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Laboratory location

Sugimoto Campus

Degree 【 display / non-display

  • Columbia University -  Ph. D

Research Areas 【 display / non-display


Research Career 【 display / non-display

  • matrix model unification, integrability in strings


    Keyword in research subject:  matrix, integrability, string

Association Memberships 【 display / non-display

  • Physical Society of Japan

Committee Memberships 【 display / non-display

  • 2005

    Physical Society of Japan  

Current Career 【 display / non-display

  • Osaka City University   Graduate School of Science   Mathematics and Physics Course   Professor  

Graduate School 【 display / non-display


    Columbia University  Graduate School of Arts and Sciences  Physics Department 

Graduating School 【 display / non-display


    The University of Tokyo   Faculty of Science   Department of Physics


Published Papers 【 display / non-display


    Nucl. Phys.  B657   53 - 78 2003

  • Discrete Painleve system and the double scaling limit of the matrix model for irregular conformal block and gauge theory

    Itoyama H., Oota T., Yano Katsuya

    PHYSICS LETTERS B  789   605 - 609 2019.02  [Refereed]


  • From Kronecker to tableau pseudo-characters in tensor models

    Itoyama H., Mironov A., Morozov A.

    PHYSICS LETTERS B  788   76 - 81 2019.01  [Refereed]

     View Summary

    We present a brief summary of the recent discovery of direct tensorial
    analogue of characters. We distinguish three degrees of generalization: (1)
    $c$-number Kronecker characters made with the help of symmetric group
    characters and inheriting most of the nice properties of conventional Schur
    functions, except for forming a complete basis for the case of rank $r>2$
    tensors: they are orthogonal, are eigenfunctions of appropriate cut-and-join
    operators and form a complete basis for the operators with non-zero Gaussian
    averages; (2) genuine matrix-valued tensorial quantities, forming an
    over-complete basis but difficult to deal with; and (3) intermediate tableau
    pseudo-characters, depending on Young tables rather than on just Young
    diagrams, in the Kronecker case, and on entire representation matrices, in the
    genuine one.


  • Cut and join operator ring in tensor models

    Itoyama H., Mironov A., Morozov A.

    NUCLEAR PHYSICS B  932   52 - 118 2018.07  [Refereed]

     View Summary

    Recent advancement of rainbow tensor models based on their superintegrability
    (manifesting itself as the existence of an explicit expression for a generic
    Gaussian correlator) has allowed us to bypass the long-standing problem seen as
    the lack of eigenvalue/determinant representation needed to establish the
    KP/Toda integrability. As the mandatory next step, we discuss in this paper how
    to provide an adequate designation to each of the connected gauge-invariant
    operators that form a double coset, which is required to cleverly formulate a
    tree-algebra generalization of the Virasoro constraints. This problem goes
    beyond the enumeration problem per se tied to the permutation group, forcing us
    to introduce a few gauge fixing procedures to the coset. We point out that the
    permutation-based labeling, which has proven to be relevant for the Gaussian
    averages is, via interesting complexity, related to the one based on the
    keystone trees, whose algebra will provide the tensor counterpart of the
    Virasoro algebra for matrix models. Moreover, our simple analysis reveals the
    existence of nontrivial kernels and co-kernels for the cut operation and for
    the join operation respectively that prevent a straightforward construction of
    the non-perturbative RG-complete partition function and the identification of
    truly independent time variables. We demonstrate these problems by the simplest
    non-trivial Aristotelian RGB model with one complex rank-3 tensor, studying its
    ring of gauge-invariant operators, generated by the keystone triple with the
    help of four operations: addition, multiplication, cut and join.


  • Elliptic algebra, Frenkel-Kac construction and root of unity limit

    Itoyama H., Oota T., Yoshioka R.


     View Summary

    We argue that the level-$1$ elliptic algebra
    $U_{q,p}(\widehat{\mathfrak{g}})$ is a dynamical symmetry realized as a part of
    2d/5d correspondence where the Drinfeld currents are the screening currents to
    the $q$-Virasoro/W block in the 2d side. For the case of
    $U_{q,p}(\widehat{\mathfrak{sl}}(2))$, the level-$1$ module has a realization
    by an elliptic version of the Frenkel-Kac construction. The module admits the
    action of the deformed Virasoro algebra. In a $r$-th root of unity limit of $p$
    with $q^2 \rightarrow 1$, the $\mathbb{Z}_r$-parafermions and a free boson
    appear and the value of the central charge that we obtain agrees with that of
    the 2d coset CFT with para-Virasoro symmetry, which corresponds to the 4d
    $\mathcal{N}=2$ $SU(2)$ gauge theory on $\mathbb{R}^4/\mathbb{Z}_r$.


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