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

The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes

This work considers the way that quantum loop effects modify the propagation of light in curved space. The calculation of the refractive index for scalar QED is reviewed and then extended for the first time to QED with spinor particles in the loop. It is shown how, in both cases, the low frequency phase velocity can be greater than c, as found originally by Drummond and Hathrell, but causality is respected in the sense that retarded Green functions vanish outside the lightcone. A "phenomenology" of the refractive index is then presented for black holes, FRW universes and gravitational waves. In some cases, some of the polarization states propagate with a refractive index having a negative imaginary part indicating a potential breakdown of the optical theorem in curved space and possible instabilities.Comment: 62 pages, 14 figures, some signs corrected in formulae and graph

Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves

We prove that M-theory plane waves with extra supersymmetries are necessarily homogeneous (but possibly time-dependent), and we show by explicit construction that such time-dependent plane waves can admit extra supersymmetries. To that end we study the Penrose limits of Goedel-like metrics, show that the Penrose limit of the M-theory Goedel metric (with 20 supercharges) is generically a time-dependent homogeneous plane wave of the anti-Mach type, and display the four extra Killings spinors in that case. We conclude with some general remarks on the Killing spinor equations for homogeneous plane waves.Comment: 20 pages, LaTeX2

BF Theories and Group-Level Duality

It is known that the partition function and correlators of the two-dimensional topological field theory $G_K(N)/ G_K(N)$ on the Riemann surface $\Sigma_{g,s}$ is given by Verlinde numbers, dim($V_{g,s,K}$) and that the large $K$ limit of dim($V_{g,s,K}$) gives Vol(${\cal M}_s$), the volume of the moduli space of flat connections of gauge group $G(N)$ on $\Sigma_{g,s}$, up to a power of $K$. Given this relationship, we complete the computation of Vol(${\cal M}_s$) using only algebraic results from conformal field theory. The group-level duality of $G(N)_K$ is used to show that if $G(N)$ is a classical group, then $\displaystyle \lim_{N\rightarrow \infty} G_K(N) / G_K(N)$ is a BF theory with gauge group $G(K)$. Therefore this limit computes Vol(${\cal M}^\prime_s$), the volume of the moduli space of flat connections of gauge group $G(K)$

String Interactions in PP-Waves

We argue that string interactions in a PP-wave spacetime are governed by an effective coupling g_{eff}=g_s(\mu p^+\apm)f(\mu p^+ \apm) where f(\mu p^+ \apm) is proportional to the light cone energy of the string states involved in the interaction. This simply follows from generalities of a Matrix String description of this background. $g_{eff}$ nicely interpolates between the expected result ($g_s$) for flat space (small \mu p^+\apm) and a recently conjectured expression from the perturbative gauge theory side (large \mu p^+\apm).Comment: 8 page

PP-waves on Superbrane Backgrounds

In this paper we discuss a method of generating supersymmetric solutions of the Einstein equations. The method involves the embedding of one supersymmetric spacetime into another. We present two examples with constituent spacetimes which support "charges", one of which was known previously and the other of which is new. Both examples have PP-waves as one of the embedding constituents.Comment: 6 pages no figure

More on Phase Structure of Nonlocal 2D Generalized Yang-Mills Theories (nlgYM2_2's)

We study the phase structure of nonlocal two dimensional generalized Yang - Mills theories (nlgYM$_2$) and it is shown that all order of $\phi^{2k}$ model of these theories has phase transition only on compact manifold with $g = 0$(on sphere), and the order of phase transition is 3. Also it is shown that the $\phi^2 + \frac{2\alpha}{3}\phi^3$ model of nlgYM$_2$ has third order phase transition on any compact manifold with $1 < g < 1+ \frac{\hat{A}}{|\eta_c|}$, and has no phase transition on sphere.Comment: 11 pages, no figure

Uniqueness of M-theory PP-Wave Background with Extra Supersymmetries

We examine Killing spinor equations of the general eleven-dimensional pp-wave backgrounds, which contain a scalar H(x^m,x^-) in the metric and a three-form \xi(x^m,x^-) in the flux. Considering non-harmonic extra Killing spinors, we show that if the backgrounds admit at least one extra Killing spinor in addition to the standard 16 Killing spinors, they can be reduced to the form with H=A_{mn}(x^-)x^mx^n and \xi(x^-) modulo coordinate transformations. We further examine the cases in which the extra Killing spinor is characterized by a set of Cartan matrices. The super-isometry algebras of the resulting backgrounds are also derived.Comment: 25 pages, LaTeX2e, comments added, version to appear in PR