Abstract
We compute the 1-loop partition function for strings in $AdS_4\times\mathbb{CP}^3$, whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.
Highlights
To type IIA string theory on AdS4 × CP3
We compute the 1-loop partition function for strings in AdS4 × CP3, whose worldsheets end along a line with small cusp angles in the boundary of AdS
Cusped Wilson lines in N = 6 super Chern-Simons-matter theory have been studied in several works both from the gauge and the string theory sides [6,7,8,9], and related to circular Wilson loops in [3, 10,11,12]
Summary
The computation of 1-loop partition functions on a static spacetime with metric g involves calculating the determinant of some operator Og. This determinant is typically computed by looking for the eigenfuctions of Og provided appropriate boundary conditions are given The staticity of spacetime provides an alternative route: Og provides a wave equation whose solutions give rise to a spectrum of states. As explained in [18], for a string ending on a straight line at the boundary of AdS5 ×S5, the 1-loop correction to the partition functions can be obtained from the vacuum energy because the total anomaly coming from the rescaling of the mode operators vanishes. We will use the vacuum energy method to obtain the corresponding determinants for the 1-loop correction to the partition function
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