Abstract
We study the leading nonperturbative corrections to the strong-coupling (ungapped) phase of the Gross-Witten-Wadia (GWW) integral over unitary matrices, to one-loop order. We compute these corrections directly in terms of eigenvalue tunneling in a holomorphic presentation of the integral over eigenvalues. The leading nonperturbative contribution to the partition function comes from a pair of complex eigenvalue instantons. We show that these are in fact “ghost instantons”, which are extrema of the one-eigenvalue effective potential on the “unphysical sheet” of the spectral curve and have been discussed in detail recently by Mariño, Schiappa, and Schwick. Further, we discuss the relationship of these instantons to the Fredholm determinant expansion of the unitary matrix integral, which has recently become an object of interest in the computations of BPS indices of supersymmetric gauge theories and black holes. We find that, after taking the ’t Hooft limit, the first correction given by the Fredholm determinant expansion of the GWW integral agrees precisely with the leading nonperturbative correction, to one-loop order.
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Acknowledgments
We would like to thank Abhijit Gadde, Ohad Mamroud, Sameer Murthy, Steve Shenker, Douglas Stanford, and Mykhaylo Usatyuk for discussions. D.S.E. is supported by the Shoucheng Zhang Graduate Fellowship. C.M. is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics under QuantISED Award DESC0019380 and contract DE-AC02-05CH11231.
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Eniceicu, D.S., Mahajan, R. & Murdia, C. Complex eigenvalue instantons and the Fredholm determinant expansion in the Gross-Witten-Wadia model. J. High Energ. Phys. 2024, 129 (2024). https://doi.org/10.1007/JHEP01(2024)129
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DOI: https://doi.org/10.1007/JHEP01(2024)129