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  • 1
    Electronic Resource
    Electronic Resource
    Metric symmetries and spin asymmetries of Ricci-flat Riemannian manifolds (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1255-1267 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Calabi–Yau and Joyce manifolds used in string and M-theory compactifications have no continuous groups of isometries, but they often have nontrivial discrete (actually finite) isometry groups. Discrete isometries of nonsimply connected Riemannian manifolds do not necessarily map spin structures into themselves, however; thus, inconsistencies are possible if a spin connection is used to construct the gauge vacuum. We consider this problem in detail and show how it may be avoided. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532799
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  • 2
    Electronic Resource
    Electronic Resource
    Calabi–Yau compactifications and the global structure of the standard group (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 493-498 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The "standard group'' of elementary particle theory is locally isomorphic to SU(3)×SU(2)×U(1). The global structure is completely fixed in unified theories, often in a subtle way; and such theories can be physically unacceptable if they predict the "wrong'' global structure for the standard group. A particularly striking example of this is provided by Calabi–Yau compactifications of string theory with the linear (rather than the more conventional spinor) connection interpreted as an E8 connection. Remarkably, these more unconventional compactifications break E8 to a group which is locally isomorphic to the standard group (instead of E6); but they are physically unacceptable, and we argue that the basic reason for this is their failure to produce the correct global structure. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531404
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  • 3
    Electronic Resource
    Electronic Resource
    Holonomy groups of compact Riemannian manifolds: A classification in dimensions up to ten (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4273-4286 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The possible holonomy groups of compact, locally irreducible Riemannian manifolds are studied. Motivated by applications arising in physics, it is not required that these manifolds be simply connected. In this paper a complete classification up to dimension ten is given, with particular emphasis on the manifolds of dimension six or less. In this latter case, there exist actual examples for every class, so that the possible holonomy groups can be characterized exactly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529999
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  • 4
    Electronic Resource
    Electronic Resource
    Complex symplectic geometry and compact locally hyper-Kählerian manifolds (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4857-4871 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Complex symplectic geometry is the study of complex manifolds admitting a global closed nondegenerate holomorphic two-form. Compact, simply connected complex symplectic manifolds are of interest for various reasons; for example, they always admit a Ricci-flat metric. In this work, the close relationship between the complex geometry of such manifolds and their Riemannian structures is exploited in order to obtain results in both directions: Riemannian techniques are used to obtain results on the complex automorphism group, and the problem of constructing examples of compact locally hyper-Kählerian manifolds with prescribed holonomy groups is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530327
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  • 5
    Electronic Resource
    Electronic Resource
    Methods of holonomy theory for Ricci-flat Riemannian manifolds (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 888-896 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Compact, Ricci-flat Riemannian manifolds often arise in physical applications, either as a technical device or as models of "internal'' space. The idea of extending the holonomy group of such a manifold to a larger gauge group ("embedding the connection in the gauge group'') plays a fundamental role in the "manifold compactification'' approach to superstring phenomenology, and the work of Gepner suggests that this idea may have equally fundamental analogs in other approaches. The holonomy theory of simply connected Ricci-flat manifolds has recently been the subject of much mathematical work, but physicists are mainly interested in the case of multiply connected manifolds. The purpose of this paper is to present some techniques for understanding the holonomy theory of compact, multiply connected Ricci-flat manifolds. These lead to a general classification theorem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529347
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  • 6
    Electronic Resource
    Electronic Resource
    Hosotani breaking of E6 to a subgroup of rank five (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2094-2104 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: On multiply connected manifolds, it is possible to construct vacuum gauge configurations with nontrivial holonomy groups. This is the basis of the Hosotani mechanism. This naturally suggests a "Hosotani inverse problem'': If we wish to break a gauge group G to a subgroup H, what are the possible finite holonomy groups having this effect, and what can one say about the fundamental groups of the underlying manifolds? Usually, this problem is too difficult to solve, but we show that, for G=E6 and H locally isomorphic to the rank five group SU(3)×SU(2)×U(1)×U(1), a complete solution is possible. It is hoped that the results will aid a search for examples of Calabi–Yau manifolds leading to a low-energy gauge group of rank five.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528662
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  • 7
    Electronic Resource
    Electronic Resource
    The semispin groups in string theory (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4699-4712 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In string theory, an important role is played by certain Lie groups which are locally isomorphic to SO(4m), m≤8. It has long been known that these groups are actually isomorphic not to SO(4m) but rather to the groups for which the half-spin representations are faithful, which we propose to call Semispin(4m). (They are known in the physics literature by the ambiguous name of "Spin(4m)/Z2.") Recent work on string duality has shown that the distinction between SO(4m) and Semispin(4m) can have a definite physical significance. This work is a survey of the relevant properties of Semispin(4m) and its subgroups. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532999
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  • 8
    Electronic Resource
    Electronic Resource
    Holonomy groups and holonomy representations (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 4450-4460 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The holonomy group of a Riemannian manifold always arises in geometry through a particular representation, not as an abstract group. One can therefore ask whether there exist pairs of (compact, locally irreducible) manifolds with holonomy groups which are isomorphic, yet distinct, because the holonomy representations are not equivalent. A theorem of Besse asserts that this is not possible in the simply connected case; however, it is possible for certain nonsimply connected manifolds. Here we identify all of these manifolds (up to space form problems) in the case where the Ricci curvature is not negative. This allows us to solve the holonomy classification problem for all compact, locally irreducible Riemannian manifolds of positive Ricci curvature. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530901
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  • 9
    Electronic Resource
    Electronic Resource
    Spontaneous splitting and internal isometries of superstring vacua (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2564-2568 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Superstring vacua are normally presumed to be of the form M×K, where dim(M)=4, dim(K)=6, and where × denotes the global Riemannian product. Since, however, one would ultimately wish to understand the external/internal distinction in terms of some dynamical mechanism ("spontaneous splitting'') involving vacuum expectation values of local fields, it may be preferable to use a local Riemannian product at the outset. Here it is shown that these spaces, which have the same local (block-diagonal) type of metric as M×K, can be described and classified by examining the isometry groups of the Calabi–Yau manifolds which have been proposed as models for the internal superstring vacua.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527746
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  • 10
    Electronic Resource
    Electronic Resource
    Spontaneous compactification and Ricci-flat manifolds with torsion (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2029-2038 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Freund–Rubin mechanism is based on the equation Rik=λgik (where λ〉0), which, via Myers' theorem, implies "spontaneous'' compactification. The difficulties connected with the cosmological constant in this approach can be resolved if torsion is introduced and λ is set equal to zero, but then compactification "by hand'' is necessary since the equation Rik =0 can be satisfied both on compact and on noncompact manifolds. In this paper we discuss the global geometry of Ricci-flat manifolds with torsion, and suggest ways of restoring the "spontaneity'' of the compactification.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527022
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