ITOYAMA Hiroshi

 Title Professor Laboratory location Sugimoto Campus

### Degree 【 display / non-display 】

• Columbia University -  Ph. D

### Research Areas 【 display / non-display 】

StringTheory,IntegrableSystems

### Research Career 【 display / non-display 】

• matrix model unification, integrability in strings

(Individual)

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 】

•
-
1979

The University of Tokyo   Faculty of Science   Department of Physics

### Published Papers 【 display / non-display 】

• THE DIJKGRAAF-VAFA PREPOTENTIAL IN THE CONTEXT OF GENERAL SEIBERG-WITTEN THEORY

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]

• 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.

• 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.

• Itoyama H., Oota T., Yoshioka R.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL  50 ( 36 )  2017.09  [Refereed]

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 $\mathbb{R}^4/\mathbb{Z}_r$.

### Books etc 【 display / non-display 】

• 糸山 浩司 (Part： Single Work )

京都大学学術出版会  2017

• 暁方 ミセイ (Part： Single Work )

河出書房新社  2016

• 糸山 浩司, 横山 順一, 川合 光, 南部 陽一郎 (Part： Single Work )

京都大学学術出版会  2013

### Review Papers (Misc) 【 display / non-display 】

• 糸山 浩美

(株)デンタルダイヤモンド社　DHstyle  12 ( 4 ) 50 - 51 2018.04  [Refereed]  [Invited]