MULTI-INSTANTON SOLUTIONS IN EIGHT-DIMENSIONAL CURVED SPACE

Starting from an SO(8)± Yang-Mills field Fab, a four-index antisymmetric, non-Abelian field Fabcd is defined. It is shown that this field satisfies a self-duality relation in eight-dimensional curved space and that its action integral is proportional to n, the winding number of the mapping from S8 onto S8 given by the octonionic transformation x→w=xn.

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Self-Duality and Energy of Solutions for the Sourceless Yang-Mills Field Equation

Progress of Theoretical Physics ◽

10.1143/ptp.59.671 ◽

1978 ◽

Vol 59 (2) ◽

pp. 671-672 ◽

Cited By ~ 3

Author(s):

C. H. Oh ◽

S. Murugesu

Keyword(s):

Field Equation ◽

Yang Mills ◽

Self Duality ◽

Mills Field

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One-loop renormalization of the Yang-Mills field theory in a curved space-time

Soviet Physics Journal ◽

10.1007/bf01882976 ◽

1983 ◽

Vol 26 (4) ◽

pp. 359-361 ◽

Cited By ~ 2

Author(s):

I. L. Bukhbinder ◽

S. D. Odintsov

Keyword(s):

Field Theory ◽

Space Time ◽

Curved Space ◽

Yang Mills ◽

Mills Field

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

Modern Physics Letters A ◽

10.1142/s0217732392001816 ◽

1992 ◽

Vol 07 (23) ◽

pp. 2077-2085 ◽

Cited By ~ 17

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.

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

Journal of High Energy Physics ◽

10.1007/jhep09(2020)133 ◽

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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