Manifestly-invariant action for self-dual supersymmetric Yang-Mills theories coupled to auxiliary supergravity
We propose a new action-formulation for the N=(1,1) multiplet (AμI,λI) of a self-dual (SD) supersymmetric Yang-Mills (YM) theory in D=2+2 dimensions using an auxiliary supergravity multiplet. We first consider non-supersymmetric case with constraint lagrangians that restrict the metric gμν to be (ημ...
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| Format: | Article |
| Language: | English |
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Elsevier
2020-05-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321320300791 |
| _version_ | 1819265350768787456 |
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| author | Hitoshi Nishino Subhash Rajpoot |
| author_facet | Hitoshi Nishino Subhash Rajpoot |
| author_sort | Hitoshi Nishino |
| collection | DOAJ |
| description | We propose a new action-formulation for the N=(1,1) multiplet (AμI,λI) of a self-dual (SD) supersymmetric Yang-Mills (YM) theory in D=2+2 dimensions using an auxiliary supergravity multiplet. We first consider non-supersymmetric case with constraint lagrangians that restrict the metric gμν to be (ημν)=diag.(+,+,−,−). We add the kinetic-term of a purely-bosonic YM-field, and show that the YM-field in the D=2+2 space-time allows only SD or anti-SD (ASD) configurations. In other words, the condition of vanishing energy-momentum (EM) tensor restricts the YM-field to be either SD or ASD, but not an admixture of them. Finally, we generalize this result to N=(1,1) supersymmetric YM multiplet (AμI,λI;DI) in D=2+2 with the off-shell supergravity multiplet (eμm,ψμ;S,P,am) as an ‘auxiliary’ multiplet without its kinetic terms. Special constraint lagrangians restrict the supergravity multiplet to be auxiliary, i.e., both the Riemann-tensor and the gravitino field strength to vanish. We show that the eμm and ψμ-field equations produce the vanishings of both the EM-tensor and spinor-current, which in turn lead only to either SD or ASD supersymmetric YM multiplet, as the only Lorentz and gauge-covariant supersymmetric solutions. A broad class of similar action-formulations with auxiliary supergravity multiplets yielding SD or ASD systems in D=2+2 or higher-dimensions may be constructed in a similar fashion. |
| first_indexed | 2024-12-23T20:43:59Z |
| format | Article |
| id | doaj.art-e2c9e9b75a394100a584df44dfc0e78c |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-23T20:43:59Z |
| publishDate | 2020-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-e2c9e9b75a394100a584df44dfc0e78c2022-12-21T17:31:51ZengElsevierNuclear Physics B0550-32132020-05-01954Manifestly-invariant action for self-dual supersymmetric Yang-Mills theories coupled to auxiliary supergravityHitoshi Nishino0Subhash Rajpoot1Corresponding author.; Department of Physics & Astronomy, California State University, 1250 Bellflower Boulevard, Long Beach, CA 90840, United States of AmericaDepartment of Physics & Astronomy, California State University, 1250 Bellflower Boulevard, Long Beach, CA 90840, United States of AmericaWe propose a new action-formulation for the N=(1,1) multiplet (AμI,λI) of a self-dual (SD) supersymmetric Yang-Mills (YM) theory in D=2+2 dimensions using an auxiliary supergravity multiplet. We first consider non-supersymmetric case with constraint lagrangians that restrict the metric gμν to be (ημν)=diag.(+,+,−,−). We add the kinetic-term of a purely-bosonic YM-field, and show that the YM-field in the D=2+2 space-time allows only SD or anti-SD (ASD) configurations. In other words, the condition of vanishing energy-momentum (EM) tensor restricts the YM-field to be either SD or ASD, but not an admixture of them. Finally, we generalize this result to N=(1,1) supersymmetric YM multiplet (AμI,λI;DI) in D=2+2 with the off-shell supergravity multiplet (eμm,ψμ;S,P,am) as an ‘auxiliary’ multiplet without its kinetic terms. Special constraint lagrangians restrict the supergravity multiplet to be auxiliary, i.e., both the Riemann-tensor and the gravitino field strength to vanish. We show that the eμm and ψμ-field equations produce the vanishings of both the EM-tensor and spinor-current, which in turn lead only to either SD or ASD supersymmetric YM multiplet, as the only Lorentz and gauge-covariant supersymmetric solutions. A broad class of similar action-formulations with auxiliary supergravity multiplets yielding SD or ASD systems in D=2+2 or higher-dimensions may be constructed in a similar fashion.http://www.sciencedirect.com/science/article/pii/S0550321320300791 |
| spellingShingle | Hitoshi Nishino Subhash Rajpoot Manifestly-invariant action for self-dual supersymmetric Yang-Mills theories coupled to auxiliary supergravity Nuclear Physics B |
| title | Manifestly-invariant action for self-dual supersymmetric Yang-Mills theories coupled to auxiliary supergravity |
| title_full | Manifestly-invariant action for self-dual supersymmetric Yang-Mills theories coupled to auxiliary supergravity |
| title_fullStr | Manifestly-invariant action for self-dual supersymmetric Yang-Mills theories coupled to auxiliary supergravity |
| title_full_unstemmed | Manifestly-invariant action for self-dual supersymmetric Yang-Mills theories coupled to auxiliary supergravity |
| title_short | Manifestly-invariant action for self-dual supersymmetric Yang-Mills theories coupled to auxiliary supergravity |
| title_sort | manifestly invariant action for self dual supersymmetric yang mills theories coupled to auxiliary supergravity |
| url | http://www.sciencedirect.com/science/article/pii/S0550321320300791 |
| work_keys_str_mv | AT hitoshinishino manifestlyinvariantactionforselfdualsupersymmetricyangmillstheoriescoupledtoauxiliarysupergravity AT subhashrajpoot manifestlyinvariantactionforselfdualsupersymmetricyangmillstheoriescoupledtoauxiliarysupergravity |