arXiv subjects

Yutaka Yoshida

Publications and source records attributed to Yutaka Yoshida.

At least 19 recordsLinked to original sources

arXiv2026

SCFT/VOA correspondence and R-twisted reductions of $(A_2,D_{3n-2})$ Argyres--Douglas theories

We study the SCFT/VOA correspondence for the $(A_2,D_{3n-2})$ Argyres--Douglas theories with $n\geq2$. From the matching of the central charges and the equality of the Schur index with the vacuum supercharacter to all orders, we propose that the associated VOA is the logarithmic doublet algebra $\mathcal A(4n-2)$ of Feigin, Feigin, and Tipunin. For $n=2$, this correspondence was studied in detail by Buican and Nishinaka, and our proposal extends it to $n\geq3$. Using the Nahm sum expression for the vacuum supercharacter, we further propose a family of 3d $\mathcal N=2$ abelian Chern--Simons matter theories that flow to the 3d $\mathcal N=4$ SCFTs obtained by the R-twisted circle reduction, generalizing the $n=2$ construction. We determine the monopole superpotential and show that the Coulomb branch is $\mathbb C^2/\mathbb Z_2$ for every $n$. The superconformal index provides quantitative evidence for the proposed infrared fixed points, including the expected enhancement to $\mathcal N=4$ supersymmetry and the Higgs and Coulomb branch structure.

hep-th↗

arXiv2026

3d $\mathcal N=4$ rank-zero mirror symmetry, TQFT interfaces, and Zagier duality of Nahm sums

Starting from the $(E_8,T_1)$ Nahm sum for the vacuum character of $T_{10}M_{\rm eff}(11,2)$, we construct a three-dimensional (3d) $\mathcal N=2$ $U(1)^8$ Chern--Simons matter theory $\mathcal T$ with level matrix $C_{E_8}$. Its $A$-twisted vacuum half-index reproduces the character exactly, while four distinguished Wilson loop half-indices agree with the remaining characters to the orders checked. Applying particle--vortex duality and gauging yields a second 3d $\mathcal N=2$ Chern--Simons matter theory $\mathcal T^\vee$ with level matrix $C_{E_8}^{-1}$. Exact superconformal-index matching supports the claim that the two theories flow to 3d $\mathcal N=4$ rank-zero mirror SCFTs. For the $(\mathcal D,D_c)$ boundary condition, the mirror map between the $A$-twisted Wilson loop half-indices of $\mathcal T$ and the $B$-twisted Wilson loop half-indices of $\mathcal T^\vee$ coincides componentwise with the Zagier transformation, realizing a Zagier duality between the complete $(E_8,T_1)$ and $(T_1,E_8)$ Nahm systems. Using the Bethe-equation formalism, we show that the corresponding $A/B$-twisted TQFT data agree up to orientation reversal and the $E_8$ framing phase $e^{-2\pi \mathrm{i}/3}$. The duality interface gives the torus bilinear $Z_{\mathcal I}(\tau)=\sum_i\chi_i(\tau)\chi_i^\vee(\tau)=\chi_{(E_8)_1}(\tau)$, where $\{\chi_i\}$ and $\{\chi_i^\vee\}$ are the corresponding five-component character bases. Thus Zagier duality is realized as part of a concrete 3d mirror and interface structure.

hep-th↗

arXiv2026

3d SUSY enhancement with non-trivial Coulomb branch via 4d $\mathcal{N}=2$ SCFT

In recent years, a variety of three-dimensional (3d) $\mathcal{N}=2$ Chern--Simons (CS) matter theories have been constructed that flow to 3d $\mathcal{N}=4$ superconformal field theories (SCFTs) obtained from $R$-twisted reductions of four-dimensional (4d) $\mathcal{N}=2$ SCFTs. In all previously studied examples, the resulting 3d $\mathcal{N}=4$ SCFTs have trivial Coulomb branches. In this paper, we construct a 3d $\mathcal{N}=2$ CS matter theory that flows to the $R$-twisted reduction of the $(A_2,D_4)$ Argyres--Douglas theory. This gives the first example in this class whose infrared 3d $\mathcal{N}=4$ SCFT has a non-trivial Coulomb branch, which we argue is given by the orbifold $\mathbb{C}^2/\mathbb{Z}_2$, while its Higgs branch is trivial. We further identify the 4d $U(1)$ R-charge as a mixing of a 3d R-charge with an emergent 3d Coulomb branch flavor charge that has no 4d origin.

hep-th↗

arXiv2026

Euler transformation for multiple $q$-hypergeometric series from wall-crossing formula of $K$-theoretic vortex partition function

We show that transformation formulas of multiple $q$-hypergeometric series agree with wall-crossing formulas of $K$-theoretic vortex partition functions obtained by Hwang, Yi and the author \cite{Hwang:2017kmk}. For the vortex partition function in 3d $\mathcal{N}=2$ gauge theory, we show that the wall-crossing formula agrees with the Kajihara transformation \cite{kajihara2004euler}. For the vortex partition function in 3d $\mathcal{N}=4$ gauge theory, we show that the wall-crossing formula agrees with the transformation formula by Hallnäs, Langmann, Noumi and Rosengren \cite{Halln_s_2022}. Since the $K$-theoretic vortex partition functions are related with indices such as the $χ_t$-genus of the handsaw quiver variety, we discuss geometric interpretation of Euler transformations in terms of wall-crossing formulas of handsaw quiver variety.

hep-th↗

arXiv2026

3d Chern--Simons matter theories from generalized Argyres--Douglas theories

We study 3d $\mathcal{N}=2$ Chern--Simons matter theories describing the R-twisted $S^1$-reduction of Argyres--Douglas theories of $(A_{M-1},A_{N-1})$ type with $\text{gcd}(M,N)=1$, via a recently-proposed 4d/3d correspondence. In particular, for the $(A_2,A_{N-1})$ and $(A_3,A_{N-1})$ theories, we identify a series of Chern--Simons matter theories with monopole superpotentials consistent with an $\mathcal{N}=4$ supersymmetry enhancement in the infrared. As a by-product, we also find a novel Nahm sum formula for the vacuum character of $(3,8)$ $W_3$ minimal model, from which we find another Chern--Simons matter theory describing the R-twisted $S^1$-reduction of the $(A_2,A_4)$ theory.

hep-th↗

arXiv2025

Longitudinal Magnetoresistance in YBa$_2$Cu$_3$O$_7$ at High Magnetic Fields of up to 100 T

The investigation of transport characteristics in high-temperature superconductors under magnetic fields is one of the most important topics in condensed matter physics and transport applications. For YBa$_2$Cu$_3$O$_7$ (YBCO), the measurements of magnetoresistance under a high magnetic field are technically challenging because the required magnetic field ($B$) to suppress the superconductivity is 100~T class. The low temperature (from 52 to 150 K) longitudinal magnetoresistance ($B$$\parallel$ab-plane$\parallel$$J$, where $J$ is an electrical current) was measured up to 103~T in optimally doped YBCO thin films. A radio frequency reflection method and the single-turn coil technique were employed. The electrical resistivity $ρ_{ab}$ exhibited a non-saturating magnetoresistance behavior until the highest field region, with the slope $β(=d ρ/d B)$ showing a pronounced deviation compared to the transverse magnetoresistance ($B$$\parallel$c-axis) case. These findings suggest a potential contribution due to the non-orbital origin in the high field phase of YBCO, because the quasiparticle orbital motion is expected to be absent in the longitudinal magnetoresistance.

cond-mat.str-el↗

arXiv2025

Quantized Coulomb branch of 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory and spherical DAHA of $(C_N^{\vee}, C_N)$-type

We study BPS loop operators in a 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory with four hypermultiplets in the fundamental representation and one hypermultiplet in the anti-symmetric representation. The algebra of BPS loop operators in the $\Omega$-background provides a deformation quantization of the Coulomb branch, which is expected to coincide with the quantized K-theoretic Coulomb branch in the mathematical literature. For the rank-one case, i.e., $Sp(1) \simeq SU(2)$, we show that the quantization of the Coulomb branch, evaluated using the supersymmetric localization formula, agrees with the polynomial representation of the spherical part of the double affine Hecke algebra (spherical DAHA) of $(C_1^{\vee}, C_1)$-type. For higher-rank cases, where $N \geq 2$, we conjecture that the quantized Coulomb branch of the 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory is isomorphic to the spherical DAHA of $(C_N^{\vee}, C_N)$-type . As evidence for this conjecture, we show that the quantization of an 't Hooft loop agrees with the Koornwinder operator in the polynomial representation of the spherical DAHA.

hep-th↗

arXiv2024

Wall-crossing for vortex partition function and handsaw quiver varierty

We investigate vortex partition functions defined from integrals over the handsaw quiver varieties of type $A_{1}$ via wall-crossing phenomena. We consider vortex partition functions defined by two types of cohomology classes, and get functional equations for each of them. We also give explicit formula for these partition functions. This gives proofs to formula suggested by physicsts. In particular, we obtain geometric interpretation of formulas for multiple hypergeometric functions including rational limit of the Kajihara transformation formula.

math.AG↗

arXiv2023

Fermionic extensions of $W$-algebras via 3d $\mathcal{N}=4$ gauge theories with a boundary

We study properties of vertex (operator) algebras associated with 3d H-twisted $\mathcal{N}=4$ supersymmetric gauge theories with a boundary. The vertex operator algebras (VOAs) are defined by BRST cohomologies of currents with symplectic bosons, complex fermions, and bc-ghosts. We point out that VOAs for 3d $\mathcal{N}=4$ abelian gauge theories are fermionic extensions of VOAs associated with toric hyper-K\"{a}hler varieties. From this relation, it follows that the VOA associated with the 3d mirror of $N$-flavor $U(1)$ SQED is a fermionic extension of a $W$-algebra $W^{-N+1}(\mathfrak{sl}_N, f_{\text{sub}})$. For $N=3$, we explicitly compute the OPE of elements in the BRST cohomology and find a new algebra that is a fermionic extension of a Bershadsky-Polyakov algebra $W^{-2}(\mathfrak{sl}_3, f_{\text{sub}})$. We also suggest an expression for the vacuum character of the fermionic extension of $W^{-N+1}(\mathfrak{sl}_N, f_{\text{sub}})$ predicted by 3d $\mathcal{N}=4$ mirror symmetry.

hep-th↗

arXiv2023

Conserved charges in the quantum simulation of integrable spin chains

When simulating the time evolution of quantum many-body systems on a digital quantum computer, one faces the challenges of quantum noise and of the Trotter error due to time discretization. The Trotter error in integrable spin chains can be under control if the discrete time evolution preserves integrability. In this work we implement, on a real quantum computer and on classical simulators, the integrable Trotterization of the spin-1/2 Heisenberg XXX spin chain. We study how quantum noise affects the time evolution of several conserved charges, and observe the decay of the expectation values. We in addition study the early time behaviors of the time evolution, which can potentially be used to benchmark quantum devices and algorithms in the future. We also provide an efficient method to generate the conserved charges at higher orders.

quant-ph↗

arXiv2021

't Hooft surface operators in five dimensions and elliptic Ruijsenaars operators

We introduce codimension three magnetically charged surface operators in five-dimensional (5d) $\mathcal{N}=1$ supersymmetric gauge on $T^2 \times \mathbb{R}^3$. We evaluate the vacuum expectation values (vevs) of surface operators by supersymmetric localization techniques. Contributions of Monopole bubbling effects to the path integral are given by elliptic genera of world volume theories on D-branes. Our result gives an elliptic deformation of the SUSY localization formula \cite{Ito:2011ea} (resp. \cite{Okuda:2019emk, Assel:2019yzd}) of BPS 't Hooft loops (resp. bare monopole operators) in 4d $\mathcal{N}=2$ (resp. 3d $\mathcal{N}=4$) gauge theories. We define deformation quantizations of vevs of surface operators in terms of the Weyl-Wigner transform, where the $Ω$-background parameter plays the role of the Planck constant. For 5d $\mathcal{N}=1^*$ gauge theory, we find that the deformation quantization of the surface operators in the anti-symmetric representations agrees with the type A elliptic Ruijsenaars operators. The mutual commutativity of these difference operators is related to the commutativity of products of 't Hooft surface operators.

hep-th↗

arXiv2021

ABCD of 't Hooft operators

We compute by supersymmetric localization the expectation values of half-BPS 't Hooft line operators in $\mathcal{N}=2$ $U(N)$, $SO(N)$ and $USp(N)$ gauge theories on $S^1 \times \mathbb{R}^3$ with an $Ω$-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the 't Hooft operators using branes and orientifolds in type II string theories.

hep-th↗

arXiv2020

Supersymmetric indices on $I \times T^2$, elliptic genera and dualities with boundaries

We study three dimensional $\mathcal{N}=2$ supersymmetric theories on $I \times M_2$ with 2d $\mathcal{N}=(0,2)$ boundary conditions at the boundaries $\partial (I \times M_2)=M_2 \sqcup M_2$, where $M_2=\mathbb{C}$ or $ T^2$. We introduce supersymmetric indices of three dimensional $\mathcal{N}=2$ theories on $I \times T^2$ that couple to elliptic genera of 2d $\mathcal{N}=(0,2)$ theories at the two boundaries. We evaluate the $I \times T^2$ indices in terms of supersymmetric localization and study dualities on the $I \times M_2$. We consider the dimensional reduction of $I \times T^2$ to $I \times S^1$ and obtain the localization formula of 2d $\mathcal{N}=(2,2)$ supersymmetric indices on $I \times S^1$. We illustrate computations of open string Witten indices based on gauged linear sigma models. Correlation functions of Wilson loops on $I \times S^1$ agree with Euler pairings in the geometric phase and also agree with cylinder amplitudes for B-type boundary states of Gepner models in the Landau-Ginzburg phase.

hep-th↗

arXiv2020

3d N=2 Chern-Simons-matter theory, Bethe ansatz, and quantum K-theory of Grassmannians

We study a correspondence between 3d $\mathcal{N}=2$ topologically twisted Chern-Simons-matter theories on $S^1 \times Σ_g$ and quantum $K$-theory of Grassmannians. Our starting point is a Frobenius algebra depending on a parameter $β$ associated with an algebraic Bethe ansatz introduced by Gorbounov-Korff. They showed that the Frobenius algebra with $β=-1$ is isomorphic to the (equivariant) small quantum $K$-ring of the Grassmannian, and the Frobenius algebra with $β=0$ is isomorphic to the equivariant small quantum cohomology of the Grassmannian. We apply supersymmetric localization formulas to the correlation functions of supersymmetric Wilson loops in the Chern-Simons-matter theory and show that the algebra of Wilson loops is isomorphic to the Frobenius algebra with $β=-1$. This allows us to identify the algebra of Wilson loops with the quantum $K$-ring of the Grassmannian. We also show that correlation functions of Wilson loops on $S^1 \times Σ_g$ satisfy the axiom of 2d TQFT. For $β=0$, we show the correspondence between an A-twisted GLSM, the Frobenius algebra for $β=0$, and the quantum cohomology of the Grassmannian. We also discuss deformations of Verlinde algebras, omega-deformations, and the $K$-theoretic $I$-functions of Grassmannians with level structures.

hep-th↗

arXiv2020

Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1 \times D^2$

We study three dimensional $\mathcal{N}=2$ supersymmetric Chern-Simons-Matter theories on the direct product of a circle and a two dimensional hemisphere ($S^1 \times D^2$) with specified boundary conditions by the method of localization. We construct boundary interactions to cancel the supersymmetric variation of the three dimensional superpotential term and the Chern-Simons term and show inflows of the bulk-boundary anomalies. It finds that the boundary conditions induce two dimensional $\mathcal{N}=(0,2)$ type supersymmetry on the boundary torus. We also study the relation between the 3d-2d coupled partition function of our model and three dimensional holomorphic blocks.

hep-th↗

arXiv2019

Residue mirror symmetry for Grassmannians

Motivated by recent works on localizations in A-twisted gauged linear sigma models, we discuss a generalization of toric residue mirror symmetry to complete intersections in Grassmannians.

math.AG↗

arXiv2019

Wall-crossing and operator ordering for 't Hooft operators in N=2 gauge theories

We study half-BPS 't Hooft line operators in 4d $\mathcal{N}=2$ $U(N)$ gauge theories on $S^1\times \mathbb{R}^3$ with an $Ω$-deformation. The recently proposed brane construction of 't Hooft operators shows that non-perturbative contributions to their correlator are identified with the Witten indices of quiver supersymmetric quantum mechanics. For the products of minimal 't Hooft operators, a chamber in the space of Fayet-Iliopoulos parameters in the quantum mechanics corresponds to an ordering of the operators inserted along a line. These considerations lead us to conjecture that the Witten indices can be read off from the Moyal products of the expectation values of the minimal 't Hooft operators, and also that wall-crossing occurs in the quantum mechanics only when the ordering of the operators changes. We confirm the conjectures by explicitly computing the Witten indices for the products of two and three minimal 't Hooft operators in all possible chambers.

hep-th↗

arXiv2019

SUSY localization for Coulomb branch operators in omega-deformed 3d N=4 gauge theories

We perform SUSY localization for Coulomb branch operators of 3d $\mathcal{N}=4$ gauge theories in $\mathbb{R}^3$ with $Ω$-deformation. For the dressed monopole operators whose expectation values do not involve non-perturbative corrections, our computations reproduce the results of the so-called abelianization procedure. For the expectation values of other operators and the correlation functions of multiple operators in $U(N)$ gauge theories, we compute the non-perturbative corrections due to monopole bubbling using matrix models obtained by brane construction. We relate the results of localization to algebraic structures discussed in the mathematical literature, and also point out a similar relation for line operators in 4d $\mathcal{N}=2$ gauge theories. For $U(N)$ (quiver) gauge theories in 3d we demonstrate a direct correspondence between wall-crossing and the ordering of operators.

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