On the Hagedorn Behaviour of Singular Scale-Invariant Plane Waves

As a step towards understanding the properties of string theory in time-dependent and singular spacetimes, we study the divergence of density operators for string ensembles in singular scale-invariant plane waves, i.e. those plane waves that arise as the Penrose limits of generic power-law spacetime singularities. We show that the scale invariance implies that the Hagedorn behaviour of bosonic and supersymmetric strings in these backgrounds, even with the inclusion of RR or NS fields, is the same as that of strings in flat space. This is in marked contrast to the behaviour of strings in the BFHP plane wave which exhibit quantitatively and qualitatively different thermodynamic properties.Comment: 15 pages, LaTeX2e, v2: JHEP3.cls, one reference adde

Localization and Diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories

We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula respectively. In each case, we first introduce the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups), and describe the finite dimensional integration formulae. We then discuss some applications to path integrals and give an overview of the relevant literature. The applications we deal with include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang-Mills theory.Comment: 72 pages (60 A4 pages), LaTeX (to appear in the Journal of Mathematical Physics Special Issue on Functional Integration (May 1995)

PP-Wave / CFT_2 Duality

We investigate the pp-wave limit of the AdS_3\times S^3\times K3 compactification of Type IIB string theory from the point of view of the dual Sym_N(K3) CFT. It is proposed that a fundamental string in this pp-wave geometry is dual to the c=6 effective string of the Sym_N(K3) CFT, with the string bits of the latter being composed of twist operators. The massive fundamental string oscillators correspond to certain twisted Virasoro generators in the effective string. It is shown that both the ground states and the genus expansion parameter (at least in the orbifold limit of the CFT) coincide. Surprisingly the latter scales like J^2/N rather than the J^4/N^2 which might have been expected. We demonstrate a leading-order agreement between the pp-wave and CFT particle spectra. For a degenerate special case (one NS 5-brane) an intriguing complete agreement is found.Comment: JHEP3 LaTeX, 20 pages; discussion of WZW levels clarified, reference adde

M-theory on a Time-dependent Plane-wave

We propose a matrix model on a homogeneous plane-wave background with 20 supersymmetries. This background is anti-Mach type and is equivalent to the time-dependent background. We study supersymmetries in this theory and calculate the superalgebra. The vacuum energy of the abelian part is also calculated. In addition we find classical solutions such as graviton solution, fuzzy sphere and hyperboloid.Comment: 19pages, no figures, LaTeX, JHEP3.cl

Strings on pp-waves and Hadrons in (softly broken) N=1 gauge theories

We study the Penrose limit of Type IIB duals of softly broken N=1 SU(N) gauge theories in four dimensions, obtained as deformations of the Maldacena-Nunez and Klebanov-Strassler backgrounds. We extract the string spectrum on the resulting pp-wave backgrounds and discuss some properties of the conjectured dual gauge theory hadrons, the so called "Annulons". The string zero-point energy on the light-cone is nontrivial, due to the loss of linearly realized worldsheet supersymmetry, and negative, even in the unbroken supersymmetric case. This causes the appearance of non-perturbative corrections to the hadronic mass spectrum. We briefly discuss the thermodynamic behavior of these string models, calculating the corresponding Hagedorn temperatures.Comment: 20 page

On zero-point energy, stability and Hagedorn behavior of Type IIB strings on pp-waves

Type IIB strings on many pp-wave backgrounds, supported either by 5-form or 3-form fluxes, have negative light-cone zero-point energy. This raises the question of their stability and poses possible problems in the definition of their thermodynamic properties. After having pointed out the correct way of calculating the zero-point energy, an issue not fully discussed in literature, we show that these Type IIB strings are classically stable and have well defined thermal properties, exhibiting a Hagedorn behavior.Comment: Latex, 13 pages. v2: regularization/renormalization prescription clarified, refs. adde

On symmetries of Chern-Simons and BF topological theories

We describe constructing solutions of the field equations of Chern-Simons and topological BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations) are considered. A method of calculating (nonlocal) dressing symmetries in Chern-Simons and topological BF theories is formulated

String Theory on Dp-plane waves

We study the spectrum of solvable string models on plane waves descending from non-conformal Dp-brane geometries. We mainly focus on S-dual F1/D1-waves in type IIB and type I/heterotic 10D superstrings. We derive the Kaluza-Klein spectrum of N=1,2 10D supergravities on D1/F1-waves. We compute helicity supertraces counting multiplicities and R-charges of string excitations in the plane wave geometry. The results are compared against the expectations coming from gauge/supergravity descriptions. In the type I case, the Klein, Annulus and Moebius one-loop amplitudes are computed for ten-dimensional D1-waves. We test the consistency of the open string descendant by showing that after modular transformations to the closed string channel, the three amplitudes combine themselves to reconstruct a complete square (|B>+|C>)^2. Tadpole conditions are also discussed.Comment: 22 pages, Minor corrections, References adde

Gravitational Lorentz Violations from M-Theory

In an attempt to bridge the gap between M-theory and braneworld phenomenology, we present various gravitational Lorentz-violating braneworlds which arise from p-brane systems. Lorentz invariance is still preserved locally on the braneworld. For certain p-brane intersections, the massless graviton is quasi-localized. This also results from an M5-brane in a C-field. In the case of a p-brane perturbed from extremality, the quasi-localized graviton is massive. For a braneworld arising from global AdS_5, gravitons travel faster when further in the bulk, thereby apparently traversing distances faster than light.Comment: 13 pages, 1 figure, LaTeX, references added, minor corrections and addition

All spacetimes with vanishing curvature invariants

All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates. Some potential applications of these spacetimes are discussed.Comment: 24 page