Results 1  10
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30
A nogo theorem for string warped compactifications
, 2000
"... We give necessary conditions for the existence of perturbative heterotic and type II string warped compactifications preserving eight and four supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connecti ..."
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Cited by 60 (21 self)
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We give necessary conditions for the existence of perturbative heterotic and type II string warped compactifications preserving eight and four supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are those on CalabiYau manifolds with constant dilaton. We obtain similar results for compactifications to six and to two dimensions.
The Srní lectures on nonintegrable geometries with torsion
 Arch. Math. (Brno
, 2006
"... Abstract. This review article intends to introduce the reader to nonintegrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections ..."
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Cited by 58 (8 self)
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Abstract. This review article intends to introduce the reader to nonintegrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skewsymmetric torsion are exhibited as one of the main tools to understand nonintegrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of intrinsic torsion and characteristic connection of a Gstructure as unifying principles. The General Holonomy Principle bridges over to parallel objects, thus motivating the discussion of geometric stabilizers, with emphasis on spinors and differential forms. Several Weitzenböck formulas for Dirac operators associated with torsion connections enable us to discuss spinorial field equations, such as those governing the common sector of type II superstring theory.
HETEROTIC SUPERSYMMETRY, ANOMALY CANCELLATION AND EQUATIONS OF MOTION
, 2009
"... We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion up to two loops in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an instanton. For heterotic compactifications in dimen ..."
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Cited by 25 (1 self)
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We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion up to two loops in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an instanton. For heterotic compactifications in dimension six this fixes an unique choice of the connection on the tangent bundle in the α′ correction of the anomaly cancellation.
Vanishing Theorems and String Backgrounds
, 2000
"... We show various vanishing theorems for the cohomology groups of compact hermitian manifolds for which the Bismut connection has (restricted) holonomy contained in SU(n) and classify all such manifolds of dimension four. In this way we provide necessary conditions for the existence of such structures ..."
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Cited by 23 (1 self)
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We show various vanishing theorems for the cohomology groups of compact hermitian manifolds for which the Bismut connection has (restricted) holonomy contained in SU(n) and classify all such manifolds of dimension four. In this way we provide necessary conditions for the existence of such structures on hermitian manifolds. Then we apply our results to solutions of the string equations and show that such solutions admit various cohomological restrictions like for example that under certain natural assumptions the plurigenera vanish. We also find that under some assumptions the string equations are equivalent to the condition Riemannian manifolds equipped with a closed form have found many applications in various branches of mathematics and physics. In physics, the classical example is that of manifolds equipped with a closed twoform which describe gravity in the presence of a Maxwell field. More recently, Riemannian or pseudoRiemannian manifolds M equipped with (closed) forms
KT and HKT geometries in strings and black hole moduli spaces
"... Some selected applications of KT and HKT geometries in string theory, supergravity, black hole moduli spaces and hermitian geometry are reviewed. It is shown that the moduli spaces of a large class of fivedimensional supersymmetric black holes are HKT spaces. In hermitian geometry, it is shown that ..."
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Cited by 12 (0 self)
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Some selected applications of KT and HKT geometries in string theory, supergravity, black hole moduli spaces and hermitian geometry are reviewed. It is shown that the moduli spaces of a large class of fivedimensional supersymmetric black holes are HKT spaces. In hermitian geometry, it is shown that a compact, conformally balanced, strong KT manifold whose associated KT connection has holonomy contained in SU(n) is CalabiYau. The implication of this result in the context of some string compactifications is explained
NonKaehler Heterotic String Compactifications with nonzero fluxes and constant dilaton
, 2008
"... We construct new explicit compact valid solutions with nonzero field strength and constant dilaton to the heterotic string equations in dimension six. We present balanced Hermitian structures on compact nilmanifolds in dimension six satisfying the heterotic supersymmetry equations with nonzero f ..."
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Cited by 7 (3 self)
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We construct new explicit compact valid solutions with nonzero field strength and constant dilaton to the heterotic string equations in dimension six. We present balanced Hermitian structures on compact nilmanifolds in dimension six satisfying the heterotic supersymmetry equations with nonzero flux and constant dilaton which obey the threeform Bianchi identity with curvature term taken with respect to either the LeviCivita, the (+)connection or the Chern connection.
COMPACT SUPERSYMMETRIC SOLUTIONS OF THE HETEROTIC EQUATIONS OF MOTION IN DIMENSION 5
, 2008
"... We construct explicit compact supersymmetric solutions with nonzero field strength, nonflat instanton and constant dilaton to the heterotic string equations in dimension five. We present a quadratic condition on the curvature which is necessary and sufficient the heterotic supersymmetry and the a ..."
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Cited by 7 (1 self)
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We construct explicit compact supersymmetric solutions with nonzero field strength, nonflat instanton and constant dilaton to the heterotic string equations in dimension five. We present a quadratic condition on the curvature which is necessary and sufficient the heterotic supersymmetry and the anomaly cancellation to imply the heterotic equations of motion in dimension five. We supply compact nilmanifold in dimension 5 satisfying the heterotic supersymmetry equations with nonzero fluxes and constant dilaton which obey the threeform Bianchi identity and solves the heterotic equations of motion in dimension five.
Solution of heterotic Killing spinor equations and special geometry, arXiv:0811.1539
"... We outline the solution of the Killing spinor equations of the heterotic supergravity. In addition, we describe the classification of all half supersymmetric Supersymmetric supergravity backgrounds are solutions of the field equations of supergravity theories which in addition solve a set of first o ..."
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Cited by 5 (1 self)
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We outline the solution of the Killing spinor equations of the heterotic supergravity. In addition, we describe the classification of all half supersymmetric Supersymmetric supergravity backgrounds are solutions of the field equations of supergravity theories which in addition solve a set of first order equations, the Killing spinor equations. These solutions are triplets (M, g, F), where M is a Lorentzian manifold with metric g, and F are the fluxes of supergravity theories which is a collection of forms
1/2, 1/4 and 1/8 BPS Equations in SUSY YangMillsHiggs Systems – Field Theoretical Brane Configurations –
, 2005
"... We systematically classify 1/2, 1/4 and 1/8 BPS equations in SUSY gauge theories in d = 6,5,4,3 and 2 with eight supercharges, with gauge groups and matter contents being arbitrary. Instantons (strings) and vortices (3branes) are only allowed 1/2 BPS solitons in d = 6 with N = 1 SUSY. We find two 1 ..."
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Cited by 3 (1 self)
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We systematically classify 1/2, 1/4 and 1/8 BPS equations in SUSY gauge theories in d = 6,5,4,3 and 2 with eight supercharges, with gauge groups and matter contents being arbitrary. Instantons (strings) and vortices (3branes) are only allowed 1/2 BPS solitons in d = 6 with N = 1 SUSY. We find two 1/4 BPS equations and the unique 1/8 BPS equation in d = 6 by considering configurations made of these field theory branes. All known BPS equations are rederived while many new 1/4 and 1/8 BPS equations are found in dimension less than six by dimensional reductions.