Some half-BPS solutions of M-theory

Spaliński, Michał

doi:10.1016/j.physletb.2006.01.068

Cited by 6 publications

(8 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3 A well-known remarkable feature of the LLM class of solutions is that supersymmetric solutions are in one-to-one correspondence with solutions to the continuum Toda equation. Despite separable solutions to the Toda existing, such as those of [39], only one regular solution is known [2]. 4 One attractive feature of the LLM spinor ansatz is that the vector spinor bilinears ǭγ µ ǫ, ǭγ 5 γ µ ǫ, ǭc γ µ ǫ one constructs are all mutually orthogonal and define a natural orthonormal frame.…”

Section: Reviewmentioning

confidence: 99%

Beyond LLM in M-theory

Colgáin

2012

J. High Energ. Phys.

View full text Add to dashboard Cite

The Lin, Lunin, Maldacena (LLM) ansatz in D = 11 supports two independent Killing directions when a general Killing spinor ansatz is considered. Here we show that these directions always commute, identify when the Killing spinors are charged, and show that both their inner product and resulting geometry are governed by two fundamental constants. In particular, setting one constant to zero leads to AdS 7 × S 4 , setting the other to zero gives AdS 4 ×S 7 , while flat spacetime is recovered when both these constants are zero. Furthermore, when the constants are equal, the spacetime is either LLM, or it corresponds to the Kowalski-Glikman solution where the constants are simply the mass parameter.

show abstract

Section: Reviewmentioning

confidence: 99%

Beyond LLM in M-theory

Colgáin

2012

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…A more detailed mathematical analysis of the origin of this divergence has unveiled the existence of a unique universal solution, the so-called attractor [25]. The novel attractor solution is intrinsically related with the mathematical theory of resurgence [20,26,27] and the details of this solution depends on the particular theory under consideration [28][29][30][31][32][33][34][35][36][37]. In simple terms, the attractor is a set of points in the phase space of the dynamical variables to which a family of solutions of an evolution equation merge after transients have died out.…”

Section: Introductionmentioning

confidence: 99%

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

2018

View full text Add to dashboard Cite

The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second-order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansions diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and the basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward an effective field theory description of hydrodynamics. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders and thus, it can be understood as an effective theory for the far-from-equilibrium fluid dynamics.

show abstract

“…Other creative proposals for solving the overshoot problem of brane inflation have appeared in[82,83,84].…”

mentioning

confidence: 99%

Brane inflation and the overshoot problem

2009

View full text Add to dashboard Cite

We investigate recent claims that brane inflation solves the overshoot problem through a combination of microphysical restrictions on the phase space of initial conditions and the existence of the Dirac-Born-Infeld attractor in regimes where the slow-roll attractor does not apply. Carrying out a comprehensive analysis of the parameter space allowed by the latest advances in brane inflation model-building, we find that these restrictions are insufficient to solve the overshoot problem. The vast majority of the phase space of initial conditions is still dominated by overshoot trajectories. We present an analytic proof that the brane-inflationary attractor must be close to the slow-roll limit, and update the predictions for observables such as non-Gaussianity, cosmic string tension and tensor modes. Contents

show abstract

Some half-BPS solutions of M-theory

Abstract: It was recently shown that half BPS-solutions of M-theory can be expressed in terms of a single function satisfying the 3-d continuum Toda equation. In this note half-BPS solutions corresponding to separable solutions of the Toda equations are examined.Comment: Typos fixed, reference adde

Cited by 6 publications

References 16 publications

Beyond LLM in M-theory

Beyond LLM in M-theory

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

Brane inflation and the overshoot problem

Contact Info

Product

Resources

About