690 research outputs found
The Mathematics of Fivebranes
Fivebranes are non-perturbative objects in string theory that generalize
two-dimensional conformal field theory and relate such diverse subjects as
moduli spaces of vector bundles on surfaces, automorphic forms, elliptic
genera, the geometry of Calabi-Yau threefolds, and generalized Kac-Moody
algebras.Comment: 10 pages, 2 figures, Lecture at ICM'9
Balanced Topological Field Theories
We describe a class of topological field theories called ``balanced
topological field theories.'' These theories are associated to moduli problems
with vanishing virtual dimension and calculate the Euler character of various
moduli spaces. We show that these theories are closely related to the geometry
and equivariant cohomology of ``iterated superspaces'' that carry two
differentials. We find the most general action for these theories, which turns
out to define Morse theory on field space. We illustrate the constructions with
numerous examples. Finally, we relate these theories to topological
sigma-models twisted using an isometry of the target space.Comment: 40 pages, harvmac, references added, to appear in Commun. Math. Phy
On the partition sum of the NS five-brane
We study the Type IIA NS five-brane wrapped on a Calabi-Yau manifold X in a
double-scaled decoupling limit. We calculate the euclidean partition function
in the presence of a flat RR 3-form field. The classical contribution is given
by a sum over fluxes of the self-dual tensor field which reduces to a
theta-function. The quantum contributions are computed using a T-dual IIB
background where the five-branes are replaced by an ALE singularity. Using the
supergravity effective action we find that the loop corrections to the free
energy are given by B-model topological string amplitudes. This seems to
provide a direct link between the double-scaled little strings on the
five-brane worldvolume and topological strings. Both the classical and quantum
contributions to the partition function satisfy (conjugate) holomorphic anomaly
equations, which explains an observation of Witten relating topological string
theory to the quantization of three-form fields.Comment: 35 page
The partition function of 2d string theory
We derive a compact and explicit expression for the generating functional of
all correlation functions of tachyon operators in 2D string theory. This
expression makes manifest relations of the system to KP flow and
constraints. Moreover we derive a Kontsevich-Penner integral
representation of this generating functional.Comment: 28 pages, 3 figures not included, harvmac. Preprint IASSNS-HEP-92/48,
YCTP-P22-9
Complex Curve of the Two Matrix Model and its Tau-function
We study the hermitean and normal two matrix models in planar approximation
for an arbitrary number of eigenvalue supports. Its planar graph interpretation
is given. The study reveals a general structure of the underlying analytic
complex curve, different from the hyperelliptic curve of the one matrix model.
The matrix model quantities are expressed through the periods of meromorphic
generating differential on this curve and the partition function of the
multiple support solution, as a function of filling numbers and coefficients of
the matrix potential, is shown to be the quasiclassical tau-function. The
relation to softly broken N=1 supersymmetric Yang-Mills theories is discussed.
A general class of solvable multimatrix models with tree-like interactions is
considered.Comment: 36 pages, 10 figures, TeX; final version appeared in special issue of
J.Phys. A on Random Matrix Theor
On fusion algebra of chiral models
We discuss some algebraic setting of chiral models in terms of
the statistical dimensions of their fields. In particular, the conformal
dimensions and the central charge of the chiral models are
calculated from their braid matrices. Futhermore, at level K=2, we present the
characteristic polynomials of their fusion matrices in a factored form.Comment: 11 pages, ioplpp
D-instantons and Matrix Models
We discuss the Matrix Model aspect of configurations saturating a fixed
number of fermionic zero modes. This number is independent of the rank of the
gauge group and the instanton number. This will allow us to define a
large- limit of the embeddeding of D-instantons in the Matrix Model
and make contact with the leading term (the measure factor) of the supergravity
computations of D-instanton effects. We show that the connection between these
two approaches is done through the Abelian modes of the Matrix variables.Comment: harvmac (b), 26 pages. v5 : polished final version for publication.
Cosmetic changes onl
Elliptic Genera of Symmetric Products and Second Quantized Strings
In this note we prove an identity that equates the elliptic genus partition
function of a supersymmetric sigma model on the N-fold symmetric product
of a manifold M to the partition function of a second quantized
string theory on the space . The generating function of these
elliptic genera is shown to be (almost) an automorphic form for O(3,2,Z). In
the context of D-brane dynamics, this result gives a precise computation of the
free energy of a gas of D-strings inside a higher-dimensional brane.Comment: 17 pages, latex, 1 figure, to appear in Commun. Math. Phy
The Bekenstein Formula and String Theory (N-brane Theory)
A review of recent progress in string theory concerning the Bekenstein
formula for black hole entropy is given. Topics discussed include p-branes,
D-branes and supersymmetry; the correspondence principle; the D- and M-brane
approach to black hole entropy; the D-brane analogue of Hawking radiation, and
information loss; D-branes as probes of black holes; and the Matrix theory
approach to charged and neutral black holes. Some introductory material is
included.Comment: 53 pages, LaTeX. v3: Typos fixed, minor updates, references added,
brief Note Added on AdS/CF
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