality-symmetric manner. An alternative super M-5-brane action coupled to this 11-dimensional background is also presented. This formulation bypasses the usual obstruction for an invariant Lagrangian for a self-dual three-form field strength, by allowing the self-duality only as a solution for field equations, but not as a necessary condition.

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.

scholarly journals DAVEY-STEWARTSON EQUATION FROM A ZERO CURVATURE AND A SELF-DUALITY CONDITION

1994 ◽  
Vol 09 (14) ◽  
pp. 1267-1272 ◽  
Author(s):  
J.C. BRUNELLI ◽  
ASHOK DAS
Keyword(s):  
The Self ◽  
Curvature Condition ◽  
Self Duality ◽  
Zero Curvature ◽  
Duality Condition

We derive the two equations of Davey-Stewartson type from a zero curvature condition associated with SL(2, ℝ) in (2+1) dimensions. We show in general how a (2+1)dimensional zero curvature condition can be obtained from the self-duality condition in (3+3) dimensions and show in particular how the Davey-Stewartson equations can be obtained from the self-duality condition associated with SL(2, ℝ) in (3+3) dimensions.

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