7,134 research outputs found
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
Conformal boundary and geodesics for and the plane wave: Their approach in the Penrose limit
Projecting on a suitable subset of coordinates, a picture is constructed in
which the conformal boundary of and that of the plane wave
resulting in the Penrose limit are located at the same line. In a second line
of arguments all and plane wave geodesics are constructed in
their integrated form. Performing the Penrose limit, the approach of null
geodesics reaching the conformal boundary of to that of the
plane wave is studied in detail. At each point these null geodesics of
form a cone which degenerates in the limit.Comment: some statements refined, chapter 5 rewritten to make it more precise,
some typos correcte
On solvable models of type IIB superstring in NS-NS and R-R plane wave backgrounds
We consider type IIB string in the two plane-wave backgrounds which may be
interpreted as special limits of the AdS_3 x S^3 metric supported by either the
NS-NS or R-R 3-form field. The NS-NS plane-wave string model is equivalent to a
direct generalization of the Nappi-Witten model, with its spectrum being
similar to that of strings in constant magnetic field. The R-R model can be
solved in the light-cone gauge, where the Green-Schwarz action describes 4
massive and 4 massless copies of free bosons and fermions. We find the spectra
of the two string models and study the asymptotic density of states. We also
discuss a more general class of exactly solvable plane-wave models with reduced
supersymmetry which is obtained by adding twists in two spatial 2-planes.Comment: 36 pages, harvmac. v2: discussion of equivalence of the supergravity
parts of the spectra of the NS-NS and R-R models added in sect.5.3; v3: added
remark on periodicity of the NS-NS spectrum; v4: minor correction in sect.6.
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
Swimming in curved space or The Baron and the cat
We study the swimming of non-relativistic deformable bodies in (empty) static
curved spaces. We focus on the case where the ambient geometry allows for rigid
body motions. In this case the swimming equations turn out to be geometric. For
a small swimmer, the swimming distance in one stroke is determined by the
Riemann curvature times certain moments of the swimmer.Comment: 19 pages 6 figure
The String Calculation of QCD Wilson Loops on Arbitrary Surfaces
Compact string expressions are found for non-intersecting Wilson loops in
SU(N) Yang-Mills theory on any surface (orientable or nonorientable) as a
weighted sum over covers of the surface. All terms from the coupled chiral
sectors of the 1/N expansion of the Wilson loop expectation values are
included.Comment: 10 pages, LaTeX, no figure
On Signature Transition and Compactification in Kaluza-Klein Cosmology
We consider an empty (4+1) dimensional Kaluza-Klein universe with a negative
cosmological constant and a Robertson-Walker type metric. It is shown that the
solutions to Einstein field equations have degenerate metric and exhibit
transitioins from a Euclidean to a Lorentzian domain. We then suggest a
mechanism, based on signature transition which leads to compactification of the
internal space in the Lorentzian region as . With the
assumption of a very small value for the cosmological constant we find that the
size of the universe and the internal scale factor would be related
according to in the Lorentzian region. The corresponding
Wheeler-DeWitt equation has exact solution in the mini-superspace giving rise
to a quantum state which peaks in the vicinity of the classical solutions
undergoing signature transition.Comment: 13 pages, 3 figure
Time-Dependent Open String Solutions in 2+1 Dimensional Gravity
We find general, time-dependent solutions produced by open string sources
carrying no momentum flow in 2+1 dimensional gravity. The local Poincar\'e
group elements associated with these solutions and the coordinate
transformations that transform these solutions into Minkowski metric are
obtained. We also find the relation between these solutions and the planar wall
solutions in 3+1 dimensions.Comment: CU-TP-619, 18 pages. (minor changes
Light-like Big Bang singularities in string and matrix theories
Important open questions in cosmology require a better understanding of the
Big Bang singularity. In string and matrix theories, light-like analogues of
cosmological singularities (singular plane wave backgrounds) turn out to be
particularly tractable. We give a status report on the current understanding of
such light-like Big Bang models, presenting both solved and open problems.Comment: 20 pages, invited review for Class. Quant. Grav; v3: section 2.3
shortened, discussion on DLCQ added in section 3.1, published versio
Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure
We continue our study of the global properties of the z=2 Schroedinger
space-time. In particular, we provide a codimension 2 isometric embedding which
naturally gives rise to the previously introduced global coordinates.
Furthermore, we study the causal structure by probing the space-time with point
particles as well as with scalar fields. We show that, even though there is no
global time function in the technical sense (Schroedinger space-time being
non-distinguishing), the time coordinate of the global Schroedinger coordinate
system is, in a precise way, the closest one can get to having such a time
function. In spite of this and the corresponding strongly Galilean and almost
pathological causal structure of this space-time, it is nevertheless possible
to define a Hilbert space of normalisable scalar modes with a well-defined
time-evolution. We also discuss how the Galilean causal structure is reflected
and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.Comment: 32 page
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