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(Anti)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory
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Titel: |
(Anti)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory |
In: | Advances in High Energy Physics, 2017, 2017, S. 1-14 |
veröffentlicht: |
Hindawi Limited
|
Umfang: | 1-14 |
ISSN: |
1687-7357 1687-7365 |
DOI: | 10.1155/2017/6138263 |
Zusammenfassung: | <jats:p>We exploit the beauty and strength of the symmetry invariant restrictions on the (anti)chiral superfields to derive the Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST, and (anti-)co-BRST symmetry transformations in the case of a two <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:mn fontstyle="italic">1</mml:mn><mml:mo>+</mml:mo><mml:mn fontstyle="italic">1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>-dimensional (2<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math>) self-dual chiral bosonic field theory within the framework of augmented (anti)chiral superfield formalism. Our 2<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math> ordinary theory is generalized onto a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mo stretchy="false">(</mml:mo><mml:mn fontstyle="italic">2,2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>-dimensional supermanifold which is parameterized by the superspace variable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:msup><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mfenced separators="|"><mml:mrow><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mi>θ</mml:mi><mml:mo>,</mml:mo><mml:mover accent="false"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:mrow></mml:mfenced></mml:math>, where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math> (with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mi>μ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0,1</mml:mn></mml:math>) are the ordinary 2<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math> bosonic coordinates and (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mml:mi>θ</mml:mi><mml:mo>,</mml:mo><mml:mover accent="false"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:math>) are a pair of Grassmannian variables with their standard relationships: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M10"><mml:msup><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mover accent="false"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M11"><mml:mi>θ</mml:mi><mml:mover accent="false"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover><mml:mo>+</mml:mo><mml:mover accent="false"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover><mml:mi>θ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:math>. We impose the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti)chiral superfields (defined on the (anti)chiral <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M12"><mml:mo stretchy="false">(</mml:mo><mml:mn fontstyle="italic">2,1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>-dimensional supersubmanifolds of the above<jats:italic> general </jats:italic><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M13"><mml:mo stretchy="false">(</mml:mo><mml:mn fontstyle="italic">2,2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>-dimensional supermanifold) to derive the above nilpotent symmetries. We do not exploit the mathematical strength of the (dual-)horizontality conditions<jats:italic> anywhere</jats:italic> in our present investigation. We also discuss the properties of nilpotency, absolute anticommutativity, and (anti-)BRST and (anti-)co-BRST symmetry invariance of the Lagrangian density within the framework of our augmented (anti)chiral superfield formalism. Our observation of the absolute anticommutativity property is a completely<jats:italic> novel</jats:italic> result in view of the fact that we have considered<jats:italic> only</jats:italic> the (anti)chiral superfields in our present endeavor.</jats:p> |
Format: | E-Article |
Quelle: | Hindawi Limited (CrossRef) |
Sprache: | Englisch |