N=4 supersymmetric Schwarzian with D(1,2;α) symmetry

Nikolay Kozyrev (Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia) ; Sergey Krivonos (Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia)

It was recently demonstrated that super-Schwarzian derivatives can be constructed from the Cartan forms of the superconformal supergroups OSp(1|2), SU(1,1|1), OSp(3|2), SU(1,1|2). Roughly speaking, the super-Schwarzian is just the component of the corresponding Cartan forms with the lowest dimension. In this paper, we apply the same approach to superalgebra D(1,2;α). The minimal set of constraints we used includes: (a) introducing new superspace coordinates the Cartan forms depend on, which are completely invariant with respect to the corresponding group; (b) nullifying the form for dilatation. In contrast to the SU(1,1|2) case, the new super-Schwarzian appears to be a dθia component of the form for su(2) automorphism.

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      "source": "APS", 
      "title": "<math><mi>N</mi><mo>=</mo><mn>4</mn></math> supersymmetric Schwarzian with <math><mi>D</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>;</mo><mi>\u03b1</mi><mo>)</mo></math> symmetry"
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  "abstracts": [
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      "source": "APS", 
      "value": "It was recently demonstrated that super-Schwarzian derivatives can be constructed from the Cartan forms of the superconformal supergroups <math><mrow><mi>O</mi><mi>S</mi><mi>p</mi><mo>(</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></mrow></math>, <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>|</mo><mn>1</mn><mo>)</mo></mrow></math>, <math><mrow><mi>O</mi><mi>S</mi><mi>p</mi><mo>(</mo><mn>3</mn><mo>|</mo><mn>2</mn><mo>)</mo></mrow></math>, <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></mrow></math>. Roughly speaking, the super-Schwarzian is just the component of the corresponding Cartan forms with the lowest dimension. In this paper, we apply the same approach to superalgebra <math><mi>D</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>;</mo><mi>\u03b1</mi><mo>)</mo></math>. The minimal set of constraints we used includes: (a) introducing new superspace coordinates the Cartan forms depend on, which are completely invariant with respect to the corresponding group; (b) nullifying the form for dilatation. In contrast to the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></math> case, the new super-Schwarzian appears to be a <math><mi>d</mi><msup><mi>\u03b8</mi><mrow><mi>i</mi><mi>a</mi></mrow></msup></math> component of the form for <math><mi>s</mi><mi>u</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> automorphism."
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Published on:
19 April 2022
Publisher:
APS
Published in:
Physical Review D , Volume 105 (2022)
Issue 8
DOI:
https://doi.org/10.1103/PhysRevD.105.085010
arXiv:
2112.14481
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

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