Black brane solutions governed by fluxbrane polynomials

Ivashchuk, V. D.

doi:10.1016/j.geomphys.2014.07.015

Cited by 23 publications

(37 citation statements)

References 37 publications

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“…Note that the parameters γ = (γ 1 , γ 2 ) are nothing but the components of the dual Weyl vector for given Lie algebra with the Cartan matrix (18). They may be represented in a explicitly symmetric form with respect to the discrete S-duality (16):…”

Section: Toda Representationmentioning

confidence: 99%

Higher-n triangular dilatonic black holes

2018

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Dilaton gravity with the form fields is known to possess dyon solutions with two horizons for the discrete ("triangular") values of the dilaton coupling constant a = n(n + 1)/2. From this sequence only n = 1, 2 members were known analytically so far. We present two new n = 3, 5 triangular solutions for the theory with different dilaton couplings a, b in electric and magnetic sectors in which case the quantization condition reads ab = n(n + 1)/2. These are derived via the Toda chains for B 2 and G 2 Lie algebras. Solutions are found in the closed form in general D space-time dimensions. They satisfy the entropy product rules and have negative binding energy in the extremal case.

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Section: Toda Representationmentioning

confidence: 99%

Higher-n triangular dilatonic black holes

2018

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“…We note that fluxbrane "master equations" (245) may be obtained from the black brane ones (246) in the limit µ → ∞ . In [166], it was shown that black brane moduli functions may be obtained from fluxbrane ones at least for small enough charge densities. For different aspects of p-brane/fluxbrane correspondence, see [152,158].…”

Section: Of 54mentioning

confidence: 99%

On Brane Solutions with Intersection Rules Related to Lie Algebras

Ivashchuk

2017

Symmetry

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Abstract:The review is devoted to exact solutions with hidden symmetries arising in a multidimensional gravitational model containing scalar fields and antisymmetric forms. These solutions are defined on a manifold of the form M = M 0 × M 1 × . . . × M n , where all M i with i ≥ 1 are fixed Einstein (e.g., Ricci-flat) spaces. We consider a warped product metric on M . Here, M 0 is a base manifold, and all scale factors (of the warped product), scalar fields and potentials for monomial forms are functions on M 0 . The monomial forms (of the electric or magnetic type) appear in the so-called composite brane ansatz for fields of forms. Under certain restrictions on branes, the sigma-model approach for the solutions to field equations was derived in earlier publications with V.N.Melnikov. The sigma model is defined on the manifold M 0 of dimension d 0 = 2 . By using the sigma-model approach, several classes of exact solutions, e.g., solutions with harmonic functions, S-brane, black brane and fluxbrane solutions, are obtained. For d 0 = 1 , the solutions are governed by moduli functions that obey Toda-like equations. For certain brane intersections related to Lie algebras of finite rank-non-singular Kac-Moody (KM) algebras-the moduli functions are governed by Toda equations corresponding to these algebras. For finite-dimensional semi-simple Lie algebras, the Toda equations are integrable, and for black brane and fluxbrane configurations, they give rise to polynomial moduli functions. Some examples of solutions, e.g., corresponding to finite dimensional semi-simple Lie algebras, hyperbolic KM algebras: H 2 (q, q) , AE 3 , H A (1) 2 , E 10 and Lorentzian KM algebra P 10 , are presented.

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“…Here as in [38] we parametrize the polynomials by using other parameters (here denoted B s ) instead of P s :…”

Section: Fluxbrane Polynomials For Lie Algebra Ementioning

confidence: 99%

“…The set of fluxbrane polynomials H s defines a special solution to open Toda chain equations [36,37] corresponding to a simple finite-dimensional Lie algebra G; see Ref. [38]. In Refs.…”

Section: Introductionmentioning

confidence: 99%

On generalized Melvin solution for the Lie algebra $$E_6$$ E 6

Bolokhov

Ivashchuk

2017

Eur. Phys. J. C

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A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model in D dimensions, D ≥ 4, contains n 2-forms and l ≥ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions H s (z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials H s (z), s = 1, . . . , 6, for the Lie algebra E 6 are obtained and a corresponding solution for l = n = 6 is presented. The polynomials depend upon integration constants Q s , s = 1, . . . , 6. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for E 6 -polynomials at large z are governed by the integer-valued matrix ν = A −1 (I + P), where A −1 is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the Z 2 -group of symmetry of the Dynkin diagram. The 2-form fluxes s , s = 1, . . . , 6, are calculated.

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Black brane solutions governed by fluxbrane polynomials

Cited by 23 publications

References 37 publications

Higher-n triangular dilatonic black holes

Higher-n triangular dilatonic black holes

On Brane Solutions with Intersection Rules Related to Lie Algebras

On generalized Melvin solution for the Lie algebra $$E_6$$ E 6

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