CONFORMALLY COVARIANT DRESSING TRANSFORMATIONS FOR SUPER SELF-DUALITY EQUATIONS IN D=4

1989 ◽  
Vol 04 (10) ◽  
pp. 971-982
Author(s):  
J. AVAN
Keyword(s):  
Linear System ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Yang Mills ◽  
Self Duality ◽  
Loop Algebras ◽  
Field Dependent

A set of conformally covariant dressing transformations is constructed for the supersym-metric N=3 self-duality equations in four dimensions, using the associated covariant linear system. They form a closed, 5+6-index algebra, up to field-dependent gauge transformations, containing the previously known loop algebras as a particular subset. This construction generalizes the formerly built set of conformally covariant DT for ordinary self-dual Yang-Mills.

scholarly journals DOUBLET GROUPS, EXTENDED LIE ALGEBRAS, AND WELL DEFINED GAUGE THEORIES FOR THE TWO-FORM FIELD

2005 ◽  
Vol 20 (12) ◽  
pp. 2673-2685 ◽  
Author(s):  
MARCELO BOTTA CANTCHEFF
Keyword(s):  
Lie Algebras ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Yang Mills ◽  
Nonassociative Algebras ◽  
Form Field ◽  
Tensor Current ◽  
Chern Simons ◽  
Matter Fields ◽  
General Connection

We propose a symmetry law for a doublet of different form fields, which resembles gauge transformations for matter fields. This may be done for general Lie groups, resulting in an extension of Lie algebras and group manifolds. It is also shown that nonassociative algebras naturally appear in this formalism, which are briefly discussed. Afterwards, a general connection which includes a two-form field is settled-down, solving the problem of setting a gauge theory for the Kalb–Ramond field for generical groups. Topological Chern–Simons theories can also be defined in four dimensions, and this approach clarifies their relation to the so-called B ∧ F theories. We also revise some standard aspects of Kalb–Ramond theories in view of these new perspectives. Since this gauge connection is built upon a pair of fields consisting of a one-form and a two-form, one may define Yang–Mills theories as usually and, remarkably, also minimal coupling with bosonic matter, where the Kalb–Ramond field appears naturally as mediator; so, a new associated conserved charge can be defined. For the Abelian case, we explicitly construct the minimal interaction between B-field and matter following a "gauge principle" and find a novel conserved tensor current. This is our most significative result from the physical viewpoint. This framework is also generalized in such a way that any p-rank tensor may be formulated as a gauge field.

scholarly journals Note on the bundle geometry of field space, variational connections, the dressing field method, & presymplectic structures of gauge theories over bounded regions

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
J. François ◽  
N. Parrini ◽  
N. Boulanger
Keyword(s):  
Gauge Theories ◽  
Field Method ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Field Independent ◽  
Field Dependent ◽  
Presymplectic Structure ◽  
The One ◽  
Phase Space Methods ◽  
Special Case

Abstract In this note, we consider how the bundle geometry of field space interplays with the covariant phase space methods so as to allow to write results of some generality on the presymplectic structure of invariant gauge theories coupled to matter. We obtain in particular the generic form of Noether charges associated with field-independent and field-dependent gauge parameters, as well as their Poisson bracket. We also provide the general field-dependent gauge transformations of the presymplectic potential and 2-form, which clearly highlights the problem posed by boundaries in generic situations. We then conduct a comparative analysis of two strategies recently considered to evade the boundary problem and associate a modified symplectic structure to a gauge theory over a bounded region: namely the use of edge modes on the one hand, and of variational connections on the other. To do so, we first try to give the clearest geometric account of both, showing in particular that edge modes are a special case of a differential geometric tool of gauge symmetry reduction known as the “dressing field method”. Applications to Yang-Mills theory and General Relativity reproduce or generalise several results of the recent literature.

CONFORMALLY COVARIANT APPROACH TO THE INTEGRABILITY OF SDYM: LINEAR SYSTEM, β-PLANES, INFINITESIMAL BÄCKLUND TRANSFORMATIONS AND INFINITE-DIMENSIONAL ALGEBRAS

1988 ◽  
Vol 03 (05) ◽  
pp. 1263-1299 ◽  
Author(s):  
J. AVAN ◽  
H.J. de VEGA
Keyword(s):  
Linear System ◽  
The Self ◽  
Bäcklund Transformations ◽  
Dimensional Algebra ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
System A ◽  
Backlund Transformations ◽  
Field Dependent ◽  
Arbitrary Analytic Function

The self-dual Yang-Mills theory is investigated with the help of a new conformally covariant linear system, where the spectral parameter is a projective twistor [Formula: see text]. We derive from this linear system conformally covariant families of β-planes, on which the potential Aµ(x) is a pure gauge. They are parametrized by a dual projective twistor [Formula: see text], orthogonal to the spectral twistor Λ. Conformally covariant infinitesimal Bäcklund transformations (B.T.) are constructed for the gauge group [Formula: see text] or [Formula: see text], and for SU (N). They are characterized by (1) a Lie-algebra index 1≤a≤ dim g; (2) the spectral twistor Λ; (3) a second twistor index 1≤α≤4, (independent of Λ); (4) an arbitrary (analytic) function of the two independent solutions of the free linear system (Aµ=0). The algebra of these infinitesimal B.T. is computed. It turns to close up to a field-dependent gauge transformation, which vanishes for equal twistor indices. The reduction of the number of components of Λ to a single projective parameter [Formula: see text] leads to a loop algebra. In general it yields an infinite-dimensional algebra with five indices.

scholarly journals OFF-SHELL FORMULATION OF N=2 SUPER YANG-MILLS THEORIES COUPLED TO MATTER WITHOUT AUXILIARY FIELDS

1995 ◽  
Vol 10 (27) ◽  
pp. 3937-3950 ◽  
Author(s):  
NICOLA MAGGIORE
Keyword(s):  
Equations Of Motion ◽  
Dimensional Algebra ◽  
Nilpotent Operator ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Field Dependent ◽  
External Sources ◽  
Shell Formulation

N=2 supersymmetric Yang-Mills theories coupled to matter are considered in the Wess-Zumino gauge. The supersymmetries are realized nonlinearly and the anticommutator between two susy charges gives, in addition to translations, gauge transformations and equations of motion. The difficulties hidden in such an algebraic structure are well known: almost always auxiliary fields can be introduced in order to put the formalism off-shell, but still the field-dependent gauge transformations give rise to an infinite-dimensional algebra quite hard to deal with. However, it is possible to avoid all these problems by collecting into a unique nilpotent operator all the symmetries defining the theory, namely ordinary BRS, supersymmetries and translations. According to this method the role of the auxiliary fields is covered by the external sources coupled, as usual, to the nonlinear variations of the quantum fields. The analysis is then formally reduced to that of ordinary Yang-Mills theory.

SELF-DUALITY AND N=2 STRING MAGIC

1990 ◽  
Vol 05 (18) ◽  
pp. 1389-1398 ◽  
Author(s):  
HIROSI OOGURI ◽  
CUMRUN VAFA
Keyword(s):  
String Theory ◽  
Critical Dimension ◽  
Degree Of Freedom ◽  
Superconformal Symmetry ◽  
Four Dimensions ◽  
Yang Mills ◽  
Self Duality ◽  
Complex Dimensions ◽  
Physical Degree

We consider strings with an N=2 local superconformal symmetry on the worldsheet. The critical dimension for this theory is four (two complex dimensions) with the signature (2, 2). A Kähler function giving rise to self-dual gravity is the only physical degree of freedom of this theory. Some miraculous symmetries are observed corresponding to the exchange of worldsheet and target moduli. The open and heterotic versions of this string theory correspond to self-dual Yang-Mills fields coupled to self-dual gravity 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.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

scholarly journals New bi-harmonic superspace formulation of 4D, $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
V. A. Ivanovskiy
Keyword(s):  
Effective Action ◽  
Harmonic Superspace ◽  
Four Dimensions ◽  
Yang Mills ◽  
Convenient Tool ◽  
Leading Term

Abstract We develop a novel bi-harmonic $$ \mathcal{N} $$ N = 4 superspace formulation of the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $$ \mathcal{N} $$ N = 4 SYM superfield constraints are solved in terms of on-shell $$ \mathcal{N} $$ N = 2 harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly $$ \mathcal{N} $$ N = 4 supersymmetric invariants and further rewriting them in $$ \mathcal{N} $$ N = 2 harmonic superspace. In particular, we present $$ \mathcal{N} $$ N = 4 superfield form of the leading term in the $$ \mathcal{N} $$ N = 4 SYM effective action which was known previously in $$ \mathcal{N} $$ N = 2 superspace formulation.

scholarly journals Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Guido Festuccia ◽  
Anastasios Gorantis ◽  
Antonio Pittelli ◽  
Konstantina Polydorou ◽  
Lorenzo Ruggeri
Keyword(s):  
Vector Field ◽  
Extended Supersymmetry ◽  
General Framework ◽  
Gauge Theories ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Explicit Result ◽  
Yang Mills ◽  
Self Duality ◽  
Witten Theory

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

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