1,595 research outputs found

### D-Branes and Topological Field Theories

In the presence of a D-brane a string theory develops a new subsector. We
show that for curved D-branes the corresponding sector is a (partially twisted)
topological field theory. We use this result to compute the degeneracy of
2-branes wrapped around $K3$ cycles as well as 3-branes wrapped around CY
threefold vanishing 3-cycles. In both cases we find the degeneracy is in accord
with expectation. The counting of BPS states of a gas of 0-branes in the
presence of a 4-brane in $K3$ is considered and it is noted that the effective
0-brane charge is shifted by 1, due to a quantum correction. This is in accord
with string duality and the fact that left-moving ground state energy of
heterotic string starts at $-1$. We also show that all the three different
topological twistings of four dimensional $N=4$ Yang-Mills theory do arise from
curved three-branes embedded in different spaces (Calabi-Yau manifolds and
manifolds with exceptional holonomy groups).Comment: 22 page

### tt* Geometry and Closed String Tachyon Potential

We propose a closed string tachyon action including kinetic and potential
terms for non-supersymmetric orbifolds. The action is given in terms of
solutions to $tt^*$ equations which captures the geometry of vacua of the
corresponding N=2 worldsheet theory. In certain cases the solutions are well
studied. In case of tachyons of ${\bf C}/Z_n$, solutions to affine toda
equations determine the action. We study the particular case of ${\bf C}/Z_3\to
{\bf C}$ in detail and find that the Tachyon action is determined in terms of a
solution to Painleve III equation.Comment: 10 page

### F-theory and linear sigma models

We present an explicit method for translating between the linear sigma model
and the spectral cover description of SU(r) stable bundles over an elliptically
fibered Calabi-Yau manifold. We use this to investigate the 4-dimensional
duality between (0,2) heterotic and F-theory compactifications. We indirectly
find that much interesting heterotic information must be contained in the
`spectral bundle' and in its dual description as a gauge theory on multiple
F-theory 7-branes.
A by-product of these efforts is a method for analyzing semistability and the
splitting type of vector bundles over an elliptic curve given as the sheaf
cohomology of a monad.Comment: 40 pages, no figures; minor cosmetic reorganization of section 4;
reference [6] update

### Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes

We develop techniques to compute higher loop string amplitudes for twisted
$N=2$ theories with $\hat c=3$ (i.e. the critical case). An important
ingredient is the discovery of an anomaly at every genus in decoupling of BRST
trivial states, captured to all orders by a master anomaly equation. In a
particular realization of the $N=2$ theories, the resulting string field theory
is equivalent to a topological theory in six dimensions, the Kodaira--Spencer
theory, which may be viewed as the closed string analog of the Chern--Simon
theory. Using the mirror map this leads to computation of the `number' of
holomorphic curves of higher genus curves in Calabi--Yau manifolds. It is shown
that topological amplitudes can also be reinterpreted as computing corrections
to superpotential terms appearing in the effective 4d theory resulting from
compactification of standard 10d superstrings on the corresponding $N=2$
theory. Relations with $c=1$ strings are also pointed out.Comment: 178 pages, 20 figure

### On ADE Quiver Models and F-Theory Compactification

Based on mirror symmetry, we discuss geometric engineering of N=1 ADE quiver
models from F-theory compactifications on elliptic K3 surfaces fibered over
certain four-dimensional base spaces. The latter are constructed as
intersecting 4-cycles according to ADE Dynkin diagrams, thereby mimicking the
construction of Calabi-Yau threefolds used in geometric engineering in type II
superstring theory. Matter is incorporated by considering D7-branes wrapping
these 4-cycles. Using a geometric procedure referred to as folding, we discuss
how the corresponding physics can be converted into a scenario with D5-branes
wrapping 2-cycles of ALE spaces.Comment: 21 pages, Latex, minor change

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