Pulsating Strings in Deformed Backgrounds

This is a brief summary on pulsating strings in beta deformed backgrounds found recently.Comment: 8 pages. Talk presented at Quantum Theory and Symmetries 7, Prague, August 7-13, 201

On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations

We give a well posed initial value formulation of the Baumgarte-Shapiro-Shibata-Nakamura form of Einstein's equations with gauge conditions given by a Bona-Masso like slicing condition for the lapse and a frozen shift. This is achieved by introducing extra variables and recasting the evolution equations into a first order symmetric hyperbolic system. We also consider the presence of artificial boundaries and derive a set of boundary conditions that guarantee that the resulting initial-boundary value problem is well posed, though not necessarily compatible with the constraints. In the case of dynamical gauge conditions for the lapse and shift we obtain a class of evolution equations which are strongly hyperbolic and so yield well posed initial value formulations

Rotating strings and D2-branes in type IIA reduction of M-theory on G2 manifold and their semiclassical limits

We consider rotating strings and D2-branes on type IIA background, which arises as dimensional reduction of M-theory on manifold of G2 holonomy, dual to N=1 gauge theory in four dimensions. We obtain exact solutions and explicit expressions for the conserved charges. By taking the semiclassical limit, we show that the rotating strings can reproduce only one type of semiclassical behavior, exhibited by rotating M2-branes on G2 manifolds. Our further investigation leads to the conclusion that the rotating D2-branes reproduce two types of the semiclassical energy-charge relations known for membranes in eleven dimensions.Comment: LaTeX, 29 pages, no figures; V2:comments added; V3:no changes, to appear in JHE

Geometry and dynamics of higher-spin frame fields

We give a systematic account of unconstrained free bosonic higher-spin fields on D-dimensional Minkowski and (Anti-)de Sitter spaces in the frame formalism. The generalized spin connections are determined by solving a chain of torsion-like constraints. Via a generalization of the vielbein postulate these allow to determine higher-spin Christoffel symbols, whose relation to the de Wit--Freedman connections is discussed. We prove that the generalized Einstein equations, despite being of higher-derivative order, give rise to the AdS Fronsdal equations in the compensator formulation. To this end we derive Damour-Deser identities for arbitrary spin on AdS. Finally we discuss the possibility of a geometrical and local action principle, which is manifestly invariant under unconstrained higher-spin symmetries.Comment: 30 pages, uses youngtab.sty, v2: minor changes, references adde

Matching Conditions in Atomistic-Continuum Modeling of Materials

A new class of matching condition between the atomistic and continuum regions is presented for the multi-scale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and at the same time minimize the reflection of phonons at the interface. These matching conditions can be made adaptive if we choose appropriate weight functions. Applications to dislocation dynamics and friction between two-dimensional atomically flat crystal surfaces are described.Comment: 6 pages, 4 figure

Numerical studies of the Lagrangian approach for reconstruction of the conductivity in a waveguide

We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate our inverse problem as an optimization problem and use Lagrangian approach to minimize the corresponding Tikhonov functional. We present a theorem of a local strong convexity of our functional and derive error estimates between computed and regularized as well as exact solutions of this functional, correspondingly. In numerical simulations we apply domain decomposition finite element-finite difference method for minimization of the Lagrangian. Our computational study shows efficiency of the proposed method in the reconstruction of the conductivity function in three dimensions

Matching Higher Conserved Charges for Strings and Spins

We demonstrate that the recently found agreement between one-loop scaling dimensions of large dimension operators in N=4 gauge theory and energies of spinning strings on AdS_5 x S^5 extends to the eigenvalues of an infinite number of hidden higher commuting charges. This dynamical agreement is of a mathematically highly intricate and non-trivial nature. In particular, on the gauge side the generating function for the commuting charges is obtained by integrable quantum spin chain techniques from the thermodynamic density distribution function of Bethe roots. On the string side the generating function, containing information to arbitrary loop order, is constructed by solving exactly the Backlund equations of the integrable classical string sigma model. Our finding should be an important step towards matching the integrable structures on the string and gauge side of the AdS/CFT correspondence.Comment: Latex, 33 pages, v2: new section added (completing the analytic proof that the entire infinite towers of commuting gauge and string charges match); references adde

Is the Helmholtz equation really sign-indefinite?

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts

Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations

We consider AdS_5 x S^5 string states with several large angular momenta along AdS_5 and S^5 directions which are dual to single-trace Super-Yang-Mills (SYM) operators built out of chiral combinations of scalars and covariant derivatives. In particular, we focus on the SU(3) sector (with three spins in S^5) and the SL(2) sector (with one spin in AdS_5 and one in S^5), generalizing recent work hep-th/0311203 and hep-th/0403120 on the SU(2) sector with two spins in S^5. We show that, in the large spin limit and at the leading order in the effective coupling expansion, the string sigma model equations of motion reduce to matrix Landau-Lifshitz equations. We then demonstrate that the coherent-state expectation value of the one-loop SYM dilatation operator restricted to the corresponding sector of single trace operators is also effectively described by the same equations. This implies a universal leading order equivalence between string energies and SYM anomalous dimensions, as well as a matching of integrable structures. We also discuss the more general 5-spin sector and comment on SO(6) states dual to non-chiral scalar operators

Pulsating Strings in Lunin-Maldacena Backgrounds

We consider pulsating strings in Lunin-Maldacena backgrounds, specifically in deformed Minkowski spacetime and deformed AdS_5xS^5. We find the relation between the energy and the oscillation number of the pulsating string when the deformation is small. Since the oscillation number is an adiabatic invariant it can be used to explore the regime of highly excited string states. We then quantize the string and look for such a sector. For the deformed Minkowski background we find a precise match with the classical results if the oscillation number is quantized as an even number. For the deformed AdS_5xS^5 we find a contribution which depends on the deformation parameter.Comment: 16 pages, 2 figures, typos fixe