Comment on the generation number in orbifold compactifications
Identifieur interne : 001D10 ( Istex/Checkpoint ); précédent : 001D09; suivant : 001D11Comment on the generation number in orbifold compactifications
Auteurs : Jens Erler [Allemagne] ; Albrecht Klemm [Allemagne]Source :
- Communications in Mathematical Physics [ 0010-3616 ] ; 1993-05-01.
English descriptors
- KwdEn :
- Algebraic geometry, Antisymmetric background field, Asymmetric orbifolds, Automorphism, Automorphisms, Background parameters, Base points, Basic cones, Bilinear form, Block structure, Characteristic polynomial, Chiral generations, Compactifications, Complex torus, Conformal field theory, Coxeter, Coxeter automorphism, Coxeter twist, Degeneracy factors, Different lattices, Discrete torsion, Divisor, Dual cone, Dual lattice, Duality, Eigenvalue, Equivalence relation, Erler, Euler number, Exceptional divisors, Exponent, Gauge part, Generation number, Group action, Heterotic, Heterotic string, Hodge, Hodge numbers, Inequivalent, Inequivalent automorphisms, Instanton sums, Intersection pattern, Invariance, Invariant lattice, Invariant sublattice, Invariant subspace, Irreducible, Irreducible blocks, Klemm, Large radius limit, Lattice, Lattice automorphism, Lattice basis, Linear relations, Loop partition function, Massive states, Massless spectrum, Matrix, Mirror maps, Modular group, Modular invariance, Modular parameters, Modular symmetry group, Moduli space, Moduli spaces, Modulus, Narain, Necessary condition, Nucl, Orbifold, Orbifold compactifications, Orbifold singularities, Orbifolds, Orbit sums, Other cases, Other hand, Outer automorphisms, Partition function, Partition functions, Phys, Point singularities, Point theorem, Poisson resummation formula, Projective spaces, Same twist eigenvalues, Self intersection numbers, Singularity, Singularity theory, Sphere tree, String compactifications, String theories, String theory, String vacua, Toms lattice, Toric, Toric varieties, Toric variety, Toroidal, Toroidal orbifolds, Torus, Torus lattice, Transition functions, Twist eigenvalues, Twist exponents, Twist matrices, Twist matrix, Vertex operators, Volume factor, Volume factors, Weyl reflections, Wilson lines, World sheet, World sheet supersymmetry, Yukawa couplings.
- Teeft :
- Algebraic geometry, Antisymmetric background field, Asymmetric orbifolds, Automorphism, Automorphisms, Background parameters, Base points, Basic cones, Bilinear form, Block structure, Characteristic polynomial, Chiral generations, Compactifications, Complex torus, Conformal field theory, Coxeter, Coxeter automorphism, Coxeter twist, Degeneracy factors, Different lattices, Discrete torsion, Divisor, Dual cone, Dual lattice, Duality, Eigenvalue, Equivalence relation, Erler, Euler number, Exceptional divisors, Exponent, Gauge part, Generation number, Group action, Heterotic, Heterotic string, Hodge, Hodge numbers, Inequivalent, Inequivalent automorphisms, Instanton sums, Intersection pattern, Invariance, Invariant lattice, Invariant sublattice, Invariant subspace, Irreducible, Irreducible blocks, Klemm, Large radius limit, Lattice, Lattice automorphism, Lattice basis, Linear relations, Loop partition function, Massive states, Massless spectrum, Matrix, Mirror maps, Modular group, Modular invariance, Modular parameters, Modular symmetry group, Moduli space, Moduli spaces, Modulus, Narain, Necessary condition, Nucl, Orbifold, Orbifold compactifications, Orbifold singularities, Orbifolds, Orbit sums, Other cases, Other hand, Outer automorphisms, Partition function, Partition functions, Phys, Point singularities, Point theorem, Poisson resummation formula, Projective spaces, Same twist eigenvalues, Self intersection numbers, Singularity, Singularity theory, Sphere tree, String compactifications, String theories, String theory, String vacua, Toms lattice, Toric, Toric varieties, Toric variety, Toroidal, Toroidal orbifolds, Torus, Torus lattice, Transition functions, Twist eigenvalues, Twist exponents, Twist matrices, Twist matrix, Vertex operators, Volume factor, Volume factors, Weyl reflections, Wilson lines, World sheet, World sheet supersymmetry, Yukawa couplings.
Abstract
Abstract: There has been some confusion concerning the number of (1, 1)-forms in orbifold compactifications of the heterotic string in numerous publications. In this note we point out the relevance of the underlying torus lattice on this number. We answer the question when different lattices mimic the same physics and when this is not the case. As a byproduct we classify all symmetricZ N -orbifolds with (2, 2) world sheet supersymmetry obtaining also some new ones.
Url:
DOI: 10.1007/BF02096954
Affiliations:
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ISTEX:D4F8DFB797A363FF1665F54F67ED5F230754D1F2Le document en format XML
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<author><name sortKey="Klemm, Albrecht" sort="Klemm, Albrecht" uniqKey="Klemm A" first="Albrecht" last="Klemm">Albrecht Klemm</name>
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<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Algebraic geometry</term>
<term>Antisymmetric background field</term>
<term>Asymmetric orbifolds</term>
<term>Automorphism</term>
<term>Automorphisms</term>
<term>Background parameters</term>
<term>Base points</term>
<term>Basic cones</term>
<term>Bilinear form</term>
<term>Block structure</term>
<term>Characteristic polynomial</term>
<term>Chiral generations</term>
<term>Compactifications</term>
<term>Complex torus</term>
<term>Conformal field theory</term>
<term>Coxeter</term>
<term>Coxeter automorphism</term>
<term>Coxeter twist</term>
<term>Degeneracy factors</term>
<term>Different lattices</term>
<term>Discrete torsion</term>
<term>Divisor</term>
<term>Dual cone</term>
<term>Dual lattice</term>
<term>Duality</term>
<term>Eigenvalue</term>
<term>Equivalence relation</term>
<term>Erler</term>
<term>Euler number</term>
<term>Exceptional divisors</term>
<term>Exponent</term>
<term>Gauge part</term>
<term>Generation number</term>
<term>Group action</term>
<term>Heterotic</term>
<term>Heterotic string</term>
<term>Hodge</term>
<term>Hodge numbers</term>
<term>Inequivalent</term>
<term>Inequivalent automorphisms</term>
<term>Instanton sums</term>
<term>Intersection pattern</term>
<term>Invariance</term>
<term>Invariant lattice</term>
<term>Invariant sublattice</term>
<term>Invariant subspace</term>
<term>Irreducible</term>
<term>Irreducible blocks</term>
<term>Klemm</term>
<term>Large radius limit</term>
<term>Lattice</term>
<term>Lattice automorphism</term>
<term>Lattice basis</term>
<term>Linear relations</term>
<term>Loop partition function</term>
<term>Massive states</term>
<term>Massless spectrum</term>
<term>Matrix</term>
<term>Mirror maps</term>
<term>Modular group</term>
<term>Modular invariance</term>
<term>Modular parameters</term>
<term>Modular symmetry group</term>
<term>Moduli space</term>
<term>Moduli spaces</term>
<term>Modulus</term>
<term>Narain</term>
<term>Necessary condition</term>
<term>Nucl</term>
<term>Orbifold</term>
<term>Orbifold compactifications</term>
<term>Orbifold singularities</term>
<term>Orbifolds</term>
<term>Orbit sums</term>
<term>Other cases</term>
<term>Other hand</term>
<term>Outer automorphisms</term>
<term>Partition function</term>
<term>Partition functions</term>
<term>Phys</term>
<term>Point singularities</term>
<term>Point theorem</term>
<term>Poisson resummation formula</term>
<term>Projective spaces</term>
<term>Same twist eigenvalues</term>
<term>Self intersection numbers</term>
<term>Singularity</term>
<term>Singularity theory</term>
<term>Sphere tree</term>
<term>String compactifications</term>
<term>String theories</term>
<term>String theory</term>
<term>String vacua</term>
<term>Toms lattice</term>
<term>Toric</term>
<term>Toric varieties</term>
<term>Toric variety</term>
<term>Toroidal</term>
<term>Toroidal orbifolds</term>
<term>Torus</term>
<term>Torus lattice</term>
<term>Transition functions</term>
<term>Twist eigenvalues</term>
<term>Twist exponents</term>
<term>Twist matrices</term>
<term>Twist matrix</term>
<term>Vertex operators</term>
<term>Volume factor</term>
<term>Volume factors</term>
<term>Weyl reflections</term>
<term>Wilson lines</term>
<term>World sheet</term>
<term>World sheet supersymmetry</term>
<term>Yukawa couplings</term>
</keywords>
<keywords scheme="Teeft" xml:lang="en"><term>Algebraic geometry</term>
<term>Antisymmetric background field</term>
<term>Asymmetric orbifolds</term>
<term>Automorphism</term>
<term>Automorphisms</term>
<term>Background parameters</term>
<term>Base points</term>
<term>Basic cones</term>
<term>Bilinear form</term>
<term>Block structure</term>
<term>Characteristic polynomial</term>
<term>Chiral generations</term>
<term>Compactifications</term>
<term>Complex torus</term>
<term>Conformal field theory</term>
<term>Coxeter</term>
<term>Coxeter automorphism</term>
<term>Coxeter twist</term>
<term>Degeneracy factors</term>
<term>Different lattices</term>
<term>Discrete torsion</term>
<term>Divisor</term>
<term>Dual cone</term>
<term>Dual lattice</term>
<term>Duality</term>
<term>Eigenvalue</term>
<term>Equivalence relation</term>
<term>Erler</term>
<term>Euler number</term>
<term>Exceptional divisors</term>
<term>Exponent</term>
<term>Gauge part</term>
<term>Generation number</term>
<term>Group action</term>
<term>Heterotic</term>
<term>Heterotic string</term>
<term>Hodge</term>
<term>Hodge numbers</term>
<term>Inequivalent</term>
<term>Inequivalent automorphisms</term>
<term>Instanton sums</term>
<term>Intersection pattern</term>
<term>Invariance</term>
<term>Invariant lattice</term>
<term>Invariant sublattice</term>
<term>Invariant subspace</term>
<term>Irreducible</term>
<term>Irreducible blocks</term>
<term>Klemm</term>
<term>Large radius limit</term>
<term>Lattice</term>
<term>Lattice automorphism</term>
<term>Lattice basis</term>
<term>Linear relations</term>
<term>Loop partition function</term>
<term>Massive states</term>
<term>Massless spectrum</term>
<term>Matrix</term>
<term>Mirror maps</term>
<term>Modular group</term>
<term>Modular invariance</term>
<term>Modular parameters</term>
<term>Modular symmetry group</term>
<term>Moduli space</term>
<term>Moduli spaces</term>
<term>Modulus</term>
<term>Narain</term>
<term>Necessary condition</term>
<term>Nucl</term>
<term>Orbifold</term>
<term>Orbifold compactifications</term>
<term>Orbifold singularities</term>
<term>Orbifolds</term>
<term>Orbit sums</term>
<term>Other cases</term>
<term>Other hand</term>
<term>Outer automorphisms</term>
<term>Partition function</term>
<term>Partition functions</term>
<term>Phys</term>
<term>Point singularities</term>
<term>Point theorem</term>
<term>Poisson resummation formula</term>
<term>Projective spaces</term>
<term>Same twist eigenvalues</term>
<term>Self intersection numbers</term>
<term>Singularity</term>
<term>Singularity theory</term>
<term>Sphere tree</term>
<term>String compactifications</term>
<term>String theories</term>
<term>String theory</term>
<term>String vacua</term>
<term>Toms lattice</term>
<term>Toric</term>
<term>Toric varieties</term>
<term>Toric variety</term>
<term>Toroidal</term>
<term>Toroidal orbifolds</term>
<term>Torus</term>
<term>Torus lattice</term>
<term>Transition functions</term>
<term>Twist eigenvalues</term>
<term>Twist exponents</term>
<term>Twist matrices</term>
<term>Twist matrix</term>
<term>Vertex operators</term>
<term>Volume factor</term>
<term>Volume factors</term>
<term>Weyl reflections</term>
<term>Wilson lines</term>
<term>World sheet</term>
<term>World sheet supersymmetry</term>
<term>Yukawa couplings</term>
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<front><div type="abstract" xml:lang="en">Abstract: There has been some confusion concerning the number of (1, 1)-forms in orbifold compactifications of the heterotic string in numerous publications. In this note we point out the relevance of the underlying torus lattice on this number. We answer the question when different lattices mimic the same physics and when this is not the case. As a byproduct we classify all symmetricZ N -orbifolds with (2, 2) world sheet supersymmetry obtaining also some new ones.</div>
</front>
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<affiliations><list><country><li>Allemagne</li>
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<li>District de Haute-Bavière</li>
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<orgName><li>Université technique de Munich</li>
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<name sortKey="Klemm, Albrecht" sort="Klemm, Albrecht" uniqKey="Klemm A" first="Albrecht" last="Klemm">Albrecht Klemm</name>
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