Multidimensional Geometrical Model of the Renormalized Electrical Charge with Splitting off the Extra Coordinates

A geometrical model of electric charge is proposed. This model has ``naked'' charge screened with a ``fur - coat'' consisting of virtual wormholes. The 5D wormhole solution in the Kaluza - Klein theory is the ``naked'' charge. The splitting off of the 5D dimension happens on the two spheres (null surfaces) bounding this 5D wormhole. This allows one to sew two Reissner - Nordstr\"om black holes onto it on both sides. The virtual wormholes entrap a part of the electrical flux lines coming into the ``naked'' charge. This effect essentially changes the charge visible at infinity so that it satisfies the real relation $m^2<e^2$.Comment: 10 pages, 1 figure, awarded Honorable Mention by Grav.Res.Found., 199

Fermi Coordinates and Penrose Limits

We propose a formulation of the Penrose plane wave limit in terms of null Fermi coordinates. This provides a physically intuitive (Fermi coordinates are direct measures of geodesic distance in space-time) and manifestly covariant description of the expansion around the plane wave metric in terms of components of the curvature tensor of the original metric, and generalises the covariant description of the lowest order Penrose limit metric itself, obtained in hep-th/0312029. We describe in some detail the construction of null Fermi coordinates and the corresponding expansion of the metric, and then study various aspects of the higher order corrections to the Penrose limit. In particular, we observe that in general the first-order corrected metric is such that it admits a light-cone gauge description in string theory. We also establish a formal analogue of the Weyl tensor peeling theorem for the Penrose limit expansion in any dimension, and we give a simple derivation of the leading (quadratic) corrections to the Penrose limit of AdS_5 x S^5.Comment: 25 page

Penrose Limits and Spacetime Singularities

We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres-Iyer ``power-law type''), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile $A(u)\sim u^{-2}$, the scale invariance of the latter reflecting the power-law behaviour of the singularities.Comment: 9 pages, LaTeX2e; v2: additional references and cosmetic correction

On the pp-wave limit and the BMN structure of new Sasaki-Einstein spaces

We construct the pp-wave string associated with the Penrose limit of $Y^{p,q}$ and $L^{p,q,r}$ families of Sasaki-Einstein geometries. We identify in the dual quiver gauge theories the chiral and the non-chiral operators that correspond to the ground state and the first excited states. We present an explicit identification in a prototype model of $L^{1,7,3}$.Comment: 21 pages, JHEP format, 5 figures, acknowledgement correcte

On Penrose limit of elliptic branes

We discuss a Penrose limit of an elliptic brane configuration with $N_1$ NS5 and $N_2$ D4 branes. This background is T-dual to $N_1$ D3 branes at a fixed point of a $\mathbf{C}^3/\mathbf{Z}_{N_2}$ singularity and the T-duality survives the Penrose limit. The triple scaling limit of $N_1$ and $N_2$ gives rise to IIA pp-wave solution with a space-like compact direction. We identify the quiver gauge theory operators and argue that upon exchange of the momentum along the compact direction and the winding number these operators coincide with the operators derived in the dual type IIB description. We also find a new Penrose limit of the type IIB background and the corresponding limit in the type IIA picture. In the coordinate system we use there are two manifest space-like isometries. The quiver gauge theory operator duals of the string states are built of three bosonic fields.Comment: 25 pages with 1 figur

Topological Aspects of Gauge Fixing Yang-Mills Theory on S4

For an $S_4$ space-time manifold global aspects of gauge-fixing are investigated using the relation to Topological Quantum Field Theory on the gauge group. The partition function of this TQFT is shown to compute the regularized Euler character of a suitably defined space of gauge transformations. Topological properties of the space of solutions to a covariant gauge conditon on the orbit of a particular instanton are found using the $SO(5)$ isometry group of the $S_4$ base manifold. We obtain that the Euler character of this space differs from that of an orbit in the topologically trivial sector. This result implies that an orbit with Pontryagin number \k=\pm1 in covariant gauges on $S_4$ contributes to physical correlation functions with a different multiplicity factor due to the Gribov copies, than an orbit in the trivial \k=0 sector. Similar topological arguments show that there is no contribution from the topologically trivial sector to physical correlation functions in gauges defined by a nondegenerate background connection. We discuss possible physical implications of the global gauge dependence of Yang-Mills theory.Comment: 13 pages, uuencoded and compressed LaTeX file, no figure

Quantizing three-spin string solution in AdS_5 x S^5

As was recently found in hep-th/0304255, there exists a simple non-supersymmetric classical solution describing a closed string rotating in S^5 and located at the center of AdS_5. It is parametrized by the angular momentum J of the center of mass and two equal SO(6) angular momenta J' in the two other orthogonal rotation planes. The dual N=4 SYM operators should be scalar operators in SU(4) representations [0,J-J',2J'] or [J'-J,0,J'+J]. This solution is stable if J' > 3/2 J and for large J + 2 J' its classical energy admits an expansion in positive powers of g_eff = \lambda/(J + 2 J')^2: E= J + 2 J' + g_eff J' + ... . This suggests a possibility of a direct comparison with perturbative SYM results for the corresponding anomalous dimensions in the sector with g_eff << 1, by analogy with the BMN case. We conjecture that all quantum sigma model string corrections are then subleading at large J', so that the classical formula for the energy is effectively exact to all orders in \lambda. It could then be interpolated to weak coupling, representing a prediction for the anomalous dimensions on the SYM side. We test this conjecture by computing the 1-loop superstring sigma model correction to the classical energy.Comment: 25 pages, harvmac. v5: minor misprints in eqs (2.6),(2.16),(2.20),(2.21) correcte

Conformal Field Theory for the Superstring in a Ramond-Ramond Plane Wave Background

A quantizable worldsheet action is constructed for the superstring in a supersymmetric plane wave background with Ramond-Ramond flux. The action is manifestly invariant under all isometries of the background and is an exact worldsheet conformal field theory.Comment: 13 pages harvma

Dissipative Hydrodynamics and Heavy Ion Collisions

Recent discussions of RHIC data emphasized the exciting possibility that the matter produced in nucleus-nucleus collisions shows properties of a near-perfect fluid. Here, we aim at delineating the applicability of fluid dynamics, which is needed to quantify the size of corresponding dissipative effects. We start from the equations for dissipative fluid dynamics, which we derive from kinetic theory up to second order (Israel-Stewart theory) in a systematic gradient expansion. In model studies, we then establish that for too early initialization of the hydrodynamic evolution (\tau_0 \lsim 1 fm/c) or for too high transverse momentum (p_T \gsim 1 GeV) in the final state, the expected dissipative corrections are too large for a fluid description to be reliable. Moreover, viscosity-induced modifications of hadronic transverse momentum spectra can be accommodated to a significant degree in an ideal fluid description by modifications of the decoupling stage. We argue that these conclusions, drawn from model studies, can also be expected to arise in significantly more complex, realistic fluid dynamics simulations of heavy ion collisions.Comment: 18 pages, 5 figures, uses revtex4; v2: references added, typos correcte

Semiclassical quantization of rotating superstring in AdS_5 x S^5

Motivated by recent proposals in hep-th/0202021 and hep-th/0204051 we develop semiclassical quantization of superstring in $AdS_5 x S^5$. We start with a classical solution describing string rotating in $AdS_5$ and boosted along large circle of $S^5$. The energy of the classical solution $E$ is a function of the spin $S$ and the momentum $J$ (R-charge) which interpolates between the limiting cases S=0 and J=0 considered previously. We derive the corresponding quadratic fluctuation action for bosonic and fermionic fields from the GS string action and compute the string 1-loop (large \lambda= {R^4\over \a'^2}) correction to the classical energy spectrum in the $(S,J)$ sector. We find that the 1-loop correction to the ground-state energy does not cancel for non-zero $S$. For large $S$ it scales as $\ln S$, i.e. as the classical term, with no higher powers of $\ln S$ appearing. This supports the conjecture made in hep-th/0204051 that the classical $E-S = a \ln S$ scaling can be interpolated to weak coupling to reproduce the corresponding operator anomalous dimension behaviour in gauge theory.Comment: harvmac, 35p. v2,3: minor corrections; v4: added remarks about higher-loop corrections in section 4 and an argument suggesting the absence of higher than log S corrections to the energy to all orders in string tension in section 6.1; v5: factor 1/2 misprints corrected in eqs. (6.6) and (6.8) and thus in (6.5) and (6.9