Gauged twistor spinors and symmetry operators

Journal of Mathematical Physics

2018

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Symmetry operators of twistor spinors and harmonic spinors can be constructed from conformal Killing-Yano forms. Transformation operators relating twistors to harmonic spinors are found in terms of potential forms. These constructions are generalized to gauged twistor spinors and gauged harmonic spinors. The operators that transform gauged twistor spinors to gauged harmonic spinors are found. Symmetry operators of gauged harmonic spinors in terms of conformal Killing-Yano forms are obtained. Algebraic conditions to obtain solutions of the Seiberg-Witten equations are discussed.

“…is a symmetry operator for the gauged twistor spinors which is proved in [14]. This is only true for constant curvature manifolds and in that case we have flat connections with F = 0.…”

Section: Gauged Twistors To Gauged Harmonic Spinorsmentioning

confidence: 94%

“…(71), the integrability conditions of the gauged twistor equation can be obtained. The resulting integrability conditions are given as follows [14]…”

Section: Gauged Twistors To Gauged Harmonic Spinorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Harmonic spinors from twistors and potential forms

Journal of Mathematical Physics

2018

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“…e a − P a (8) and its components correspond to the Schouten tensor. C ab are conformal 2-forms which are written in terms of the curvature characteristics and defined for n > 2 as…”

Section: Spin Changing Operators For Massless Field Equationsmentioning

confidence: 99%

“…Supersymmetry generators of both superconformal field theories in curved backgrounds and conformal supergravity theories correspond to twistor spinors [2][3][4][5]. They are also used in the construction of extended conformal superalgebras and are related to the conformal hidden symmetries of a background that are conformal Killing-Yano forms [6][7][8][9]. Twistor spinors contain Killing spinors and parallel spinors as special cases which are supersymmetry generators of supersymmetric field theories and supergravity theories.…”

Section: Introductionmentioning

confidence: 99%

Spin raising and lowering operators for Rarita-Schwinger fields

Açık

2018

Phys. Rev. D

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Spin raising and lowering operators for massless field equations constructed from twistor spinors are considered. Solutions of the spin-3 2 massless Rarita-Schwinger equation from source-free Maxwell fields and twistor spinors are constructed. It is shown that this construction requires Ricci-flat backgrounds due to the gauge invariance of the massless Rarita-Schwinger equation. Constraints to construct spin raising and lowering operators for Rarita-Schwinger fields are found. Symmetry operators for Rarita-Schwinger fields via twistor spinors are obtained.

Twistor spinors and extended conformal superalgebras

Journal of Geometry and Physics

2020

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We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in constant curvature backgrounds and from normal conformal Killing-Yano forms in Einstein manifolds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting symmetry operators of twistor spinors. Conformal superalgebras which consist of conformal Killing vectors and twistor spinors and play important roles in supersymmetric field theories in conformal backgrounds are extended to more general superalgebras by using the graded Lie algebra structure of conformal Killing-Yano forms and the symmetry operators of twistor spinors. The even part of the extended conformal superalgebra corresponds to conformal Killing-Yano forms and the odd part consists of twistor spinors.