41 research outputs found
Modular Invariant Critical Superstrings on Four-dimensional Minkowski Space Two-dimensional Black Hole
Extending the seminal work of Bilal and Gervais, we construct a tachyon-free,
modular invariant partition function for critical superstrings on
four-dimensional Minkowski x two-dimensional black hole. This model may be
thought of as an SL(2,R)/U(1) version of Gepner models and corresponds to a
conifold point on the moduli space of Calabi-Yau compactifications. We directly
deal with N=2, c=9 unitary superconformal characters. Modular invariance is
achieved by requiring the string to have a momentum along an extra noncompact
direction, in agreement with the picture of singular CFTs advocated by Witten.
The four-dimensional massless spectrum coincides with that of the tensionless
strings, suggesting a possible dual description of type II strings on a
conifold in terms of two intersecting NS5-branes. An interesting relation to
D=6, N=4 gauged supergravity is also discussed.Comment: 18 pages, 2 figure
Rational Conformal Field Theory and Multi-Wormhole Partition Function in 3-dimensional Gravity
We study the Turaev-Viro invariant as the Euclidean Chern-Simons-Witten
gravity partition function with positive cosmological constant. After
explaining why it can be identified as the partition function of 3-dimensional
gravity, we show that the initial data of the TV invariant can be constructed
from the duality data of a certain class of rational conformal field theories,
and that, in particular, the original Turaev-Viro's initial data is associated
with the modular invariant WZW model. As a corollary we then show
that the partition function is bounded from above by , where is
the smallest genus of handlebodies with which can be presented by Hegaard
splitting. is generically very large near if is
neither nor a lens space, and many-wormholeconfigurations dominate near
in the sense that generically tends to diverge faster
as the ``number of wormholes'' becomes larger.Comment: 27page
Lower-dimensional superstrings in the double-spinor formalism
We study lower-dimensional superstrings in the double-spinor formalism
introduced by Aisaka and Kazama. These superstrings can be consistently
quantized and are equivalent to the lower-dimensional pure-spinor superstrings
proposed by Grassi and Wyllard. The unexpected physical spectrum of the
pure-spinor superstrings may thus be regarded as a manifestation of
noncriticality. We also discuss how to couple these covariant superstrings to
the compactified degrees of freedom described by the N=2 superconformal field
theory.Comment: 32 pages, version published in Prog. Theor. Phy
On Discrete U-duality in M-theory
We give a complete set of generators for the discrete exceptional U-duality
groups of toroidal compactified type II theory and M-theory in d>2. For this,
we use the DSZ quantization in d=4 as originally proposed by Hull and Townsend,
and determine the discrete group inducing integer shifts on the charge lattice.
It is generated by fundamental unipotents, which are constructed by
exponentiating the Chevalley generators of the corresponding Lie algebra. We
then extend a method suggested by the above authors and used by Sen for the
heterotic string to get the discrete U-duality group in d=3, thereby obtaining
a quantized symmetry in d=3 from a d=4 quantization condition. This is studied
first in a toy model, corresponding to d=5 simple supergravity, and then
applied to M-theory. It turns out that, in the toy model, the resulting
U-duality group in d=3 is strictly smaller than the one generated by the
fundamental unipotents corresponding to all Chevalley generators. However, for
M-theory, both groups agree. We illustrate the compactification to d=3 by an
embedding of d=4 particle multiplets into the d=3 theory.Comment: 50 pages, 6 figures, some typos corrected, accepted for publication
in Class.Quant.Gra