88 research outputs found
Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
We develop techniques to compute higher loop string amplitudes for twisted
theories with (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 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
theory. Relations with strings are also pointed out.Comment: 178 pages, 20 figure
Planar Gravitational Corrections For Supersymmetric Gauge Theories
In this paper we discuss the contribution of planar diagrams to gravitational
F-terms for N=1 supersymmetric gauge theories admitting a large N description.
We show how the planar diagrams lead to a universal contribution at the
extremum of the glueball superpotential, leaving only the genus one
contributions, as was previously conjectured. We also discuss the physical
meaning of gravitational F-terms.Comment: 20 pages, 4 figure
S-duality and Topological Strings
In this paper we show how S-duality of type IIB superstrings leads to an
S-duality relating A and B model topological strings on the same Calabi-Yau as
had been conjectured recently: D-instantons of the B-model correspond to
A-model perturbative amplitudes and D-instantons of the A-model capture
perturbative B-model amplitudes.
Moreover this confirms the existence of new branes in the two models.
As an application we explain the recent results concerning A-model
topological strings on Calabi-Yau and its equivalence to the statistical
mechanical model of melting crystal.Comment: 13 page
Link Homologies and the Refined Topological Vertex
We establish a direct map between refined topological vertex and sl(N)
homological invariants of the of Hopf link, which include Khovanov-Rozansky
homology as a special case. This relation provides an exact answer for
homological invariants of the of Hopf link, whose components are colored by
arbitrary representations of sl(N). At present, the mathematical formulation of
such homological invariants is available only for the fundamental
representation (the Khovanov-Rozansky theory) and the relation with the refined
topological vertex should be useful for categorifying quantum group invariants
associated with other representations (R_1, R_2). Our result is a first direct
verification of a series of conjectures which identifies link homologies with
the Hilbert space of BPS states in the presence of branes, where the physical
interpretation of gradings is in terms of charges of the branes ending on
Lagrangian branes.Comment: 38 pages, 5 figure
Refined topological amplitudes in N=1 flux compactification
We study the implication of refined topological string amplitudes in the
supersymmetric N=1 flux compactification. They generate higher derivative
couplings among the vector multiplets and graviphoton with generically
non-holomorphic moduli dependence. For a particular term, we can compute them
by assuming the geometric engineering. We claim that the Dijkgraaf-Vafa large N
matrix model with the beta-ensemble measure directly computes the higher
derivative corrections to the supersymmetric effective action of the
supersymmetric N=1$ gauge theory.Comment: 16 pages, v2: reference adde
Gravitational Correction and Weak Gravity Conjecture
We consider the gravitational correction to the running of gauge coupling.
Weak gravity conjecture implies that the gauge theories break down when the
gravitational correction becomes greater than the contribution from gauge
theories. This observation can be generalized to non-Abelian gauge theories in
diverse dimensions and the cases with large extra dimensions.Comment: 8 pages; minor correction and refs adde
Meta-Stable Brane Configurations with Seven NS5-Branes
We present the intersecting brane configurations consisting of NS-branes,
D4-branes(and anti D4-branes) and O6-plane, of type IIA string theory
corresponding to the meta-stable nonsupersymmetric vacua in four dimensional
N=1 supersymmetric SU(N_c) x SU(N_c') x SU(N_c'') gauge theory with a symmetric
tensor field, a conjugate symmetric tensor field and bifundamental fields. We
also describe the intersecting brane configurations of type IIA string theory
corresponding to the nonsupersymmetric meta-stable vacua in the above gauge
theory with an antisymmetric tensor field, a conjugate symmetric tensor field,
eight fundamental flavors and bifundamentals. These brane configurations
consist of NS-branes, D4-branes(and anti D4-branes), D6-branes and O6-planes.Comment: 34pp, 9 figures; Improved the draft and added some footnotes; Figure
1, footnote 7 and captions of Figures 7,8,9 added or improved and to appear
in CQ
Khovanov-Rozansky Homology and Topological Strings
We conjecture a relation between the sl(N) knot homology, recently introduced
by Khovanov and Rozansky, and the spectrum of BPS states captured by open
topological strings. This conjecture leads to new regularities among the sl(N)
knot homology groups and suggests that they can be interpreted directly in
topological string theory. We use this approach in various examples to predict
the sl(N) knot homology groups for all values of N. We verify that our
predictions pass some non-trivial checks.Comment: 25 pages, 2 figures, harvmac; minor corrections, references adde
Holomorphic Anomalies in Topological Field Theories
We study the stringy genus one partition function of SCFT's. It is
shown how to compute this using an anomaly in decoupling of BRST trivial states
from the partition function. A particular limit of this partition function
yields the partition function of topological theory coupled to topological
gravity. As an application we compute the number of holomorphic elliptic curves
over certain Calabi-Yau manifolds including the quintic threefold. This may be
viewed as the first application of mirror symmetry at the string quantum level.Comment: 32 pages. Appendix by S.Kat
Gravitational corrections in supersymmetric gauge theory and matrix models
Gravitational corrections in N=1 and N=2 supersymmetric gauge theories are
obtained from topological string amplitudes. We show how they are recovered in
matrix model computations. This provides a test of the proposal by Dijkgraaf
and Vafa beyond the planar limit. Both, matrix model and topological string
theory, are used to check a conjecture of Nekrasov concerning these
gravitational couplings in Seiberg-Witten theory. Our analysis is performed for
those gauge theories which are related to the cubic matrix model, i.e. pure
SU(2) Seiberg-Witten theory and N=2 U(N) SYM broken to N=1 via a cubic
superpotential. We outline the computation of the topological amplitudes for
the local Calabi-Yau manifolds which are relevant for these two cases.Comment: 27 pages, one eps figur
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