T-duality in the string theory effective action with a string source

We consider the T-duality transformations of the low-energy quantum string theory effective action in the presence of classical fundamental string source and demonstrate explicitly that T-duality still holds.Comment: 11 pages, Latex. Typos fixed, cfs., Refs. and acknowledgements adde

Hidden Symmetries of M-Theory and Its Dynamical Realization

We discuss hidden symmetries of M-theory, its feedback on the construction of the M-theory effective action, and a response of the effective action when locality is preserved. In particular, the locality of special symmetries of the duality-symmetric linearized gravity constraints the index structure of the dual to graviton field in the same manner as it is required to separate the levels 0 and 1 generators subalgebra from the infinite-dimensional hidden symmetry algebra of gravitational theory. This conclusion fails once matter fields are taken into account and we give arguments for that. We end up outlining current problems and development perspectives.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Duality-Symmetric Approach to General Relativity and Supergravity

We review the application of a duality-symmetric approach to gravity and supergravity with emphasizing benefits and disadvantages of the formulation. Contents of these notes includes: 1) Introduction with putting the accent on the role of dual gravity within M-theory; 2) Dualization of gravity with a cosmological constant in D = 3; 3) On-shell description of dual gravity in D > 3; 4) Construction of the duality-symmetric action for General Relativity with/without matter fields; 5) On-shell description of dual gravity in linearized approximation; 6) Brief summary of the paper.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Liouville mode in Gauge/Gravity Duality

We establish solutions corresponding to AdS4 static charged black holes with inhomogeneous two-dimensional horizon surfaces of constant curvature. Depending on the choice of the 2D constant curvature space, the metric potential of the internal geometry of the horizon satisfies the elliptic wave/elliptic Liouville equations. We calculate the charge diffusion and transport coefficients in the hydrodynamic limit of gauge/gravity duality and observe the exponential suppression in the diffusion coefficient and in the shear viscosity-per-entropy density ratio in the presence of an inhomogeneity on black hole horizons with planar, spherical, and hyperbolic geometry. We discuss the subtleties of the approach developed for a planar black hole with inhomogeneity distribution on the horizon surface in more detail and find, among others, a trial distribution function, which generates values of the shear viscosity-per-entropy density ratio falling within the experimentally relevant range. The solutions obtained are also extended to higher-dimensional AdS space. We observe two different DC conductivities in 4D and higher-dimensional effective strongly coupled dual media and formulate conditions under which the appropriate ratio of different conductivities is qualitatively the same as that observed in an anisotropic strongly coupled fluid. We briefly discuss ways of how the Liouville field could appear in condensed matter physics and outline prospects of further employing the gauge/gravity duality in CMP problems.Comment: 1+22 pages, 1 Fig; v.2: eqs. (2.2), (3.16), (3.18) and (5.2) corrected, Refs. added; v.3: 1+28 pages, expanded version, Refs. added; v.4: published versio