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We address issues on the origin of gravity and the cosmological constant problem based on a recent understanding about the correspondence between noncommutative field theory and gravity.
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More precisely, ∂ μ \partial_{\mu} in D μ D_{\mu} must also be regarded as a background. Indeed ∂ μ \partial_{\mu} and y a / κ y^{a}/\kappa are related to each other by a ‘matrix T-duality’ hsy6 ; i D μ ↔ Φ a iD_{\mu}\leftrightarrow\Phi^{a}
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