Running decompactification, sliding towers, and the distance conjecture
Muldrow Etheredge, Ben Heidenreich, Jacob McNamara, Tom Rudelius, Ignacio Ruiz, Irene Valenzuela
Abstract
A bstract We study towers of light particles that appear in infinite-distance limits of moduli spaces of 9-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 string theories, some of which notably feature decompactification limits with running string coupling. The lightest tower in such decompactification limits consists of the non-BPS Kaluza-Klein modes of Type I ′ string theory, whose masses depend nontrivially on the moduli of the theory. We work out the moduli-dependence by explicit computation, finding that despite the running decompactification the Distance Conjecture remains satisfied with an exponential decay rate $$ \alpha \ge 1/\sqrt{d-2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msqrt> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msqrt> </mml:math> in accordance with the sharpened Distance Conjecture. The related sharpened Convex Hull Scalar Weak Gravity Conjecture also passes stringent tests. Our results non-trivially test the Emergent String Conjecture, while highlighting the important subtlety that decompactifcation can lead to a running solution rather than to a higher-dimensional vacuum.