Nahm sums, quiver A-polynomials and topological recursion
A bstract We consider a large class of q -series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and classification of classical and quantum A-polynomials associated to such q -series. These quantum quiver A-polyno...
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| Vydané v: | The journal of high energy physics Ročník 2020; číslo 7; s. 1 - 52 |
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| Hlavní autori: | , , , |
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| Jazyk: | English |
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01.07.2020
Springer Nature B.V SpringerOpen |
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| Abstract | A
bstract
We consider a large class of
q
-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and classification of classical and quantum A-polynomials associated to such
q
-series. These quantum quiver A-polynomials encode recursion relations satisfied by the above series, while classical A-polynomials encode asymptotic expansion of those series. Second, we postulate that those series, as well as their quantum quiver A-polynomials, can be reconstructed by means of the topological recursion. There is a large class of interesting quiver A-polynomials of genus zero, and for a number of them we confirm the above conjecture by explicit calculations. In view of recently found dualities, for an appropriate choice of quivers, these results have a direct interpretation in topological string theory, knot theory, counting of lattice paths, and related topics. In particular it follows, that various quantities characterizing those systems, such as motivic Donaldson-Thomas invariants, various knot invariants, etc., have the structure compatible with the topological recursion and can be reconstructed by its means. |
|---|---|
| AbstractList | Abstract We consider a large class of q-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and classification of classical and quantum A-polynomials associated to such q-series. These quantum quiver A-polynomials encode recursion relations satisfied by the above series, while classical A-polynomials encode asymptotic expansion of those series. Second, we postulate that those series, as well as their quantum quiver A-polynomials, can be reconstructed by means of the topological recursion. There is a large class of interesting quiver A-polynomials of genus zero, and for a number of them we confirm the above conjecture by explicit calculations. In view of recently found dualities, for an appropriate choice of quivers, these results have a direct interpretation in topological string theory, knot theory, counting of lattice paths, and related topics. In particular it follows, that various quantities characterizing those systems, such as motivic Donaldson-Thomas invariants, various knot invariants, etc., have the structure compatible with the topological recursion and can be reconstructed by its means. We consider a large class of q-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and classification of classical and quantum A-polynomials associated to such q-series. These quantum quiver A-polynomials encode recursion relations satisfied by the above series, while classical A-polynomials encode asymptotic expansion of those series. Second, we postulate that those series, as well as their quantum quiver A-polynomials, can be reconstructed by means of the topological recursion. There is a large class of interesting quiver A-polynomials of genus zero, and for a number of them we confirm the above conjecture by explicit calculations. In view of recently found dualities, for an appropriate choice of quivers, these results have a direct interpretation in topological string theory, knot theory, counting of lattice paths, and related topics. In particular it follows, that various quantities characterizing those systems, such as motivic Donaldson-Thomas invariants, various knot invariants, etc., have the structure compatible with the topological recursion and can be reconstructed by its means. We consider a large class of q -series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and classification of classical and quantum A-polynomials associated to such q -series. These quantum quiver A-polynomials encode recursion relations satisfied by the above series, while classical A-polynomials encode asymptotic expansion of those series. Second, we postulate that those series, as well as their quantum quiver A-polynomials, can be reconstructed by means of the topological recursion. There is a large class of interesting quiver A-polynomials of genus zero, and for a number of them we confirm the above conjecture by explicit calculations. In view of recently found dualities, for an appropriate choice of quivers, these results have a direct interpretation in topological string theory, knot theory, counting of lattice paths, and related topics. In particular it follows, that various quantities characterizing those systems, such as motivic Donaldson-Thomas invariants, various knot invariants, etc., have the structure compatible with the topological recursion and can be reconstructed by its means. A bstract We consider a large class of q -series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and classification of classical and quantum A-polynomials associated to such q -series. These quantum quiver A-polynomials encode recursion relations satisfied by the above series, while classical A-polynomials encode asymptotic expansion of those series. Second, we postulate that those series, as well as their quantum quiver A-polynomials, can be reconstructed by means of the topological recursion. There is a large class of interesting quiver A-polynomials of genus zero, and for a number of them we confirm the above conjecture by explicit calculations. In view of recently found dualities, for an appropriate choice of quivers, these results have a direct interpretation in topological string theory, knot theory, counting of lattice paths, and related topics. In particular it follows, that various quantities characterizing those systems, such as motivic Donaldson-Thomas invariants, various knot invariants, etc., have the structure compatible with the topological recursion and can be reconstructed by its means. |
| ArticleNumber | 151 |
| Author | Larraguível, Hélder Panfil, Miłosz Noshchenko, Dmitry Sułkowski, Piotr |
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| Cites_doi | 10.1112/S0010437X1000521X 10.4310/ATMP.2012.v16.n5.a3 10.1007/JHEP02(2012)070 10.1007/s00220-015-2361-5 10.1016/0370-2693(93)90292-P 10.1007/978-0-8176-4771-1 10.4310/ATMP.2019.v23.n7.a4 10.4310/CNTP.2011.v5.n2.a1 10.1007/JHEP02(2020)018 10.1007/s00220-008-0620-4 10.1088/1126-6708/2006/12/026 10.1016/j.nuclphysb.2011.03.014 10.4171/dm/359 10.1007/s00220-016-2682-z 10.1007/978-3-540-30308-4_2 10.1088/1126-6708/2004/11/031 10.1007/JHEP08(2017)139 10.1007/s002200100374 10.1088/1126-6708/2000/11/007 10.1103/PhysRevD.96.121902 10.1016/S0550-3213(00)00118-8 10.1088/1126-6708/2006/03/014 10.1007/BF01049953 10.1007/978-3-540-30308-4_1 10.1016/S0550-3213(00)00761-6 10.1090/conm/593/11867 10.1007/s11232-011-0012-3 10.1007/JHEP01(2019)124 10.1007/JHEP11(2016)120 10.1186/2197-9847-2-1 10.1007/JHEP02(2013)143 10.4310/CNTP.2007.v1.n2.a4 10.1103/PhysRevD.98.026022 |
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bstract
We consider a large class of
q
-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we... We consider a large class of q -series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a... We consider a large class of q-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a... Abstract We consider a large class of q-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate... |
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| SubjectTerms | Asymptotic series Classical and Quantum Gravitation Differential and Algebraic Geometry Elementary Particles High energy physics Invariants Knot theory Matrix Models Physics Physics and Astronomy Polynomials Quantum Field Theories Quantum Field Theory Quantum Physics Regular Article - Theoretical Physics Relativity Theory String Theory Sums Topological Strings Topology |
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| Title | Nahm sums, quiver A-polynomials and topological recursion |
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