Remark on the consistent gauge anomaly in supersymmetric theories

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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Supersymmetric gauge anomaly with general homotopic paths

Nuclear Physics B ◽

10.1016/s0550-3213(00)00676-3 ◽

2001 ◽

Vol 596 (1-2) ◽

pp. 315-347 ◽

Cited By ~ 12

Author(s):

S.James Gates ◽

Marcus T. Grisaru ◽

Marcia E. Knutt ◽

Silvia Penati ◽

Hiroshi Suzuki

Keyword(s):

Supersymmetric Gauge ◽

Gauge Anomaly

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A note on gauge anomaly cancellation in effective field theories

Journal of High Energy Physics ◽

10.1007/jhep03(2021)128 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Ferruccio Feruglio

Keyword(s):

Effective Field Theories ◽

Effective Field ◽

Field Theories ◽

Anomaly Cancellation ◽

Charge Assignment ◽

The Standard Model ◽

Renormalizable Theory ◽

Complete Set ◽

Gauge Anomalies ◽

Gauge Anomaly

Abstract The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.

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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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