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390
N=4 topological strings
 Nucl. Phys. B
, 1995
"... We show how to make a topological string theory starting from an N = 4 superconformal theory. The critical dimension for this theory is ĉ = 2 (c = 6). It is shown that superstrings (in both the RNS and GS formulations) and critical N = 2 strings are special cases of this topological theory. Applicat ..."
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Cited by 226 (23 self)
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We show how to make a topological string theory starting from an N = 4 superconformal theory. The critical dimension for this theory is ĉ = 2 (c = 6). It is shown that superstrings (in both the RNS and GS formulations) and critical N = 2 strings are special cases of this topological theory. Applications for this new topological theory include: 1) Proving the vanishing to all orders of all scattering amplitudes for the selfdual N = 2 string with flat background, with the exception of the threepoint function and the closedstring partition function; 2) Showing that the topological partition function of the N = 2 string on the K3 background may be interpreted as computing the superpotential in harmonic superspace generated upon compactification of type II superstrings from 10 to 6 dimensions; and 3) Providing a new prescription for calculating superstring amplitudes which appears to be free of totalderivative ambiguities. July
Mirror Symmetry is TDuality
, 1996
"... It is argued that every CalabiYau manifold X with a mirror Y admits a family of supersymmetric toroidal 3cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space Y . The mirror transformation is equivalent to Tduality on the 3cycles. The geomet ..."
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Cited by 191 (10 self)
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It is argued that every CalabiYau manifold X with a mirror Y admits a family of supersymmetric toroidal 3cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space Y . The mirror transformation is equivalent to Tduality on the 3cycles. The geometry of moduli space is addressed in a general framework. Several examples are discussed. y email: andy@denali.physics.ucsb.edu yy email: yau@abel.math.harvard.edu yyy email: zaslow@abel.math.harvard.edu 1. Introduction The discovery of mirror symmetry in string theory [1] has led to a number of mathematical surprises. Most investigations have focused on the implications of mirror symmetry of the geometry of CalabiYau moduli spaces. In this paper we shall consider the implications of mirror symmetry of the spectrum of BPS soliton states, which are associated to minimal cycles in the CalabiYau. New surprises will be found. The basic idea we will investigate is briefly as follows. Cons...
DBranes on CalabiYau Spaces and Their Mirrors
, 1996
"... We study the boundary states of Dbranes wrapped around supersymmetric cycles in a general CalabiYau manifold. In particular, we show how the geometric data on the cycles are encoded in the boundary states. As an application, we analyze how the mirror symmetry transforms Dbranes, and we verify tha ..."
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Cited by 186 (11 self)
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We study the boundary states of Dbranes wrapped around supersymmetric cycles in a general CalabiYau manifold. In particular, we show how the geometric data on the cycles are encoded in the boundary states. As an application, we analyze how the mirror symmetry transforms Dbranes, and we verify that it is consistent with the conjectured periodicity and the monodromy of the RamondRamond field configuration on a CalabiYau manifold. This also enables us to study open string worldsheet instanton corrections and relate them to closed string instanton counting. The cases when the mirror symmetry is realized as Tduality are also discussed. Permanent address: Department of Particle Physics, Weizmann Institute of Science, 76100 Rehovot Israel. 1 Introduction Dbranes in type II string theories have been identified as RamondRamond charged BPS states [1]. In the presence of a Dbrane, the boundary conditions for open strings are modified in such a way that Dirichlet boundary conditions ...
Nonlinear Instantons from Supersymmetric Pbranes
, 1999
"... Supersymmetric configurations of type II Dbranes with nonzero gauge field strengths in general supersymmetric backgrounds with nonzero B fields are analyzed using the κsymmetric worldvolume action. It is found in dimension four or greater that the usual instanton equation for the gauge field obtai ..."
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Cited by 152 (6 self)
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Supersymmetric configurations of type II Dbranes with nonzero gauge field strengths in general supersymmetric backgrounds with nonzero B fields are analyzed using the κsymmetric worldvolume action. It is found in dimension four or greater that the usual instanton equation for the gauge field obtains a nonlinear deformation. The deformation is parameterized by the topological data of the Bfield, the background geometry and the cycle wrapped by the brane. In the appropriate dimensions, limits and settings these equations reduce to deformed instanton equations recently found in the context of noncommutative geometry as well as those following from Lagrangians based on BottChern forms. We further consider instantons comprised of M5branes wrapping a CalabiYau space with nonvanishing threeform field strengths. It is shown that the instanton equations for the threeform are related to the KodairaSpencer equations.
Fourdimensional String Compactifications with DBranes, Orientifolds and Fluxes
"... This review article provides a pedagogical introduction into various classes of chiral string compactifications to four dimensions with Dbranes and fluxes. The main concern is to provide all necessary technical tools to explicitly construct fourdimensional orientifold vacua, with the final aim to ..."
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Cited by 149 (15 self)
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This review article provides a pedagogical introduction into various classes of chiral string compactifications to four dimensions with Dbranes and fluxes. The main concern is to provide all necessary technical tools to explicitly construct fourdimensional orientifold vacua, with the final aim to come as close as possible to the supersymmetric Standard Model. Furthermore, we outline the available methods to derive the resulting fourdimensional effective action. Finally, we summarize recent attempts to address the
Boundary deformation theory and moduli spaces of Dbranes
, 1999
"... Boundary conformal field theory is the suitable framework for a microscopic treatment of Dbranes in arbitrary CFT backgrounds. In this work, we develop boundary deformation theory in order to study the changes of boundary conditions generated by marginal boundary fields. The deformation parameters ..."
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Cited by 142 (27 self)
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Boundary conformal field theory is the suitable framework for a microscopic treatment of Dbranes in arbitrary CFT backgrounds. In this work, we develop boundary deformation theory in order to study the changes of boundary conditions generated by marginal boundary fields. The deformation parameters may be regarded as continuous moduli of Dbranes. We identify a large class of boundary fields which are shown to be truly marginal, and we derive closed formulas describing the associated deformations to all orders in perturbation theory. This allows us to study the global topology properties of the moduli space rather than local aspects only. As an example, we analyse in detail the moduli space of c = 1 theories, which displays various stringy phenomena.
Spacetime Instanton Corrections in 4D String Vacua (The Seesaw Mechanism for DBrane Models)
, 2006
"... We systematically investigate instanton corrections from wrapped Euclidean Dbranes to the matter field superpotential of various classes of N=1 supersymmetric Dbrane models in four dimensions. Both gauge invariance and counting fermionic zero modes provide strong constraints on the allowed nonper ..."
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Cited by 139 (28 self)
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We systematically investigate instanton corrections from wrapped Euclidean Dbranes to the matter field superpotential of various classes of N=1 supersymmetric Dbrane models in four dimensions. Both gauge invariance and counting fermionic zero modes provide strong constraints on the allowed nonperturbative superpotential couplings. We outline how the complete instanton computation boils down to the computation of open string disc diagrams for boundary changing operators multiplied by a oneloop vacuum diagram. For concreteness we focus on E2instanton effects in Type IIA vacua with intersecting D6branes, however the same structure emerges for Type IIB and heterotic vacua. The instantons wrapping rigid cycles can potentially destabilise the vacuum or generate perturbatively absent matter couplings such as proton decay operators, µparameter or righthanded neutrino Majorana mass terms. The latter allow the realization of the seesaw mechanism for MSSM like intersecting Dbrane models.
Categorical mirror symmetry: the elliptic curve
 Adv. Theor. Math. Phys
, 1998
"... We describe an isomorphism of categories conjectured by Kontsevich. If M and ˜ M are mirror pairs then the conjectural equivalence is between the derived category of coherent sheaves on M and a suitable version of Fukaya’s category of Lagrangian submanifolds on ˜ M. We prove this equivalence when M ..."
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Cited by 110 (11 self)
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We describe an isomorphism of categories conjectured by Kontsevich. If M and ˜ M are mirror pairs then the conjectural equivalence is between the derived category of coherent sheaves on M and a suitable version of Fukaya’s category of Lagrangian submanifolds on ˜ M. We prove this equivalence when M is an elliptic curve and ˜ M is its dual curve, exhibiting the dictionary in detail.
The effective action of type IIA CalabiYau orientifolds
"... The N = 1 effective action for generic type IIA CalabiYau orientifolds in the presence of background fluxes is computed from a KaluzaKlein reduction. The Kähler potential, the gauge kinetic functions and the fluxinduced superpotential are determined in terms of geometrical data of the CalabiYau ..."
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Cited by 97 (6 self)
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The N = 1 effective action for generic type IIA CalabiYau orientifolds in the presence of background fluxes is computed from a KaluzaKlein reduction. The Kähler potential, the gauge kinetic functions and the fluxinduced superpotential are determined in terms of geometrical data of the CalabiYau orientifold and the background fluxes. The moduli space is found to be a Kähler subspace of the N = 2 moduli space and shown to coincide with the moduli space arising in compactification of Mtheory on a specific class of G2 manifolds. The superpotential depends on all geometrical moduli and vanishes at leading order when background fluxes are turned off. The N = 1 chiral coordinates linearize the appropriate instanton actions such that instanton effects can lead to holomorphic corrections of the superpotential. Mirror symmetry between type IIA and type IIB orientifolds is shown to hold at the level of the effective action in the large volume – large complex structure limit.