Constraints on Low-Dimensional String Compactifications

Abstract

We study the restrictions imposed by cancellation of the tadpoles for two, three, and four-form gauge fields in string theory, M-theory and F-theory compactified to two, three and four dimensions, respectively. For a large class of supersymmetric vacua, turning on a sufficient number of strings, membranes and three-branes, respectively, can cancel the tadpoles, and preserve supersymmetry. However, there are cases where the tadpole cannot be removed in this way, either because the tadpole is fractional, or because of its sign. For M-theory and F-theory compactifications, we also explore the relation of the membranes and three-branes to the nonperturbative space-time superpotential.

16 pages, harvmac

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• Gravitational Wave Constraints on Multi-Brane Inflation
• Gravitational Memory and Compact Extra Dimensions
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• Small flux superpotential in F-theory compactifications
• A Small Cosmological Constant, Grand Unification and Warped Geometry
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• Statistics of Flux Vacua for Particle Physics
• On the Flux Vacua in F-theory Compactifications
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• Brane Inflation, Solitons and Cosmological Solutions: I
• Spin(7)-Manifolds as Generalized Connected Sums and 3d N=1 Theories
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• Type IIA and Heterotic String Vacua in D=2
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• Strings from Orientifolds
• A Note on Heterotic Dualities via M-theory
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• Holomorphic Couplings In Non-Perturbative String Compactifications
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• F-theory models with 3 to 8 U(1) factors on K3 surfaces
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• (0,2) Target Space Duality, CICYs and Reflexive Sheaves
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• On generalized Sethi-Vafa-Witten formulas
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• Noncommutative Universe and Chameleon Field Dynamics
• SU(N) transitions in M-theory on Calabi-Yau fourfolds and background fluxes
• Structure of stable degeneration of K3 surfaces into pairs of rational elliptic surfaces
• Dilaton stabilization in KKLT revisited
• A Landscape of Field Theories
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• PP-Waves, M-Theory and Fluxes
• Gauge symmetry breaking with fluxes and natural Standard Model structure from exceptional GUTs in F-theory
• Flux Compactification of M-theory on Compact Manifolds with Spin(7) Holonomy
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• N=1 Dual String Pairs and their Modular Superpotentials
• F-Theory, Seiberg-Witten Curves and N = 2 Dualities
• Towards natural and realistic $E_7$ GUTs in F-theory
• Chiral Multiplets in N=1 Dual String Pairs
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• Calabi-Yau Four/Five/Six-folds as ${\mathbb{P}}_{\text{w}}^n$ Hypersurfaces: Machine Learning, Approximation, and Generation
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• Aspects of N=1 String Dynamics