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A.n. Schellekens - One of the best experts on this subject based on the ideXlab platform.
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simple currents versus orbifolds with discrete torsion a Complete Classification
Nuclear Physics, 1994Co-Authors: M Kreuzer, A.n. SchellekensAbstract:Abstract We give a Complete Classification of all simple current modular invariants, extending previous results for (Z p ) k to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this end, we find a one-to-one correspondence between simple current invariants and subgroups of the center with discrete torsions. As a by-product, we prove the conjectured monodromy independence of the total number of such invariants. The orbifold approach works in a straightforward way for symmetries of odd order, but some modifications are required to deal with symmetries of even order. With these modifications the orbifold construction with descrete torsion is Complete within the class of simple current invariants. Surprisingly, there are cases where discrete torsion is a necessity rather than a possibility.
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Simple currents versus orbifolds with discrete torsion — a Complete Classification
Nuclear Physics B, 1994Co-Authors: M Kreuzer, A.n. SchellekensAbstract:Abstract We give a Complete Classification of all simple current modular invariants, extending previous results for (Z p ) k to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this end, we find a one-to-one correspondence between simple current invariants and subgroups of the center with discrete torsions. As a by-product, we prove the conjectured monodromy independence of the total number of such invariants. The orbifold approach works in a straightforward way for symmetries of odd order, but some modifications are required to deal with symmetries of even order. With these modifications the orbifold construction with descrete torsion is Complete within the class of simple current invariants. Surprisingly, there are cases where discrete torsion is a necessity rather than a possibility.
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simple currents versus orbifolds with discrete torsion a Complete Classification
arXiv: High Energy Physics - Theory, 1993Co-Authors: M Kreuzer, A.n. SchellekensAbstract:We give a Complete Classification of all simple current modular invariants, extending previous results for $(\Zbf_p)^k$ to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this end, we find a one-to-one correspondence between simple current invariants and subgroups of the center with discrete torsions. As a by-product, we prove the conjectured monodromy independence of the total number of such invariants. The orbifold approach works in a straightforward way for symmetries of odd order, but some modifications are required to deal with symmetries of even order. With these modifications the orbifold construction with discrete torsion is Complete within the class of simple current invariants. Surprisingly, there are cases where discrete torsion is a necessity rather than a possibility.
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Complete Classification of simple current automorphisms
Nuclear Physics B, 1991Co-Authors: Beatriz Gato-rivera, A.n. SchellekensAbstract:Abstract The Complete Classification of all fusion rule automorphisms within simple current orbits is presented.
M Kreuzer - One of the best experts on this subject based on the ideXlab platform.
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simple currents versus orbifolds with discrete torsion a Complete Classification
Nuclear Physics, 1994Co-Authors: M Kreuzer, A.n. SchellekensAbstract:Abstract We give a Complete Classification of all simple current modular invariants, extending previous results for (Z p ) k to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this end, we find a one-to-one correspondence between simple current invariants and subgroups of the center with discrete torsions. As a by-product, we prove the conjectured monodromy independence of the total number of such invariants. The orbifold approach works in a straightforward way for symmetries of odd order, but some modifications are required to deal with symmetries of even order. With these modifications the orbifold construction with descrete torsion is Complete within the class of simple current invariants. Surprisingly, there are cases where discrete torsion is a necessity rather than a possibility.
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Simple currents versus orbifolds with discrete torsion — a Complete Classification
Nuclear Physics B, 1994Co-Authors: M Kreuzer, A.n. SchellekensAbstract:Abstract We give a Complete Classification of all simple current modular invariants, extending previous results for (Z p ) k to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this end, we find a one-to-one correspondence between simple current invariants and subgroups of the center with discrete torsions. As a by-product, we prove the conjectured monodromy independence of the total number of such invariants. The orbifold approach works in a straightforward way for symmetries of odd order, but some modifications are required to deal with symmetries of even order. With these modifications the orbifold construction with descrete torsion is Complete within the class of simple current invariants. Surprisingly, there are cases where discrete torsion is a necessity rather than a possibility.
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simple currents versus orbifolds with discrete torsion a Complete Classification
arXiv: High Energy Physics - Theory, 1993Co-Authors: M Kreuzer, A.n. SchellekensAbstract:We give a Complete Classification of all simple current modular invariants, extending previous results for $(\Zbf_p)^k$ to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this end, we find a one-to-one correspondence between simple current invariants and subgroups of the center with discrete torsions. As a by-product, we prove the conjectured monodromy independence of the total number of such invariants. The orbifold approach works in a straightforward way for symmetries of odd order, but some modifications are required to deal with symmetries of even order. With these modifications the orbifold construction with discrete torsion is Complete within the class of simple current invariants. Surprisingly, there are cases where discrete torsion is a necessity rather than a possibility.
Oliver Gray - One of the best experts on this subject based on the ideXlab platform.
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On the Complete Classification of Unitary N = 2 Minimal Superconformal Field Theories
Communications in Mathematical Physics, 2012Co-Authors: Oliver GrayAbstract:Aiming at a Complete Classification of unitary N = 2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate partition function of such a theory is indeed the partition function of a fully-fledged unitary N = 2 minimal model, subject to the assumptions that orbifolding is a ‘physical’ process and that the space-time supersymmetric $${\mathcal{A}}$$ - $${\mathcal{D}}$$ - $${\mathcal{E}}$$ models are physical. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models then demonstrates that there exists a unitary N = 2 minimal model for every one of the allowed partition functions in the list obtained from Gannon’s work (Gannon in Nucl Phys B 491:659–688, 1997 ). Kreuzer and Schellekens’ conjecture (Nucl Phys B 411:97–121, 1994 ) that all simple current invariants can be obtained as orbifolds of the diagonal model, even when the extra assumption of higher-genus modular invariance is dropped, is confirmed in the case of the unitary N = 2 minimal models by simple counting arguments.
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On the Complete Classification of the unitary N=2 minimal superconformal field theories
Communications in Mathematical Physics, 2012Co-Authors: Oliver GrayAbstract:Aiming at a Complete Classification of unitary N=2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate of a partition function for such a theory is indeed the partition function of a minimal model. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models demonstrates that there exists a unitary N=2 minimal model for every one of the allowed partition functions in the list obtained from Gannon's work. Kreuzer and Schellekens' conjecture that all simple current invariants can be obtained as orbifolds of the diagonal model, even when the extra assumption of higher-genus modular invariance is dropped, is confirmed in the case of the unitary N=2 minimal models by simple counting arguments.
Cain Edie-michell - One of the best experts on this subject based on the ideXlab platform.
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A Complete Classification of Unitary Fusion Categories Tensor Generated by an Object of Dimension
International Mathematics Research Notices, 2020Co-Authors: Cain Edie-michellAbstract:Abstract In this paper we give a Complete Classification of unitary fusion categories $\otimes $-generated by an object of dimension $\frac{1 + \sqrt{5}}{2}$. We show that all such categories arise as certain wreath products of either the Fibonacci category or of the dual even part of the $2D2$ subfactor. As a by-product of proving our main Classification result we produce a Classification of finite unitarizable quotients of $\operatorname{Fib}^{*N}$ satisfying a certain symmetry condition.
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A Complete Classification of pivotal fusion categories $\otimes$-generated by an object of dimension $\frac{1 + \sqrt{5}}{2}$
arXiv: Quantum Algebra, 2019Co-Authors: Cain Edie-michellAbstract:In this paper we give a Complete Classification of pivotal fusion categories $\otimes$-generated by an object of dimension $\frac{1 + \sqrt{5}}{2}$. We show that all such categories arise as certain wreath products of either the Fibonacci category, or of the dual even part of the $2D2$ subfactor. As a by-product of proving our main Classification result we produce a Classification of finite quotients of $\operatorname{Fib}^{*N}$ satisfying a certain symmetry condition.
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A Complete Classification of unitary fusion categories tensor generated by an object of dimension $\frac{1 + \sqrt{5}}{2}$
arXiv: Quantum Algebra, 2019Co-Authors: Cain Edie-michellAbstract:In this paper we give a Complete Classification of unitary fusion categories $\otimes$-generated by an object of dimension $\frac{1 + \sqrt{5}}{2}$. We show that all such categories arise as certain wreath products of either the Fibonacci category, or of the dual even part of the $2D2$ subfactor. As a by-product of proving our main Classification result we produce a Classification of finite unitarizable quotients of $\operatorname{Fib}^{*N}$ satisfying a certain symmetry condition.
Sajid Ali - One of the best experts on this subject based on the ideXlab platform.
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Complete Classification of spherically symmetric static spacetimes via Noether symmetries
Theoretical and Mathematical Physics, 2015Co-Authors: Farhad Ali, Tooba Feroze, Sajid AliAbstract:In this paper we give a Complete Classification of spherically symmetric static space-times by their Noether symmetries. The determining equations for Noether symmetries are obtained by using the usual Lagrangian of a general spherically symmetric static spacetime which are integrated for each case. In particular we observe that spherically symmetric static spacetimes are categorized into six distinct classes corresponding to Noether algebra of dimensions 5, 6, 7, 9, 11 and 17. Using Noether`s theorem we also write down the first integrals for each class of such spacetimes corresponding to their Noether symmetries. Some new spherically symmetric static solutions have also been obtained.
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Complete Classification of spherically symmetric static space times via noether symmetries
Theoretical and Mathematical Physics, 2015Co-Authors: Farhad Ali, Tooba Feroze, Sajid AliAbstract:We provide a Complete Classification of spherically symmetric static space—times by their Noether symmetries. We obtain the determining equations for the Noether symmetries using the usual Lagrangian of a general spherically symmetric static space—time and integrate them in each considered case. In particular, we find that spherically symmetric static space–times are categorized into six distinct classes corresponding to the Noether algebras of dimensions 5, 6, 7, 9, 11, and 17. Using Noether‘s theorem, we also find the first integrals corresponding to each symmetry. Moreover, we obtain some new spherically symmetric static solutions.
