Gauss-Bonnet for matrix conformally rescaled Dirac
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hep-thmath-phmath.MPmath.OA
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diracconformallygauss-bonnetmatrixrescaledcurvaturederivediagonalizable
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We derive an explicit formula for the scalar curvature over a two-torus with a Dirac operator conformally rescaled by a globally diagonalizable matrix. We show that the Gauss-Bonnet theorem holds and extend the result to all Riemann surfaces with Dirac operators modified in the same way.
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