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Hierarchies from Fluxes in String Compactifications
, 2002
"... Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory a ..."
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Cited by 724 (33 self)
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Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory and Ftheory compactifications on CalabiYau fourfolds. In each case, the hierarchy of scales is fixed by a choice of RR and NS fluxes in the compact manifold. Our solutions involve compactifications of the KlebanovStrassler gravity dual to a confining N = 1 supersymmetric gauge theory, and the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory.
The selfduality equations on a Riemann surface
 Proc. Lond. Math. Soc., III. Ser
, 1987
"... In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled 'instanton ..."
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Cited by 524 (6 self)
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In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled 'instantons'. The same equations may be
Existence of minimal models for varieties of log general type
 J. AMER. MATH. SOC
, 2008
"... We prove that the canonical ring of a smooth projective variety is finitely generated. ..."
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Cited by 386 (34 self)
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We prove that the canonical ring of a smooth projective variety is finitely generated.
Fivebranes, Membranes And NonPerturbative String Theory
, 1995
"... Nonperturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a CalabiYau space are derived and found to contain order e \Gamma1=g s contributions, where g s is the string coupling. The computation reduces to a weighted sum of supersymmetric extrema ..."
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Cited by 394 (7 self)
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Nonperturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a CalabiYau space are derived and found to contain order e \Gamma1=g s contributions, where g s is the string coupling. The computation reduces to a weighted sum of supersymmetric
Generalized CalabiYau manifolds
 Q. J. Math
"... A geometrical structure on evendimensional manifolds is defined which generalizes the notion of a CalabiYau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of both diffeomorphisms and closed 2forms. In the special case o ..."
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Cited by 330 (3 self)
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A geometrical structure on evendimensional manifolds is defined which generalizes the notion of a CalabiYau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of both diffeomorphisms and closed 2forms. In the special case
EXERCISES IN THE BIRATIONAL GEOMETRY OF ALGEBRAIC VARIETIES
, 2008
"... The book [KM98] gave an introduction to the birational geometry of algebraic varieties, as the subject stood in 1998. The developments of the last decade made the more advanced parts of Chapters 6 and 7 less important and the detailed treatment of surface singularities in Chapter 4 less necessary. H ..."
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Cited by 328 (2 self)
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smooth projective surfaces is a composite of blowups and blowdowns. Theorem 2. There are 3 species of “purebred ” surfaces: (Rational): For these surfaces the internal birational geometry is very complicated, but, up to birational equivalence, we have only P 2. These frequently appear in the classical
ElectricMagnetic duality and the geometric Langlands program
, 2006
"... The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t H ..."
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Cited by 300 (26 self)
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The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t
Results 1  10
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13,582