Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4
We consider generalized Melvin-like solutions associated with nonexceptional Lie algebras of rank 4 (namely, A4, B4, C4, and D4) corresponding to certain internal symmetries of the solutions. The system under consideration is a static cylindrically symmetric gravitational configuration in D dimensio...
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2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/8179570 |
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| author | S. V. Bolokhov V. D. Ivashchuk |
| author_facet | S. V. Bolokhov V. D. Ivashchuk |
| author_sort | S. V. Bolokhov |
| collection | DOAJ |
| description | We consider generalized Melvin-like solutions associated with nonexceptional Lie algebras of rank 4 (namely, A4, B4, C4, and D4) corresponding to certain internal symmetries of the solutions. The system under consideration is a static cylindrically symmetric gravitational configuration in D dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions Hs(z) (s=1,…,4) of squared radial coordinate z=ρ2 obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers (n1,n2,n3,n4)=(4,6,6,4),(8,14,18,10),(7,12,15,16),(6,10,6,6) for Lie algebras A4, B4, C4, and D4, respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued 4×4 matrix ν connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in A4 case) the matrix representing a generator of the Z2-group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances. We also calculate 2-form flux integrals over 2-dimensional discs and corresponding Wilson loop factors over their boundaries. |
| format | Article |
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| institution | Kabale University |
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| language | English |
| publishDate | 2018-01-01 |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-3cf3f6d5946b4fd7be747c93809d40a52025-02-03T01:24:58ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/81795708179570Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4S. V. Bolokhov0V. D. Ivashchuk1Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., Moscow 117198, RussiaInstitute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., Moscow 117198, RussiaWe consider generalized Melvin-like solutions associated with nonexceptional Lie algebras of rank 4 (namely, A4, B4, C4, and D4) corresponding to certain internal symmetries of the solutions. The system under consideration is a static cylindrically symmetric gravitational configuration in D dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions Hs(z) (s=1,…,4) of squared radial coordinate z=ρ2 obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers (n1,n2,n3,n4)=(4,6,6,4),(8,14,18,10),(7,12,15,16),(6,10,6,6) for Lie algebras A4, B4, C4, and D4, respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued 4×4 matrix ν connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in A4 case) the matrix representing a generator of the Z2-group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances. We also calculate 2-form flux integrals over 2-dimensional discs and corresponding Wilson loop factors over their boundaries.http://dx.doi.org/10.1155/2018/8179570 |
| spellingShingle | S. V. Bolokhov V. D. Ivashchuk Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4 Advances in Mathematical Physics |
| title | Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4 |
| title_full | Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4 |
| title_fullStr | Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4 |
| title_full_unstemmed | Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4 |
| title_short | Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4 |
| title_sort | duality identities for moduli functions of generalized melvin solutions related to classical lie algebras of rank 4 |
| url | http://dx.doi.org/10.1155/2018/8179570 |
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