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Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning. (English) Zbl 1466.83111
Summary: We use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and speed. Knowing these metrics has numerous applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical normalizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, to mirror symmetry and the SYZ conjecture. In the case of SU(3) structure, our machine learning approach allows us to engineer metrics with certain torsion properties. Our methods are demonstrated for Calabi-Yau and SU(3)-structure manifolds based on a one-parameter family of quintic hypersurfaces in $$\mathbb{P}^4$$.
##### MSC:
 83E30 String and superstring theories in gravitational theory 81T12 Effective quantum field theories 32Q25 Calabi-Yau theory (complex-analytic aspects) 68T05 Learning and adaptive systems in artificial intelligence
##### Software:
JAX; Adam; TensorFlow; GitHub; SymPy; PyTorch; Fermat.m
Full Text:
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