A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is presented. The gravitational model 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 obeying n ordinary differential equations with certain boundary conditions. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). A program (in Maple) for calculating of these polynomials for classical series of Lie algebras is suggested (see Appendix). The polynomials corresponding to the Lie algebra D 4 are obtained. It is conjectured that the polynomials for A n -, B nand C n -series may be obtained from polynomials for D n+1 -series by using certain reduction formulas.
Using black brane solutions in 5d Lifshitz-like backgrounds with arbitrary dynamical exponent ν, we construct the Vaidya geometry, asymptoting to the Lifshitz-like spacetime, which represents a thin shell infalling at the speed of light. We apply the new Lifshitz-Vaidya background to study the thermalization process of the quark-gluon plasma via the thin shell approach previously successfully used in several backgrounds. We find that the thermalization depends on the chosen direction because of the spatial anisotropy. The plasma thermalizes thus faster in the transversal direction than in the longitudinal one. To probe the system described by the Lifshitz-like backgrounds, we also calculate the holographic entanglement entropy for the subsystems delineated along both transversal and longitudinal directions. We show that the entropy has some universality in the behavior for both subsystems. At the same time, we find that certain characteristics strongly depend on the critical exponent ν.
We study vacua and walls of mass-deformed Kähler nonlinear sigma models on Sp(N )/U (N ). We identify elementary walls with the simple roots of U Sp(2N ) and discuss compressed walls, penetrable walls and multiwalls by using the moduli matrix formalism.Kähler and hyper-Kähler nonlinear sigma models are studied in [1,2,3]. Massive hyper-Kähler nonlinear sigma models have a potential which is proportional to the square of a tri-holomorphic Killing vector field of the hyper-Kähler target space [4]. Fixed points of the Killing vector field are realized as discrete vacua. It was shown that there exist 1/2 supersymmetric kink solutions that interpolate the discrete vacua [5]. A more general potential is possible for a hyper-Kähler target space of quaternionic dimension two or more, and exact non-singular solutions representing intersecting domain walls are constructed in [6]. Multi-domain walls are studied in [7].The moduli matrix formalism [8,9] was proposed to construct walls systematically in non-Abelian gauge theories with N = 2 supersymmetry in four-dimensional spacetime. The model considered in [8,9] becomes massive hyper-Kähler nonlinear sigma models on the cotangent bundle over the Grassmann manifold T * G N F ,N C 1 when the gauge coupling is taken to be infinity. In this limit, multiwalls are constructed as well as single walls. Multiwalls are along one spatial direction and their positions depend on moduli parameters and mass parameters. Walls can be compressed to single walls by changing moduli parameters in Abelian gauge theories and in non-Abelian gauge theories. These walls are called compressed walls. A distinguishing feature in the non-Abelian gauge theories is that walls can pass through each other [9]. Such walls are called penetrable walls. It was also shown in [9] that there is a bundle structure for nondegenerate masses, so that the vacua and the walls are on the Kähler manifold.The walls of Kähler nonlinear sigma models on SO(2N )/U (N ) are studied in [10,11]. The Hermitian symmetric space SO(2N )/U (N ) is realized as a quadric in the Grassmann manifold G 2N,N in accordance with [12,13]. As SO(4)/U (2) CP 1 and SO(6)/U (3) CP 3 [14], the nonlinear sigma models on SO(2N )/U (N ) with N = 2 and N = 3 are actually Abelian gauge theories. The walls of the nonlinear sigma models on SO(2N )/U (N ) with N = 2, 3 are studied in [10]. The walls of the nonlinear sigma models on SO(2N )/U (N ) for any N are studied in [11]. Penetrable walls, which are related to non-Abelian nature, appear in N ≥ 4 cases. The vacua and the walls of N ≤ 7 cases are presented in pictorial representations where vacua and elementary walls correspond to the vertices and the segments of the representations. It is shown that there is a recurrence of a two dimensional diagram for each N mod 4 in the vacuum structures that are connected to the maximum number of elementary walls. The vacuum structures are proved by induction.The purpose of this paper is to construct walls of mass-deformed Kähler nonlinear sigmaSU (N C )×SU (N F −N C...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.