PRECISE COMPUTATION OF MODULI SPACE FOR STANDARD EMBEDDING.
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This thesis has undertaken the task of clearly defining the full heterotic moduli space for E_8 x E_8 heterotic string theory in standard embedding while utilizing the mathematical tools offered by the deformation theory of holomorphic structure. Our approach involved simultaneous deformations of the complex structure J on a Calabi-Yau manifold X and the connection, A, on the bundle, V. We drew inspiration from Atiya's work, which focused on the deformations of holomorphic bundles on complex manifolds. We introduced a bundle, Q as an extension of the cotangent bundle T*(X) which result from the simultaneous deformation of the complex structure and the connection. We defined an operator D on Q and demonstrated explicitly that in standard embedding the cohomology class on $Q$, defined as H_D(Q) provides the complete moduli spectrum of E_8 x E_8 heterotic theory.