Organization
Graduate School of Mathematics Division of Mathematics Natural Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science
Title
Professor
KANNO, Hiroaki
Degree 1
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Doctor of Science （ Kyoto University ）
Research Areas 2
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Others / Others / Elementary Particle/Atomic Nucleus/Cosmic Ray/Space Physics
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Others / Others / Geometry
Current Research Project and SDGs 1
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Topological Quantum Field Theory
Education 2
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Kyoto University Graduate School, Division of Natural Science
- 1989
Country： Japan
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Kyoto University Faculty of Science
- 1984
Country： Japan
Professional Memberships 2
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日本物理学会
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日本数学会
Papers 52
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Solitons in open N=2 string theory
Hamanaka Masashi, Huang Shan-Chi, Kanno Hiroaki
PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS Vol. 2023 ( 4 ) 2023.4
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Quasi-Hopf twist and elliptic Nekrasov factor
Cheewaphutthisakun Panupong, Kanno Hiroaki
JOURNAL OF HIGH ENERGY PHYSICS ( 12 ) 2021.12
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MacMahon KZ equation for Ding-Iohara-Miki algebra
Cheewaphutthisakun Panupong, Kanno Hiroaki
JOURNAL OF HIGH ENERGY PHYSICS ( 4 ) 2021.4
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Quiver matrix model of ADHM type and BPS state counting in diverse dimensions
Kanno Hiroaki
PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS Vol. 2020 ( 11 ) 2020.11
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Shiraishi functor and non-Kerov deformation of Macdonald polynomials
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei
EUROPEAN PHYSICAL JOURNAL C Vol. 80 ( 10 ) 2020.10
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Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei
JOURNAL OF HIGH ENERGY PHYSICS ( 8 ) 2020.8
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On a complete solution of the quantum Dell system
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei
JOURNAL OF HIGH ENERGY PHYSICS ( 4 ) 2020.4
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Can tangle calculus be applicable to hyperpolynomials?
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei
NUCLEAR PHYSICS B Vol. 949 2019.12
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The MacMahon R-matrix
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Suetake Kazuma, Zenkevich Yegor
JOURNAL OF HIGH ENERGY PHYSICS ( 4 ) 2019.4
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Equivariant U(N) Verlinde algebra from Bethe/gauge correspondence
Kanno Hiroaki, Sugiyama Katsuyuki, Yoshida Yutaka
JOURNAL OF HIGH ENERGY PHYSICS ( 2 ) 2019.2
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Nontorus link from topological vertex
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Morozov Andrey
PHYSICAL REVIEW D Vol. 98 ( 4 ) 2018.8
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(q,t)-KZ Equations for quantum toroidal algebra and Nekrasov partition function on ALE spaces Reviewed
H.Awata, H.Kanno, A.Mironov, A.Morozov, K.Suetake and Y.Zenkevich
Journal of High Energy Physics Vol. 1803 ( 3 ) 2018.3
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Generalized Knizhnik-Zamolodchikov equation for Ding-Iohara-Miki algebra
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Morozov Andrey, Ohkubo Yusuke, Zenkevich Yegor
PHYSICAL REVIEW D Vol. 96 ( 2 ) 2017.7
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Anomaly in RTT relation for DIM algebra and network matrix models
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Morozov Andrey, Ohkubo Yusuke, Zenkevich Yegor
NUCLEAR PHYSICS B Vol. 918 page： 358-385 2017.5
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Anomaly in RTT relation for DIM algebra and Network Matrix Models Reviewed
H.Awata, H.Kanno, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich
Nuclear Physics B Vol. 918 page： 358-385 2017.3
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Generalized Knizhnik-Zamolodchikov Equation for Ding-Iohara-Miki algebra, Reviewed
H.Awata, H.Kanno, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich
Phys. Rev. D Vol. 96 page： 026021 2017
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Toric Calabi-Yau manifolds as Quantum Integrable Systems; R-matrix and RTT relations
H.Awata, H.Kanno, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich
Journal of High Energy Physics Vol. 1610 page： 047 2016.10
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Explicit Examples of DIM Constraints for Network Matrix Models Reviewed
H.Awata, H.Kanno, T.Matsumoto, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich
Journal of High Energy Physics Vol. 1607 page： 103 2016.7
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Hyperkaehler Metrics from Monopole Walls Reviewed
M.Hamanaka, H.Kanno and D.Muranaka
Phys. Rev. Vol. D 89 2014.3
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W_3 irregular states and isolated N=2 superconformal field theories Reviewed
H.Kanno, K.Maruyoshi, S.Shiba and M.Taki
Journal of High Energy Physics Vol. 1303 page： 147 2013.3
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Changing the preferred direction of the refined topological vertex Reviewed
H.Awata and H.Kanno
Journal of Geometry and Physics Vol. 64 page： 91-110 2013
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Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String Reviewed
H.Awata, H.Fuji, H.Kanno, M.Manabe and Y.Yamada
Advances in Theoretical and Mathematical Physics Vol. 16 ( 3 ) page： 725 - 804 2012.6
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Generalized Whittaker states for instanton counting with fundamental hypermultiplets Reviewed
H.Kanno and M.Taki
Journal of High Energy Physics Vol. 1205 page： 052 2012.5
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Instanton counting with a surface operator and the chain-saw quiver
H.Kanno, and Y.Tachikawa
Journal of High Energy Physics Vol. 11 ( 06 ) page： 119 2011.6
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Macdonald operators and homological invariants of the colored Hopf link Reviewed
H.Awata and H.Kanno
J. Phys. A: Math. Theor. Vol. 44 page： 375201 2011
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Quiver matrix model and and topological partition function in six dimensions Reviewed
H.Awata and H.Kanno
Journal of High Energy Physics Vol. 9 ( 7 ) page： 076 2009.7
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Refined BPS state counting from Nekrasov's formula and Macdonald functions Reviewed
H.Awata and H.Kanno
International Journal of Modern Physics A Vol. 24 ( 12 ) page： 2253-2306 2009
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Instanton Counting and the Chiral Ring Relations in Supersymmetric Gauge Theories Reviewed
H.Kanno
Adv. Stud. Pure Math. Vol. 55 page： 51-67 2009
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Instanton Calculus and Chiral One-point Functions in Supersymmetric Gauge Theories Reviewed
S.Fujii, H.Kanno, S.Moriyama and S.Okada
Adv. Theor. Math. Phys. Vol. 12 page： 1401-1428 2008
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Instanton Calculus and Loop Operator in Supersymmetric Gauge Theory Reviewed
H.Kanno and S.Moriyama
Phys. Rev.D Vol. 77 page： 126001 2008
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Universal Character and Large N Factorizationin Topological Gauge/String Theory Reviewed
H.Kanno
Nuclear Physics Vol. B745 [PM] page： 165-175 2006
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Instanton counting, Macdonald function and the moduli space of D-branes Reviewed
H.Awata and H.Kanno
Journal of High Energy Physics Vol. 5 page： 039 2005
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Whitham Prepotential and Superpotential Reviewed
H.Itoyama and H.Kanno
Nuclear Physics Vol. B686 page： 155-164 2004
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Geometric transitions, Chern-Simons gauge theory and Veneziano type amplitudes Reviewed
T.Eguchi and H.Kanno
Physics Letters Vol. B585 page： 163-172 2004
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*Topological Strings and Nekrasov's Formulas Reviewed
T.Eguchi and H.Kanno
Journal of High Energy Physics Vol. 12 page： 006 2003
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Supereigenvalue Model and Dijkgraaf-Vafa Proposal Reviewed
H.Itoyama and H.Kanno
Physics Letters Vol. B573 page： 227-234 2003
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On Spin(7) Holonomy Metric Based on SU(3)/U(1) II Reviewed
H.Kanno and Y.Yasui
Journal of Geometry and Physics Vol. 43 page： 310-326 2002
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On Spin(7) Holonomy Metric Based on SU(3)/U(1) Reviewed
H.Kanno and Y.Yasui
Journal of Geometry and Physics Vol. 43 page： 293-309 2002
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Octonionic Yang-Mills instanton on quaternionic line bundle of Spin(7) holonomy
H.Kanno and Y.Yasui
Journal of Geometry and Physics Vol. 34 page： 302 2000
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Five-Dimensional Gauge Theories and Local Mirror Symmetry Reviewed
T.Eguchi and H.Kanno
Nuclear Physics Vol. B586 page： 331 2000
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*Special Quantum Field Theories in Eight and Other Dimensions Reviewed
L.Baulieu, H.Kanno and I.M.Singer
Communications in Mathematical Physics Vol. 194 page： 149 1998
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Donaldson-Witten functions of massless N=2 supersymmetric QCD
H.Kanno and S.-K.Yang
Nuclear Physics Vol. B535 page： 512 1998
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Picard-Fuchs equation and prepotential of five-dimensional SUSY gauge theory compactified on a circle
Nuclear Physics Vol. B530 page： 73 1998
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Two-toroidal Lie Algebra as Current Algebra of Four-dimensional Kaehler WZW Model Reviewed
T.Inami, H.Kanno, T.Ueno and C.S.Xiong
Physics Letters Vol. B399 page： 97 1997
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Topological strings with scaling violation and Toda lattice hierarchy Reviewed
H.Kanno and Y.Ohta
Nuclear Physics Vol. B442 page： 179 1995
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BRST cohomology ring in 2D gravity coupled to minimal models
H.Kanno and M.H.Sarmadi
International Journal of Modern Physics Vol. A9 page： 39 1994
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Toda lattice hierarchy and the topological description of the c=1 string theory
T.Eguchi and H.Kanno
Physics Letters Vol. B331 page： 330 1994
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Woo algebra in a two-dimensional black hole Reviewed
T.Eguchi, H.Kanno and S.-K.Yang
Physics Letters B Vol. 298 page： 73 1993
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Topological strings, flat coordinates and gravitational descendants Reviewed
T.Eguchi, H.Kanno, Y.Yamada and S.-K.Yang
Physics Letters B Vol. 305 page： 235 1993
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SO(2, C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with C<1 matter Reviewed
N.Chair, V.K.Dobrev and H.Kanno
Physics Letters B Vol. 283 page： 194 1992
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*Lie superalgebraic approach to super Toda lattice and gereralized super KdV Equations Reviewed
T.Inami and H.Kanno
Communications in Mathematical Physics Vol. 136 page： 519 1991
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*Weil algebra structure and geometrical meaning of BRST transformation in topological guantum field theory Reviewed
Zeitschrift fur Physik C Vol. 43 page： 477 1989
Books 1
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BRS Cohomology in Topological String Theory and Integrable Systems
BRS Symmetry 1996
Research Project for Joint Research, Competitive Funding, etc. 1
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ゲージ・重力理論対応と可積分系
2008.10 - 2010.3
大幸財団
Grant type：Competitive
KAKENHI (Grants-in-Aid for Scientific Research) 5
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Grant number：23K03087 2023.4 - 2027.3
科学研究費助成事業 基盤研究(C)
菅野 浩明
Authorship：Principal investigator
Grant amount：\2860000 （ Direct Cost: \2200000 、 Indirect Cost：\660000 ）
座標と運動量がともに二重周期性を持つ可積分系である二重楕円型可積分系について，超対称ゲージ理論との対応関係を通して，その性質を明らかにする．互いに可換なハミルトニアンの同時固有関数は，対応する超対称ゲージ理論側で枠付き放物層の数え上げに関する分配関数で与えられると予想されている．楕円量子群の表現論を用いて，分配関数を絡み作用素の同変指標として書き換えることにより，分配関数の満たす差分方程式を求める．また二重楕円型可積分系は座標と運動量の入れ替えに関して自己双対性をもつことが期待されている．分配関数のもつ対称性を明らかにすることによって自己双対性が実現されていることを示す．
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Grant number：18K03274 2018.4 - 2023.3
科学研究費助成事業 基盤研究(C)
菅野 浩明
Authorship：Principal investigator
Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）
Ding-Iohara-Miki 代数（gl_1型の量子トロイダル代数）の MacMahon 表現の表現空間は平面分割でラベルされる基底をもち,対応する量子アフィン代数の表現論における Evaluation 加群と同様の役割を果たす. MacMahon 表現と自由場表現の絡み作用素の真空期待値 （相関関数）が満たす KZ 型の差分方程式を導いた.この際,絡み作用素のスペクトル変数のシフトを生成する作用素が普遍 R 行列から導かれることが鍵となっている．また KZ 型の差分方程式に現れる R 行列が”対角的”であるという性質から,解は自由場の相関関数に対する Wick の定理と同様に２点関数の積で書くことができる．この２点関数はインスタントン分配関数の構成要素である Nekrasov 因子を拡張したものとなっているが,その物理的意味については,まだよく分かっていない.
量子アフィン代数の場合は,準 Hopf ツイストという余積構造の捻りによって,楕円型の量子群を構成できることが知られている. Ding-Iohara-Miki 代数について同様に準 Hopf ツイストを行って楕円型変形を考え,対応する絡み作用素を構成した.準 Hopf ツイストを行った後で KZ 型の差分方程式を導くためには真空期待値の代わりに絡み作用素の合成のトレースを考えなければならない.また差分方程式の導出にあたっては,トレースの巡回置換対称性を利用する.トレースが満たすKZ 型の差分方程式の解として６次元超対称ゲージ理論の分配関数の構成要素である楕円型 Nekrasov 因子が得られることが確かめられた.さらに準 Hopf ツイストを用いて楕円型の Virasoro 代数や W 代数の構成を試みたが,これについては残念ながら期待される結果は得られなかった.
コロナウィルス感染拡大の影響で，国際共同研究の進捗に支障が出た.
最近，面欠陥作用素を入れた５次元超対称ゲージ理論のインスタントン分配関数が満たす差分方程式について，新たな進展がみられた.幾何学的には affine Laumon 空間の同変 K 理論と関連していることが期待される.ただし affine Laumon 空間はハイパーケーラー商として記述すすることができないので，この点を踏まえて差分方程式の幾何学的意味を明らかにすることを目標とする.表現論的にはアフィン遮蔽作用素の役割を解明することが鍵になると考えている. -
Research of lattices, automorphic forms and moduli spaces
Grant number：15H05738 2015.5 - 2020.3
Kondo Shigeyuki
Authorship：Coinvestigator(s)
We studied symmetries of manifolds from a wide-angle. We obtained a complete classification of Enriques surfaces with finite automorphism group and results on automorphisms of K3 and Enriques surfaces related with complex dynamical systems, and discovered a new phenomenon of Enriques surfaces by using the theory of a famous lattice, called Leech lattice, in sphere packing problem. And we studied moduli problems. In particular, we determined an important invariant, called the Kodaira dimensions, of some moduli spaces by applying the theory of automorphic forms. We also obtained several results related with Mathematical Physics and representation theory, for example, a duality phenomenon in Mathieu moonshine.
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M ブレインと量子可積分系
2012.4
科学研究費補助金 基盤研究(C)
Authorship：Principal investigator
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弦双対性が予言するアクセサリパラメータ付き特殊関数
2007 - 2009
科学研究費補助金 萌芽研究，課題番号：19654007
菅野 浩明
Authorship：Principal investigator
Teaching Experience (On-campus) 1
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Linear Algebra II
2011