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Phys."],"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc>\n          <\/jats:title>\n          <jats:p>We consider four-dimensional dyonic single-center BPS black holes in the <jats:italic>N<\/jats:italic> = 2 STU model of Sen and Vafa. By working in a region of moduli space where the real part of two of the three complex scalars <jats:italic>S, T , U<\/jats:italic> are taken to be large, we evaluate the quantum entropy function for these BPS black holes. In this regime, the subleading corrections point to a microstate counting formula partly based on a Siegel modular form of weight two. This is supplemented by another modular object that takes into account the dependence on <jats:italic>Y<\/jats:italic>\n            <jats:sup>0<\/jats:sup>, a complex scalar field belonging to one of the four off-shell vector multiplets of the underlying supergravity theory. We also observe interesting connections to the rational Calogero model and to formal deformation of a Poisson algebra, and suggest a string web picture of our counting proposal.<\/jats:p>","DOI":"10.1007\/jhep08(2020)057","type":"journal-article","created":{"date-parts":[[2020,8,13]],"date-time":"2020-08-13T02:02:43Z","timestamp":1597284163000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An approach to BPS black hole microstate counting in an N = 2 STU model"],"prefix":"10.1007","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2024-5753","authenticated-orcid":false,"given":"G.L.","family":"Cardoso","sequence":"first","affiliation":[]},{"given":"S.","family":"Nampuri","sequence":"additional","affiliation":[]},{"given":"D.","family":"Polini","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,8,12]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"R. 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Reys, Single-centered black hole microstate degeneracies from instantons in supergravity, JHEP 04 (2016) 052 [arXiv:1512.01553] [INSPIRE].","key":"13588_CR37","DOI":"10.1007\/JHEP04(2016)052"},{"doi-asserted-by":"crossref","unstructured":"A. Sen, Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].","key":"13588_CR38","DOI":"10.1007\/s10714-008-0626-4"},{"doi-asserted-by":"crossref","unstructured":"M.-x. Huang, S. Katz and A. Klemm, Topological String on elliptic CY 3-folds and the ring of Jacobi forms, JHEP 10 (2015) 125 [arXiv:1501.04891] [INSPIRE].","key":"13588_CR39","DOI":"10.1007\/JHEP10(2015)125"},{"doi-asserted-by":"crossref","unstructured":"B. de Wit, N = 2 electric-magnetic duality in a chiral background, Nucl. Phys. B Proc. Suppl. 49 (1996) 191 [hep-th\/9602060] [INSPIRE].","key":"13588_CR40","DOI":"10.1016\/0920-5632(96)00335-0"},{"doi-asserted-by":"crossref","unstructured":"G. Lopes Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black hole entropy, Phys. Lett. B 451 (1999) 309 [hep-th\/9812082] [INSPIRE].","key":"13588_CR41","DOI":"10.1016\/S0370-2693(99)00227-0"},{"doi-asserted-by":"crossref","unstructured":"H. Ooguri, A. Strominger and C. Vafa, Black hole attractors and the topological string, Phys. Rev. D 70 (2004) 106007 [hep-th\/0405146] [INSPIRE].","key":"13588_CR42","DOI":"10.1103\/PhysRevD.70.106007"},{"doi-asserted-by":"crossref","unstructured":"S. Murthy and V. Reys, Functional determinants, index theorems, and exact quantum black hole entropy, JHEP 12 (2015) 028 [arXiv:1504.01400] [INSPIRE].","key":"13588_CR43","DOI":"10.1007\/JHEP12(2015)028"},{"doi-asserted-by":"crossref","unstructured":"R.K. Gupta, Y. Ito and I. Jeon, Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets, JHEP 11 (2015) 197 [arXiv:1504.01700] [INSPIRE].","key":"13588_CR44","DOI":"10.1007\/JHEP11(2015)197"},{"doi-asserted-by":"crossref","unstructured":"B. de Wit, S. Murthy and V. Reys, BRST quantization and equivariant cohomology: localization with asymptotic boundaries, JHEP 09 (2018) 084 [arXiv:1806.03690] [INSPIRE].","key":"13588_CR45","DOI":"10.1007\/JHEP09(2018)084"},{"doi-asserted-by":"crossref","unstructured":"I. Jeon and S. Murthy, Twisting and localization in supergravity: equivariant cohomology of BPS black holes, JHEP 03 (2019) 140 [arXiv:1806.04479] [INSPIRE].","key":"13588_CR46","DOI":"10.1007\/JHEP03(2019)140"},{"doi-asserted-by":"crossref","unstructured":"B. de Wit and A. Van Proeyen, Potentials and Symmetries of General Gauged N = 2 Supergravity: Yang-Mills Models, Nucl. Phys. B 245 (1984) 89 [INSPIRE].","key":"13588_CR47","DOI":"10.1016\/0550-3213(84)90425-5"},{"doi-asserted-by":"crossref","unstructured":"G. Lopes Cardoso, B. de Wit, J. Kappeli and T. Mohaupt, Black hole partition functions and duality, JHEP 03 (2006) 074 [hep-th\/0601108] [INSPIRE].","key":"13588_CR48","DOI":"10.1088\/1126-6708\/2006\/03\/074"},{"doi-asserted-by":"crossref","unstructured":"G.L. Cardoso, B. de Wit and S. Mahapatra, Subleading and non-holomorphic corrections to N = 2 BPS black hole entropy, JHEP 02 (2009) 006 [arXiv:0808.2627] [INSPIRE].","key":"13588_CR49","DOI":"10.1088\/1126-6708\/2009\/02\/006"},{"doi-asserted-by":"crossref","unstructured":"K. Behrndt, G. Lopes Cardoso, B. de Wit, R. Kallosh, D. L\u00fcst and T. Mohaupt, Classical and quantum N = 2 supersymmetric black holes, Nucl. Phys. B 488 (1997) 236 [hep-th\/9610105] [INSPIRE].","key":"13588_CR50","DOI":"10.1016\/S0550-3213(97)00028-X"},{"doi-asserted-by":"crossref","unstructured":"F. Denef and G.W. Moore, Split states, entropy enigmas, holes and halos, JHEP 11 (2011) 129 [hep-th\/0702146] [INSPIRE].","key":"13588_CR51","DOI":"10.1007\/JHEP11(2011)129"},{"doi-asserted-by":"crossref","unstructured":"G.L. Cardoso, B. de Wit and S. Mahapatra, Deformations of special geometry: in search of the topological string, JHEP 09 (2014) 096 [arXiv:1406.5478] [INSPIRE].","key":"13588_CR52","DOI":"10.1007\/JHEP09(2014)096"},{"doi-asserted-by":"crossref","unstructured":"A. Gregori, C. Kounnas and P.M. Petropoulos, Nonperturbative triality in heterotic and type-II N = 2 strings, Nucl. Phys. B 553 (1999) 108 [hep-th\/9901117] [INSPIRE].","key":"13588_CR53","DOI":"10.1016\/S0550-3213(99)00281-3"},{"doi-asserted-by":"crossref","unstructured":"H. Farkas and I. Kra, Theta Constants, Riemann Surfaces and the Modular Group, Graduate Studies in Mathematics 37, American Mathematical Society (2001).","key":"13588_CR54","DOI":"10.1090\/gsm\/037"},{"doi-asserted-by":"crossref","unstructured":"H. Hahn, Eisenstein series associated with \u03930(2), Ramanujan J. 15 (2008) 235 [arXiv:1507.04425].","key":"13588_CR55","DOI":"10.1007\/s11139-007-9075-z"},{"unstructured":"F. Martin and E. Royer, Rankin-Cohen brackets on quasimodular forms, J. Ramanujan Math. Soc. 24 (2009) 213 [math\/0509653].","key":"13588_CR56"},{"doi-asserted-by":"crossref","unstructured":"V. de Alfaro, S. Fubini and G. Furlan, Conformal Invariance in Quantum Mechanics, Nuovo Cim. A 34 (1976) 569 [INSPIRE].","key":"13588_CR57","DOI":"10.1007\/BF02785666"},{"doi-asserted-by":"crossref","unstructured":"N. Banerjee, D.P. Jatkar and A. Sen, Asymptotic Expansion of the N = 4 Dyon Degeneracy, JHEP 05 (2009) 121 [arXiv:0810.3472] [INSPIRE].","key":"13588_CR58","DOI":"10.1088\/1126-6708\/2009\/05\/121"},{"unstructured":"F. Diamond and J. Shurman, A First Course in Modular Forms, Graduate Texts in Mathematics 228, Springer (2005).","key":"13588_CR59"},{"doi-asserted-by":"publisher","unstructured":"J.H. Bruinier, G.v.d. 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