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Register a new userM-theory as a dynamical system generator
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Added by
Georgios Linardopoulos
Publication date
2020
fields
Physics
and research's language is
English
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We review our recent work on ellipsoidal M2-brane solutions in the large-N limit of the BMN matrix model. These bosonic finite-energy membranes live inside SO(3)xSO(6) symmetric plane-wave spacetimes and correspond to local extrema of the energy functional. They are static in SO(3) and stationary in SO(6). Chaos appears at the level of radial stability analysis through the explicitly derived spectrum of eigenvalues. The angular perturbation analysis is suggestive of the presence of weak turbulence instabilities that propagate from low to high orders in perturbation theory.
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In the quest for mathematical foundations of M-theory, the Hypothesis H that fluxes are quantized in Cohomotopy theory, implies, on flat but possibly singular spacetimes, that M-brane charges locally organize into equivariant homotopy groups of spheres. Here we show how this leads to a correspondence between phenomena conjectured in M-theory and fundamental mathematical concepts/results in stable homotopy, generalized cohomology and Cobordism theory Mf: Stems of homotopy groups correspond to charges of probe p-branes near black b-branes; stabilization within a stem is the boundary-bulk transition; the Adams d-invariant measures G4-flux; trivialization of the d-invariant corresponds to H3-flux; refined Toda brackets measure H3-flux; the refined Adams e-invariant sees the H3-charge lattice; vanishing Adams e-invariant implies consistent global C3-fields; Conner-Floyds e-invariant is H3-flux seen in the Green-Schwarz mechanism; the Hopf invariant is the M2-brane Page charge (G7-flux); the Pontrjagin-Thom theorem associates the polarized brane worldvolumes sourcing all these charges. Cobordism in the third stable stem witnesses spontaneous KK-compactification on K3-surfaces; the order of the third stable stem implies 24 NS5/D7-branes in M/F-theory on K3. Quaternionic orientations correspond to unit H3-fluxes near M2-branes; complex orientations lift these unit H3-fluxes to heterotic M-theory with heterotic line bundles. In fact, we find quaternionic/complex Ravenel-orientations bounded in dimension; and we find the bound to be 10, as befits spacetime dimension 10+1.
We show how a recently proposed large $N$ duality in the context of type IIA strings with ${cal N}=1$ supersymmetry in 4 dimensions can be derived from purely geometric considerations by embedding type IIA strings in M-theory. The phase structure of M-theory on $G_2$ holonomy manifolds and an $S^3$ flop are the key ingredients in this derivation.
We study a two-dimensional low-dissipation dynamical system with a control parameter that is swept linearly in time across a transcritical bifurcation. We investigate the relaxation time of a perturbation applied to a variable of the system and we show that critical slowing down may occur at a parameter value well above the bifurcation point. We test experimentally the occurrence of critical slowing down by applying a perturbation to the accessible control parameter and we find that this perturbation leaves the system behavior unaltered, thus providing no useful information on the occurrence of critical slowing down. The theoretical analysis reveals the reasons why these tests fail in predicting an incoming bifurcation.
We study the orbits in a Manko-Novikov type metric (MN) which is a perturbed Kerr metric. There are periodic, quasi-periodic, and chaotic orbits, which are found in configuration space and on a surface of section for various values of the energy E and the z-component of the angular momentum Lz. For relatively large Lz there are two permissible regions of non-plunging motion bounded by two closed curves of zero velocity (CZV), while in the Kerr metric there is only one closed CZV of non-plunging motion. The inner permissible region of the MN metric contains mainly chaotic orbits, but it contains also a large island of stability. We find the positions of the main periodic orbits as functions of Lz and E, and their bifurcations. Around the main periodic orbit of the outer region there are islands of stability that do not appear in the Kerr metric. In a realistic binary system, because of the gravitational radiation, the energy E and the angular momentum Lz of an inspiraling compact object decrease and therefore the orbit of the object is non-geodesic. In fact in an EMRI system the energy E and the angular momentum Lz decrease adiabatically and therefore the motion of the inspiraling object is characterized by the fundamental frequencies which are drifting slowly in time. In the Kerr metric the ratio of the fundamental frequencies changes strictly monotonically in time. However, in the MN metric when an orbit is trapped inside an island the ratio of the fundamental frequencies remains constant for some time. Hence, if such a phenomenon is observed this will indicate that the system is non integrable and therefore the central object is not a Kerr black hole.
It is shown that the previously noticed internal dynamical $SO(D-1)$ symmetry arXiv:1003.5189 for relativistic M-branes moving in $D$-dimensional space-time is naturally realized in the (extended by powers of $frac{1}{p_+}$) enveloping algebra of the Poincare algebra.
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