31 research outputs found
Quivers from Matrix Factorizations
We discuss how matrix factorizations offer a practical method of computing
the quiver and associated superpotential for a hypersurface singularity. This
method also yields explicit geometrical interpretations of D-branes (i.e.,
quiver representations) on a resolution given in terms of Grassmannians. As an
example we analyze some non-toric singularities which are resolved by a single
CP1 but have "length" greater than one. These examples have a much richer
structure than conifolds. A picture is proposed that relates matrix
factorizations in Landau-Ginzburg theories to the way that matrix
factorizations are used in this paper to perform noncommutative resolutions.Comment: 33 pages, (minor changes
New Form of the T-Duality Due to the Stability of a Compact Dimension
We study behaviors of a compact dimension and the -duality, in the
presence of the wrapped closed bosonic strings. When the closed strings
interact and form another system of strings, the radius of compactification
increases. This modifies the -duality, which we call it as -duality-like.
Some effects of the -duality-like will be studied.Comment: 12 pages, Latex, no figur
Evidence for Heterotic/Heterotic Duality
We re-examine the question of heterotic - heterotic string duality in six
dimensions and argue that the heterotic string, compactified on
with equal instanton numbers in the two 's, has a self-duality that
inverts the coupling, dualizes the antisymmetric tensor, acts non-trivially on
the hypermultiplets, and exchanges gauge fields that can be seen in
perturbation theory with gauge fields of a non-perturbative origin. The special
role of the symmetric embedding of the anomaly in the two 's can be seen
from field theory considerations or from an eleven-dimensional point of view.
The duality can be deduced by looking in two different ways at
eleven-dimensional -theory compactified on .Comment: 36 pages, LaTe
Four Dimensional String/String/String Triality
In six spacetime dimensions, the heterotic string is dual to a Type
string. On further toroidal compactification to four spacetime dimensions, the
heterotic string acquires an SL(2,\BbbZ)_S strong/weak coupling duality and
an SL(2,\BbbZ)_T \times SL(2,\BbbZ)_U target space duality acting on the
dilaton/axion, complex Kahler form and the complex structure fields
respectively. Strong/weak duality in interchanges the roles of and
in yielding a Type string with fields . This suggests
the existence of a third string (whose six-dimensional interpretation is more
obscure) that interchanges the roles of and . It corresponds in fact to
a Type string with fields leading to a four-dimensional
string/string/string triality. Since SL(2,\BbbZ)_S is perturbative for the
Type string, this triality implies -duality for the heterotic
string and thus fills a gap left by duality. For all three strings the
total symmetry is SL(2,\BbbZ)_S \times O(6,22;\BbbZ)_{TU}. The
O(6,22;\BbbZ) is {\it perturbative} for the heterotic string but contains the
conjectured {\it non-perturbative} SL(2,\BbbZ)_X, where is the complex
scalar of the Type string. Thus four-dimensional triality also
provides a (post-compactification) justification for this conjecture. We
interpret the Bogomol'nyi spectrum from all three points of view. In
particular we generalize the Sen-Schwarz formula for short multiplets to
include intermediate multiplets also and discuss the corresponding black hole
spectrum both for the theory and for a truncated ---- symmetric
theory. Just as the first two strings are described by the
four-dimensional {\it elementary} and {\it dual solitonic} solutions, so theComment: 36 pages, Latex, 2 figures, some references changed, minor changes in
formulas and tables; to appear in Nucl. Phys.
Introduction to M Theory and AdS/CFT Duality
An introductory survey of some of the developments that have taken place in
superstring theory in the past few years is presented. The main focus is on
three particular dualities. The first one is the appearance of an 11th
dimension in the strong coupling limit of the type IIA theory, which give rise
to M theory. The second one is the duality between the type IIB theory
compactified on a circle and M theory on a two-torus. The final topic is an
introduction to the recently proposed duality between superstring theory or M
theory on certain anti de Sitter space backgrounds and conformally invariant
quantum field theories.Comment: 26 pages; To be published in the Proceedings of a conference held in
Corfu, Greece in September 1998. v2: reference adde
The local Gromov-Witten theory of CP^1 and integrable hierarchies
In this paper we begin the study of the relationship between the local
Gromov-Witten theory of Calabi-Yau rank two bundles over the projective line
and the theory of integrable hierarchies. We first of all construct explicitly,
in a large number of cases, the Hamiltonian dispersionless hierarchies that
govern the full descendent genus zero theory. Our main tool is the application
of Dubrovin's formalism, based on associativity equations, to the known results
on the genus zero theory from local mirror symmetry and localization. The
hierarchies we find are apparently new, with the exception of the resolved
conifold O(-1) + O(-1) -> P1 in the equivariantly Calabi-Yau case. For this
example the relevant dispersionless system turns out to be related to the
long-wave limit of the Ablowitz-Ladik lattice. This identification provides us
with a complete procedure to reconstruct the dispersive hierarchy which should
conjecturally be related to the higher genus theory of the resolved conifold.
We give a complete proof of this conjecture for genus g<=1; our methods are
based on establishing, analogously to the case of KdV, a "quasi-triviality"
property for the Ablowitz-Ladik hierarchy at the leading order of the
dispersive expansion. We furthermore provide compelling evidence in favour of
the resolved conifold/Ablowitz-Ladik correspondence at higher genus by testing
it successfully in the primary sector for g=2.Comment: 30 pages; v2: an issue involving constant maps contributions is
pointed out in Sec. 3.3-3.4 and is now taken into account in the proofs of
Thm 1.3-1.4, whose statements are unchanged. Several typos, formulae,
notational inconsistencies have been fixed. v3: typos fixed, minor textual
changes, version to appear on Comm. Math. Phy
Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
We present the most complete list of mirror pairs of Calabi-Yau complete
intersections in toric ambient varieties and develop the methods to solve the
topological string and to calculate higher genus amplitudes on these compact
Calabi-Yau spaces. These symplectic invariants are used to remove redundancies
in examples. The construction of the B-model propagators leads to compatibility
conditions, which constrain multi-parameter mirror maps. For K3 fibered
Calabi-Yau spaces without reducible fibers we find closed formulas for all
genus contributions in the fiber direction from the geometry of the fibration.
If the heterotic dual to this geometry is known, the higher genus invariants
can be identified with the degeneracies of BPS states contributing to
gravitational threshold corrections and all genus checks on string duality in
the perturbative regime are accomplished. We find, however, that the BPS
degeneracies do not uniquely fix the non-perturbative completion of the
heterotic string. For these geometries we can write the topological partition
function in terms of the Donaldson-Thomas invariants and we perform a
non-trivial check of S-duality in topological strings. We further investigate
transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2
quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur
Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions
We compute logarithmic corrections to the entropy of rotating extremal black
holes using quantum entropy function i.e. Euclidean quantum gravity approach.
Our analysis includes five dimensional supersymmetric BMPV black holes in type
IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL
models, and also non-supersymmetric extremal Kerr black hole and slowly
rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black
holes our results are in perfect agreement with the microscopic results derived
from string theory. In particular we reproduce correctly the dependence of the
logarithmic corrections on the number of U(1) gauge fields in the theory, and
on the angular momentum carried by the black hole in different scaling limits.
We also explain the shortcomings of the Cardy limit in explaining the
logarithmic corrections in the limit in which the (super)gravity description of
these black holes becomes a valid approximation. For non-supersymmetric
extremal black holes, e.g. for the extremal Kerr black hole in four dimensions,
our result provides a stringent testing ground for any microscopic explanation
of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation
between boundary condition and choice of ensemble, modified analysis for
slowly rotating black holes, all results remain unchanged, typos corrected;
v3: minor additions and correction
Gauge Theory and the Excision of Repulson Singularities
We study brane configurations that give rise to large-N gauge theories with
eight supersymmetries and no hypermultiplets. These configurations include a
variety of wrapped, fractional, and stretched branes or strings. The
corresponding spacetime geometries which we study have a distinct kind of
singularity known as a repulson. We find that this singularity is removed by a
distinctive mechanism, leaving a smooth geometry with a core having an enhanced
gauge symmetry. The spacetime geometry can be related to large-N Seiberg-Witten
theory.Comment: 31 pages LaTeX, 2 figures (v3: references added
4-D gauged supergravity analysis of Type IIB vacua on
We analyze vacua of type IIB string theory on in
presence of three-form fluxes from a four dimensional supergravity viewpoint.
The quaternionic geometry of the moduli space together with the special
geometry of the NS and R-R dilatons and of the -complex structure moduli
play a crucial role in the analysis. The introduction of fluxes corresponds to
a particular gauging of N=2, D=4 supergravity. Our results agree with a recent
work of Tripathy and Trivedi. The present formulation shows the power of
supergravity in the study of effective theories with broken supersymmetry.Comment: AMS-LaTeX, 29 page