Exact BPS Couplings and Black Hole Counting

Duration: 58 mins 37 secs

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Description:	Pioline, B Tuesday 25th May 2021 - 14:30 to 15:30


Created:	2021-05-26 17:18
Collection:	New connections in number theory and physics
Publisher:	Isaac Newton Institute for Mathematical Sciences
Copyright:	Pioline, B
Language:	eng (English)


Abstract:	In order to determine the exact spectrum of BPS states in four-dimensional string vacua with extended supersymmetry, a useful strategy is to consider certain BPS-saturated couplings in the low-energy effective action in three dimensions, after compactifying on a circle. These couplings are highly constrained by supersymmetry and dualities, and can sometimes be determined exactly. The BPS indices can then be read off from the Fourier expansion in the large radius limit. This strategy has been applied to the counting of 1/8-BPS (respectively 1/4, 1/2) states in string vacua with N=8 (respectively, 4,2) supersymmetry in four dimensions, leading to rather exotic types of automorphic functions from the point of view of mathematics, but quite natural from the point of view of physics. This includes theta liftings of genus two Siegel modular forms (in the N=8 and N=4 cases), as well as mock modular forms of higher depth (in the N=2 case, or in the closely related set up of N=4 super-Yang Mills theory).

Abstract:

In order to determine the exact spectrum of BPS states in four-dimensional string vacua with extended supersymmetry, a useful strategy is to consider certain BPS-saturated couplings in the low-energy effective action in three dimensions, after compactifying on a circle. These couplings are highly constrained by supersymmetry and dualities, and can sometimes be determined exactly. The BPS indices can then be read off from the Fourier expansion in the large radius limit. This strategy has been applied to the counting of 1/8-BPS (respectively 1/4, 1/2) states in string vacua with N=8 (respectively, 4,2) supersymmetry in four dimensions, leading to rather exotic types of automorphic functions from the point of view of mathematics, but quite natural from the point of view of physics. This includes theta liftings of genus two Siegel modular forms (in the N=8 and N=4 cases), as well as mock modular forms of higher depth (in the N=2 case, or in the closely related set up of N=4 super-Yang Mills theory).

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