1,212 research outputs found

### Distributions of flux vacua

We give results for the distribution and number of flux vacua of various
types, supersymmetric and nonsupersymmetric, in IIb string theory compactified
on Calabi-Yau manifolds. We compare this with related problems such as counting
attractor points.Comment: 43 pages, 7 figures. v2: improved discussion of finding vacua with
discrete flux, references adde

### BPS branes in discrete torsion orbifolds

We investigate D-branes in a Z_3xZ_3 orbifold with discrete torsion. For this
class of orbifolds the only known objects which couple to twisted RR potentials
have been non-BPS branes. By using more general gluing conditions we construct
here a D-brane which is BPS and couples to RR potentials in the twisted and in
the untwisted sectors.Comment: 20 pages, LaTe

### D-branes and Discrete Torsion II

We derive D-brane gauge theories for C^3/Z_n x Z_n orbifolds with discrete
torsion and study the moduli space of a D-brane at a point. We show that, as
suggested in previous work, closed string moduli do not fully resolve the
singularity, but the resulting space -- containing n-1 conifold singularities
-- is somewhat surprising. Fractional branes also have unusual properties.
We also define an index which is the CFT analog of the intersection form in
geometric compactification, and use this to show that the elementary D6-brane
wrapped about T^6/Z_n x Z_n must have U(n) world-volume gauge symmetry.Comment: harvmac, 25 p

### Reverse geometric engineering of singularities

One can geometrically engineer supersymmetric field theories theories by
placing D-branes at or near singularities. The opposite process is described,
where one can reconstruct the singularities from quiver theories. The
description is in terms of a noncommutative quiver algebra which is constructed
from the quiver diagram and the superpotential. The center of this
noncommutative algebra is a commutative algebra, which is the ring of
holomorphic functions on a variety V. If certain algebraic conditions are met,
then the reverse geometric engineering produces V as the geometry that D-branes
probe. It is also argued that the identification of V is invariant under
Seiberg dualities.Comment: 17 pages, Latex. v2: updates reference

### On D0-branes in Gepner models

We show why and when D0-branes at the Gepner point of Calabi-Yau manifolds
given as Fermat hypersurfaces exist.Comment: 22 pages, substantial improvements in sections 2 and 3, references
added, version to be publishe

### Asymptotics and Dimensional Dependence of the Number of Critical Points of Random Holomorphic Sections

We prove two conjectures from [M. R. Douglas, B. Shiffman and S. Zelditch,
Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics.
J. Differential Geom. 72 (2006), no. 3, 381-427] concerning the expected number
of critical points of random holomorphic sections of a positive line bundle. We
show that, on average, the critical points of minimal Morse index are the most
plentiful for holomorphic sections of {\mathcal O}(N) \to \CP^m and, in an
asymptotic sense, for those of line bundles over general K\"ahler manifolds. We
calculate the expected number of these critical points for the respective cases
and use these to obtain growth rates and asymptotic bounds for the total
expected number of critical points in these cases. This line of research was
motivated by landscape problems in string theory and spin glasses.Comment: 14 pages, corrected typo

### The Breakdown of Topology at Small Scales

We discuss how a topology (the Zariski topology) on a space can appear to
break down at small distances due to D-brane decay. The mechanism proposed
coincides perfectly with the phase picture of Calabi-Yau moduli spaces. The
topology breaks down as one approaches non-geometric phases. This picture is
not without its limitations, which are also discussed.Comment: 12 pages, 2 figure

### A Point's Point of View of Stringy Geometry

The notion of a "point" is essential to describe the topology of spacetime.
Despite this, a point probably does not play a particularly distinguished role
in any intrinsic formulation of string theory. We discuss one way to try to
determine the notion of a point from a worldsheet point of view. The derived
category description of D-branes is the key tool. The case of a flop is
analyzed and Pi-stability in this context is tied in to some ideas of
Bridgeland. Monodromy associated to the flop is also computed via Pi-stability
and shown to be consistent with previous conjectures.Comment: 15 pages, 3 figures, ref adde

### Stability and BPS branes

We define the concept of Pi-stability, a generalization of mu-stability of
vector bundles, and argue that it characterizes N=1 supersymmetric brane
configurations and BPS states in very general string theory compactifications
with N=2 supersymmetry in four dimensions.Comment: harvmac, 18 p

### The complex geometry of holographic flows of quiver gauge theories

We argue that the complete Klebanov-Witten flow solution must be described by
a Calabi-Yau metric on the conifold, interpolating between the orbifold at
infinity and the cone over T^(1,1) in the interior. We show that the complete
flow solution is characterized completely by a single, simple, quasi-linear,
second order PDE, or "master equation," in two variables. We show that the
Pilch-Warner flow solution is almost Calabi-Yau: It has a complex structure, a
hermitian metric, and a holomorphic (3,0)-form that is a square root of the
volume form. It is, however, not Kahler. We discuss the relationship between
the master equation derived here for Calabi-Yau geometries and such equations
encountered elsewhere and that govern supersymmetric backgrounds with multiple,
independent fluxes.Comment: 26 pages, harvmac + amssy

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