Symmetries and Observables for BF-theories in Superspace

The supersymmetric version of a topological quantum field theory describing flat connections, the super BF-theory, is studied in the superspace formalism. A set of observables related to topological invariants is derived from the curvature of the superspace. Analogously to the non-supersymmetric versions, the theory exhibits a vector-like supersymmetry. The role of the vector supersymmetry and an additional new symmetry of the action in the construction of observables is explained.Comment: 11 pages, LaTe

The non-Abelian gauge theory of matrix big bangs

We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantisation to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t=0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.Comment: 29 pages, 8 eps figures, v2: minor changes, references added: v3 small typographical changes

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

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

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

Penrose Limits of Orbifolds and Orientifolds

We study the Penrose limit of various AdS_p X S^q orbifolds. The limiting spaces are waves with parallel rays and singular wave fronts. In particular, we consider the orbifolds AdS_3 X S^3/\Gamma, AdS_5 X S^5/\Gamma and AdS_{4,7} X S^{7,4}/\Gamma where \Gamma acts on the sphere and/or the AdS factor. In the pp-wave limit, the wave fronts are the orbifolds C^2/\Gamma, C^4/\Gamma and R XC^4/\Gamma, respectively. When desingularization is possible, we get asymptotically locally pp-wave backgrounds (ALpp). The Penrose limit of orientifolds are also discussed. In the AdS_5 X RP^5 case, the limiting singularity can be resolved by an Eguchi-Hanson gravitational instanton. The pp-wave limit of D3-branes near singularities in F-theory is also presented. Finally, we give the embedding of D-dimensional pp-waves in flat M^{2,D} space.Comment: 20 pages, references adde

Power-law singularities in string theory and M-theory

We extend the definition of the Szekeres-Iyer power-law singularities to supergravity, string and M-theory backgrounds, and find that are characterized by Kasner type exponents. The near singularity geometries of brane and some intersecting brane backgrounds are investigated and the exponents are computed. The Penrose limits of some of these power-law singularities have profiles $A\sim {\rm u}^{-\gamma}$ for $\gamma\geq 2$. We find the range of the exponents for which $\gamma=2$ and the frequency squares are bounded by 1/4. We propose some qualitative tests for deciding whether a null or timelike spacetime singularity can be resolved within string theory and M-theory based on the near singularity geometry and its Penrose limits.Comment: 32 page

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

Canonical formulation of N = 2 supergravity in terms of the Ashtekar variable

We reconstruct the Ashtekar's canonical formulation of N = 2 supergravity (SUGRA) starting from the N = 2 chiral Lagrangian derived by closely following the method employed in the usual SUGRA. In order to get the full graded algebra of the Gauss, U(1) gauge and right-handed supersymmetry (SUSY) constraints, we extend the internal, global O(2) invariance to local one by introducing a cosmological constant to the chiral Lagrangian. The resultant Lagrangian does not contain any auxiliary fields in contrast with the 2-form SUGRA and the SUSY transformation parameters are not constrained at all. We derive the canonical formulation of the N = 2 theory in such a manner as the relation with the usual SUGRA be explicit at least in classical level, and show that the algebra of the Gauss, U(1) gauge and right-handed SUSY constraints form the graded algebra, G^2SU(2)(Osp(2,2)). Furthermore, we introduce the graded variables associated with the G^2SU(2)(Osp(2,2)) algebra and we rewrite the canonical constraints in a simple form in terms of these variables. We quantize the theory in the graded-connection representation and discuss the solutions of quantum constraints.Comment: 19 pages, Latex, corrected some typos and added a referenc

Kaigorodov spaces and their Penrose limits

Kaigorodov spaces arise, after spherical compactification, as near horizon limits of M2, M5, and D3-branes with a particular pp-wave propagating in a world volume direction. We show that the uncompactified near horizon configurations K\times S are solutions of D=11 or D=10 IIB supergravity which correspond to perturbed versions of their AdS \times S analogues. We derive the Penrose-Gueven limits of the Kaigorodov space and the total spaces and analyse their symmetries. An Inonu-Wigner contraction of the Lie algebra is shown to occur, although there is a symmetry enhancement. We compare the results to the maximally supersymmetric CW spaces found as limits of AdS\times S spacetimes: the initial gravitational perturbation on the brane and its near horizon geometry remains after taking non-trivial Penrose limits, but seems to decouple. One particuliar limit yields a time-dependent homogeneous plane-wave background whose string theory is solvable, while in the other cases we find inhomogeneous backgrounds.Comment: latex2e, 24 page