Finite N=1 supersymmetric theories of classical groups

The motivation for supersymmetry. The algebra, the superspace, and the representations. Field theory models and the non-renormalisation theorems. Spontaneous and explicit breaking of super-symmetry. The generalisation of the Montonen–Olive duality conjecture in supersymmetric theories. The remarkable properties of extended supersymmetric theories. A brief discussion of twisted supersymmetry in connection with topological field theories. Attempts to build a supersymmetric extention of the standard model and its experimental consequences. The property of gauge supersymmetry to include general relativity and the supergravity models.

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TOPOLOGICAL NOETHERIANITY FOR ALGEBRAIC REPRESENTATIONS OF INFINITE RANK CLASSICAL GROUPS

Transformation Groups ◽

10.1007/s00031-021-09656-x ◽

2021 ◽

Author(s):

R. H. EGGERMONT ◽

A. SNOWDEN

Keyword(s):

Classical Groups ◽

Infinite Rank ◽

Polynomial Representations ◽

Algebraic Representations

AbstractDraisma recently proved that polynomial representations of GL∞ are topologically noetherian. We generalize this result to algebraic representations of infinite rank classical groups.

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Killing superalgebras for lorentzian five-manifolds

Journal of High Energy Physics ◽

10.1007/jhep07(2021)209 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Andrew Beckett ◽

José Figueroa-O’Farrill

Keyword(s):

Spin Manifold ◽

Field Equations ◽

Spinor Bundle ◽

Killing Spinors ◽

Spinor Connection ◽

Spencer Cohomology ◽

Definition Of ◽

Supersymmetric Theories ◽

Filtered Deformations

Abstract We calculate the relevant Spencer cohomology of the minimal Poincaré superalgebra in 5 spacetime dimensions and use it to define Killing spinors via a connection on the spinor bundle of a 5-dimensional lorentzian spin manifold. We give a definition of bosonic backgrounds in terms of this data. By imposing constraints on the curvature of the spinor connection, we recover the field equations of minimal (ungauged) 5-dimensional supergravity, but also find a set of field equations for an $$ \mathfrak{sp} $$ sp (1)-valued one-form which we interpret as the bosonic data of a class of rigid supersymmetric theories on curved backgrounds. We define the Killing superalgebra of bosonic backgrounds and show that their existence is implied by the field equations. The maximally supersymmetric backgrounds are characterised and their Killing superalgebras are explicitly described as filtered deformations of the Poincaré superalgebra.

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