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@@ -69,6 +69,28 @@ <h1>Fabian Ruehle - Research</h1>
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+					<div class="newstitle">Attractors, Geodesics, and the Geometry of Moduli Spaces</div>
+					<div style="font-size:14px;"><a href="https://arxiv.org/abs/2408.00830" target="_blank">[arxiv:2408.00830]</a></div>
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+			<td><div class="newsimg"><p><img src="./img/news/2408.00830.png" alt="Split attractor flows" width=240 /></p></div>
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+				We study a series of recent conjectures using the attractor mechanism. First, we observed in <a href='https://arxiv.org/abs/2304.00027' target='_blank'>[2304.00027]</a> a relation between attractor points and degeneracies in the spectrum of the scalar Laplacian. A recent conjecture by Etheridge <a href='https://arxiv.org/abs/2311.18693' target='_blank'>[2311.18693]</a> states that the eigenvalues of the scalar Laplacian with respect to the Calabi-Yau metric are eigenfunctions of the Laplacian on the moduli space with respect to the Weil-Petersson metric. We show that this is true for T^2, but fails e.g. for T^4.<br/> 
+				Another interesting conjecture by Raman and Vafa in <a href='https://arxiv.org/abs/2405.11611' target='_blank'>[2405.11611]</a> states that the marked moduli space of a Calabi-Yau manifold is contractible, which is related to the statement that geodesics in the marked moduli space are unique. Since attractor flows are geodesics, we discuss potential failure modes when attractor flows split along walls of marginal stability (see figure). Another way geodesic uniqueness could break down is when there are flop walls in the K\"ahler moduli space that separate isomorphic Calabi-Yaus. We discuss both cases, which are counter-examples in the moduli space but not in the marked moduli space. 
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