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Stabilizing the complex structure in heterotic Calabi-Yau vacua. (English) Zbl 1294.81153
Summary: In this paper, we show that the presence of gauge fields in heterotic Calabi-Yau compactifications can cause the stabilization of some, or all, of the complex structure moduli while maintaining a Minkowski vacuum. Certain deformations of the Calabi-Yau complex structure, with all other moduli held fixed, can lead to the gauge bundle becoming non-holomorphic and, hence, non-supersymmetric. This is manifested by a positive F-term potential which stabilizes the corresponding complex structure moduli. We use 10-and 4-dimensional field theory arguments as well as a derivation based purely on algebraic geometry to show that this picture is indeed correct. An explicit example is presented in which a large subset of complex structure moduli is fixed. We demonstrate that this type of theory can serve as the hidden sector in heterotic vacua with realistic particle physics.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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