On the Vacuum Structure of the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Conformal Supergravity
We consider <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math><...
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| Main Authors: | , , , |
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| Format: | article |
| Language: | EN |
| Published: |
MDPI AG
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/b9196fa6a62747739d23a6e66620fbd1 |
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| Summary: | We consider <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> conformal supergravity with an arbitrary holomorphic function of the complex scalar <i>S</i> which parametrizes the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>/</mo><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> coset. Assuming non-vanishings vevs for <i>S</i> and the scalars in a symmetric matrix <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></semantics></math></inline-formula> of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mn mathvariant="bold">10</mn><mo>¯</mo></mover></semantics></math></inline-formula> of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><mo>)</mo></mrow></semantics></math></inline-formula> R-symmetry group, we determine the vacuum structure of the theory. We find that the possible vacua are classified by the number of zero eigenvalues of the scalar matrix and the spacetime is either Minkowski, de Sitter, or anti-de Sitter. We determine the spectrum of the scalar fluctuations and we find that it contains tachyonic states which, however, can be removed by appropriate choice of the unspecified at the supergravity level holomorphic function. Finally, we also establish that <i>S</i>-supersymmetry is always broken whereas <i>Q</i>-supersymmetry exists only on flat Minkowski spacetime. |
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