arXiv subjects

Reiji Yoshioka

Publications and source records attributed to Reiji Yoshioka.

At least 19 recordsLinked to original sources

arXiv2026

Notes on phase structure and non-vanishing $β$ functions of one-unitary matrix model

Unitary matrix models, among other things, play an important role in representing the irregular conformal block and hence LEEA of some asymptotically free susy gauge theories. Here, we develop a method of how to determine the qualitative structure of phase diagram by the deformation of classical potential, and illustrate this by the examples that contain term up to $\cos nα$, $n \leq 3$. We point out that a set of $β$ functions on critical ``lines" is nowhere a vanishing vector. This generalizes the $n =1$ GWW case and tells us the third order (rather than second order) phase transition in conformity with the range of values for the susceptibility exponent.

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arXiv2024

Phases and triple(multiple) point: critical phenomena around the AD singularity

Continuing with our previous series of work, we present a case study of the critical phenomena around Argyres-Douglas singularity of ${\cal N} =2$ susy made at $(A_1, A_{4k-1} ), k =1, 2$ realized by one-unitary matrix model. We determine the phase diagram, which is recast into LEEA of $\mathcal{N}=2$, 4d gauge theory by the 0d-4d connection. There are three distinct phases, each corresponding to an eigenvalue distribution with 0, 1, and 2 gaps. These form an entire phase diagram with a triple point. Examining the behavior of the planar free energy, we show, among other things,that the transition line between 1- and 2-gap phases ending at the triple point is the $k=2$ multicritical one.

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arXiv2024

Large order behavior near the AD point: the case of $\mathcal{N} =2$, $su(2)$, $N_f =2$

A non-perturbative effect in $κ$ (renormalized string coupling) obtained from the large order behavior in the vicinity of the prototypical Argyres-Douglas critical point of $su(2)$, $N_f =2$, $\mathcal{N} =2$ susy gauge theory can be studied in the GWW unitary matrix model with the log term: the one as the work done against the barrier of the effective potential by a single eigenvalue lifted from the sea and the other as a non-perturbative function contained in the solutions of the nonlinear differential equation PII that goes beyond the asymptotic series. The leading behaviors are of the form $\exp (-\frac{4}{3}\frac{1}κ \, (1, \left(\frac{s}{K}\right)^{\frac{3}{2}} ))$ respectively. We make comments on their agreement.

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arXiv2023

Construction of irregular conformal/W block and flavor mass relations of $\mathcal{N}=2$ SUSY gauge theory from the $A_{n-1}$ quiver matrix model

A sequence of massive scaling limits of the $β$-deformed $A_{n-1}$ quiver matrix model that keeps the size of the matrices finite and that corresponds to the $N_{f} =2n \rightarrow 2n-1, 2n-2$ limits on the number of flavors at 4d $su(n)$ ${\cal N} = 2$ SUSY gauge theory side is carried out to provide us with the integral representation of $su(n)$ irregular conformal/W block. The original paths are naturally deformed into those in the complex plane, permitting us to convert into an $su(n)$ extension of the unitary matrix model of GWW type with a set of log potentials for all species of eigenvalues. Looking at the region in the parameter space that enjoys the maximal symmetry of the model, we derive a set of relations among the mass parameters which may serve as evidence for the existence of the Argyres-Douglas critical hypersurface.

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arXiv2022

A-D hypersurface of $su(n)$ $\mathcal{N}=2$ supersymmetric gauge theory with $N_f = 2n-2$ flavors

In the previous letter, arXiv:2210.16738[hep-th], we found a set of flavor mass relations as constraints that the $β$-deformed $A_{n-1}$ quiver matrix model restores the maximal symmetry in the massive scaling limit and reported the existence of Argyres-Douglas critical hypersurface. In this letter, we derive the concrete conditions on moduli parameters which maximally degenerates the Seiberg-Witten curve while maintaining the flavor mass relations. These conditions define the A-D hypersurface.

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arXiv2019

Generalized cut operation associated with higher order variation in tensor models

The cut and join operations play important roles in tensor models in general. We introduce a generalization of the cut operation associated with the higher order variations and demonstrate how they generate operators in the Aristotelian tensor model. We point out that, by successive choices of appropriate variations, the cut operation generalized this way can generate those operators which do not appear in the ring of the join operation, providing a tool to enumerate the operators by a level by level analysis recursively. We present a set of rules that control the emergence of such operators.

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arXiv2017

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

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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arXiv2016

Cubic constraints for the resolvents of the ABJM matrix model and its cousins

A set of Schwinger-Dyson equations forming constraints for at most three resolvent functions are considered for a class of Chern-Simons matter matrix models with two nodes labelled by a non-vanishing number $n$. The two cases $n=2$ and $n= -2$ label respectively the ABJM matrix model, which is the hyperbolic lift of the affine $A_1^{(1)}$ quiver matrix model, and the lens space matrix model. In the planar limit, we derive two cubic loop equations for the two planar resolvents. One of these reduces to the quadratic one when $n = \pm 2$.

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arXiv2016

q-Vertex Operator from 5D Nekrasov Function

The five dimensional AGT correspondence implies the connection between the q-deformed Virasoro block and the 5d Nekrasov partition function. In this paper, we determine a q-deformation of the four-point block in the Coulomb gas representation from the 5d Nekrasov function, and obtain an expression of the q-deformed vertex operator. If we use only one kind of the q-vertex operators, one of the insertion points of them must be modified in order to hold the 2d/5d correspondence.

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arXiv2015

The integral representation of solutions of KZ equation and a modification by $\mathcal{K}$ operator insertion

A root of unity limit of the $q$-deformed Virasoro algebra is considered. The $\widehat{sl}(2)_k$ current algebra and the integral formulas of the solutions of the KZ equations can be realized by the $q$-deformed boson at the limit and an additional boson. We explicitly construct the integral representation of the four-point blocks with a $\mathcal{K}$-operator insertion.

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arXiv2015

Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models

This is a semi-pedagogical review of a medium size on the exact determination of and the role played by the low energy effective prepotential ${\cal F}$ in QFT with (broken) extended supersymmetry, which began with the work of Seiberg and Witten in 1994. While paying an attention to an overall view of this subject lasting long over the two decades, we probe several corners marked in the three major stages of the developments, emphasizing uses of the deformation theory on the attendant Riemann surface as well as its close relation to matrix models. Examples picked here in different contexts tell us that the effective prepotential is to be identified as the suitably defined free energy $F$ of a matrix model: ${\cal F} = F$. To be submitted to PTEP as an invited review article and based in part on the talk delivered by one of the authors (H.I.) in the workshop held at Shizuoka University, Shizuoka, Japan, on December 5, 2014.

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arXiv2014

$q$-Virasoro/W Algebra at Root of Unity and Parafermions

We demonstrate that the parafermions appear in the $r$-th root of unity limit of $q$-Virasoro/$W_n$ algebra. The proper value of the central charge of the coset model $ \frac{\widehat{\mathfrak{sl}}(n)_r \oplus \widehat{\mathfrak{sl}}(n)_{m-n}}{\widehat{\mathfrak{sl}}(n)_{m-n+r}}$ is given from the parafermion construction of the block in the limit.

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arXiv2013

2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space

We propose and demonstrate a limiting procedure in which, starting from the q-lifted version (or K-theoretic five dimensional version) of the (W)AGT conjecture to be assumed in this paper, the Virasoro/W block is generated in the r-th root of unity limit in q in the 2d side, while the same limit automatically generates the projection of the five dimensional instanton partition function onto that on the ALE space R^4/Z_r. This circumvents case-by-case conjectures to be made in a wealth of examples found so far. In the 2d side, we successfully generate the super-Virasoro algebra and the proper screening charge in the q -> -1, t -> -1 limit, from the defining relation of the q-Virasoro algebra and the q-deformed Heisenberg algebra. The central charge obtained coincides with that of the minimal series carrying odd integers of the N=1 superconformal algebra. In the r-th root of unity limit in q in the 2d side, we give some evidence of the appearance of the parafermion-like currents. Exploiting the q-analysis literatures, q-deformed su(n) block is readily generated both at generic q, t and the r-th root of unity limit. In the 4d side, we derive the proper normalization function for general (n, r) that accomplishes the automatic projection through the limit.

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arXiv2012

On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain

We study the link between WZW model and the spin-1/2 XYZ chain. This is achieved by comparing the second-order differential equations from them. In the former case, the equation is the Ward-Takahashi identity satisfied by one-point toric conformal blocks. In the latter case, it arises from Baxter's TQ relation. We find that the dimension of the representation space w.r.t. the V-valued primary field in these conformal blocks gets mapped to the total number of chain sites. By doing so, Stroganov's "The Importance of being Odd" (cond-mat/0012035) can be consistently understood in terms of WZW model language. We first confirm this correspondence by taking a trigonometric limit of the XYZ chain. That eigenstates of the resultant two-body Sutherland model from Baxter's TQ relation can be obtained by deforming toric conformal blocks supports our proposal.

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arXiv2011

Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and Ω-deformed Seiberg-Witten prepotential

We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondence emerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theories having the above different gauge groups are encoded simultaneously in one Baxter's T-Q equation which captures their spectral curves. For example, while one is SU(N_c) with N_f=2N_c flavors the other turns out to be SU(2)^{N_c-3} with N_c hyper-multiplets (N_c > 3). It is seen that the corresponding Seiberg-Witten differential supports our proposal.

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arXiv2010

Effects of Matrix Orientifolding to Two-Loop Effective Action of Bosonic IIB Matrix Model

We study the spacetime structures which are described by the IIB matrix model with orientifolding. Matrix orientifolding that preserves supersymmetries yields the mirror image point with respect to a four-dimensional plane for each spacetime point that corresponds to the eigenvalue of the bosonic matrix. In order to consider the upper bound on the distance between two eigenvalues in this model, we calculate the effective action for the eigenvalues up to two-loop. The eigenvalues distribute in a tubular region around the four-dimensional plane.

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arXiv2009

Orientifolded Matrices and Supersymmetries that Give Rise to Spacetime Directional Asymmetry of Effective Interactions

Effects of matrix orientifolding that preserves supersymmetries are considered in the IIB matrix model with regard to its effective dynamics generated for diagonal elements. Taking the case of maximal supersymmetries and the long distance expansion of the one-loop effective action as well as cases where the size of the matrices is small, we demonstrate that the directional asymmetry of spacetime brought upon by this setup in fact leads to that of the forces exerting on the spacetime points: in addition to the two-body attraction between two points, there are attractions toward the four dimensional plate.

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arXiv2008

Nambu-Goto Like Action for the AdS_5 x S^5 Superstrings in the Generalized Light-Cone Gauge

We reinvestigate the kappa-symmetry-fixed Green-Schwarz action in the AdS_5 x S^5 background in a version of the light-cone gauge. In the generalized light-cone gauge, the action has been written in the phase space variables. We convert it into the standard action written in terms of the fields and their derivatives. We obtain a Nambu-Goto type action which has the correct flat-space limit.

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