44 research outputs found
Continuum Annulus Amplitude from the Two-Matrix Model
An explicit expression for continuum annulus amplitudes having boundary
lengths and is obtained from the two-matrix model for the
case of the unitary series; . In the limit of vanishing
cosmological constant, we find an integral representation of these amplitudes
which is reproduced, for the cases of the and the , by a continuum approach consisting of quantum mechanics of loops
and a matter system integrated over the modular parameter of the annulus. We
comment on a possible relation to the unconventional branch of the Liouville
gravity.Comment: 9 pages, OU-HET 190, revised version. A part of the conclusions has
been corrected. A new result on integral representation of the annulus
amplitudes has been adde
Vacuum Energy Cancellation in a Non-supersymmetric String
We present a nonsupersymmetric orbifold of type II string theory and show
that it has vanishing cosmological constant at the one and two loop level. We
argue heuristically that the cancellation persists at higher loops.Comment: 31 pages harvmac big, 6 figures. New version includes the 2-loop
analysis of hep-th/9810129 and elimination of one of the two heuristic
arguments for higher loop cancellatio
M-branes and N=2 Strings
The string field theory of N=(2,1) heterotic strings describes a set of
self-dual Yang-Mills fields coupled to self-dual gravity in 2+2 dimensions. We
show that the exact classical action for this field theory is a certain
complexification of the Green-Schwarz/Dirac-Born-Infeld string action, closely
related to the four dimensional Wess-Zumino action describing self-dual gauge
fields. This action describes the world-volume of a 2+2d ``M-brane'', which
gives rise upon different null reductions to critical strings and membranes. We
discuss a number of further properties of N=2 heterotic strings, such as the
geometry of null reduction, general features of a covariant formulation, and
possible relations to BPS and GKM algebras.Comment: 49 pages, harvmac; 1 figure (uses epsf.tex). References adde
Spherical Casimir energies and Dedekind sums
Casimir energies on space-times having general lens spaces as their spatial
sections are shown to be given in terms of generalised Dedekind sums related to
Zagier's. These are evaluated explicitly in certain cases as functions of the
order of the lens space. An easily implemented recursion approach is used.Comment: 18 pages, 2 figures, v2:typos corrected, inessential equation in
Discussion altered. v3:typos corrected, 1 reference and comments added.
v4:typos corrected. Ancillary results added in an appendi
Localized Tachyons and the Quantum McKay Correspondence
The condensation of closed string tachyons localized at the fixed point of a
C^d/\Gamma orbifold can be studied in the framework of renormalization group
flow in a gauged linear sigma model. The evolution of the Higgs branch along
the flow describes a resolution of singularities via the process of tachyon
condensation. The study of the fate of D-branes in this process has lead to a
notion of a ``quantum McKay correspondence.'' This is a hypothetical
correspondence between fractional branes in an orbifold singularity in the
ultraviolet with the Coulomb and Higgs branch branes in the infrared. In this
paper we present some nontrivial evidence for this correspondence in the case
C^2/Z_n by relating the intersection form of fractional branes to that of
``Higgs branch branes,'' the latter being branes which wrap nontrivial cycles
in the resolved space.Comment: 25 pages; harvma
Closed string tachyons, flips and conifolds
Following the analysis of tachyons and orbifold flips described in
hep-th/0412337, we study nonsupersymmetric analogs of the supersymmetric
conifold singularity and show using their toric geometry description that they
are nonsupersymmetric orbifolds of the latter. Using linear sigma models, we
see that these are unstable to localized closed string tachyon condensation and
exhibit flip transitions between their two small resolutions (involving
2-cycles), in the process mediating mild dynamical topology change. Our
analysis shows that the structure of these nonsupersymmetric conifolds as
quotients of the supersymmetric conifold obstructs the 3-cycle deformation of
such singularities, suggesting that these nonsupersymmetric conifolds decay by
evolving towards their stable small resolutions.Comment: Latex, 22 pgs, 2 figs. v4: matches JHEP version, 29 pgs, 3 figures,
more elaborate Introduction, various clarifications adde
Theta Vectors and Quantum Theta Functions
In this paper, we clarify the relation between Manin's quantum theta function
and Schwarz's theta vector in comparison with the kq representation, which is
equivalent to the classical theta function, and the corresponding coordinate
space wavefunction. We first explain the equivalence relation between the
classical theta function and the kq representation in which the translation
operators of the phase space are commuting. When the translation operators of
the phase space are not commuting, then the kq representation is no more
meaningful. We explain why Manin's quantum theta function obtained via algebra
(quantum tori) valued inner product of the theta vector is a natural choice for
quantum version of the classical theta function (kq representation). We then
show that this approach holds for a more general theta vector with constant
obtained from a holomorphic connection of constant curvature than the simple
Gaussian one used in the Manin's construction. We further discuss the
properties of the theta vector and of the quantum theta function, both of which
have similar symmetry properties under translation.Comment: LaTeX 21 pages, give more explicit explanations for notions given in
the tex
A Note on Background (In)dependence
In general quantum systems there are two kinds of spacetime modes, those that
fluctuate and those that do not. Fluctuating modes have normalizable
wavefunctions. In the context of 2D gravity and ``non-critical'' string theory
these are called macroscopic states. The theory is independent of the initial
Euclidean background values of these modes. Non-fluctuating modes have
non-normalizable wavefunctions and correspond to microscopic states. The theory
depends on the background value of these non-fluctuating modes, at least to all
orders in perturbation theory. They are superselection parameters and should
not be minimized over. Such superselection parameters are well known in field
theory. Examples in string theory include the couplings (including the
cosmological constant) in the matrix models and the mass of the two-dimensional
Euclidean black hole. We use our analysis to argue for the finiteness of the
string perturbation expansion around these backgrounds.Comment: 16 page
The Solution Space of the Unitary Matrix Model String Equation and the Sato Grassmannian
The space of all solutions to the string equation of the symmetric unitary
one-matrix model is determined. It is shown that the string equation is
equivalent to simple conditions on points and in the big cell \Gr
of the Sato Grassmannian . This is a consequence of a well-defined
continuum limit in which the string equation has the simple form \lb \cp
,\cq_- \rb =\hbox{\rm 1}, with \cp and \cq_- matrices of
differential operators. These conditions on and yield a simple
system of first order differential equations whose analysis determines the
space of all solutions to the string equation. This geometric formulation leads
directly to the Virasoro constraints \L_n\,(n\geq 0), where \L_n annihilate
the two modified-KdV \t-functions whose product gives the partition function
of the Unitary Matrix Model.Comment: 21 page
Notes on the algebraic curves in (p,q) minimal string theory
Loop amplitudes in (p,q) minimal string theory are studied in terms of the
continuum string field theory based on the free fermion realization of the KP
hierarchy. We derive the Schwinger-Dyson equations for FZZT disk amplitudes
directly from the W_{1+\infty} constraints in the string field formulation and
give explicitly the algebraic curves of disk amplitudes for general
backgrounds. We further give annulus amplitudes of FZZT-FZZT, FZZT-ZZ and ZZ-ZZ
branes, generalizing our previous D-instanton calculus from the minimal unitary
series (p,p+1) to general (p,q) series. We also give a detailed explanation on
the equivalence between the Douglas equation and the string field theory based
on the KP hierarchy under the W_{1+\infty} constraints.Comment: 61 pages, 1 figure, section 2.5 and Appendix B added, references
added, final version to appear in JHE