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Taro Kimura

Publications and source records attributed to Taro Kimura.

At least 73 records · Page 4Linked to original sources
arXiv2019

Conformal field theory analysis for QCD Kondo effect

We study non-perturbative aspects of QCD Kondo effect, which has been recently proposed for the finite density and strong magnetic field systems, using conformal field theory describing the low energy physics near the IR fixed point. We clarify the symmetry class of QCD Kondo effect both for the finite density and magnetic field systems, and show how the IR fixed point is non-perturbatively characterized by the boundary condition, which incorporates the impurity effect in Kondo problem. We also obtain the low temperature behavior of several quantities of QCD Kondo effect in the vicinity of the IR fixed point based on the conformal field theory analysis.

hep-ph↗
arXiv2018

Refined geometric transition and $qq$-characters

We show the refinement of the prescription for the geometric transition in the refined topological string theory and, as its application, discuss a possibility to describe $qq$-characters from the string theory point of view. Though the suggested way to operate the refined geometric transition has passed through several checks, it is additionally found in this paper that the presence of the preferred direction brings a nontrivial effect. We provide the modified formula involving this point. We then apply our prescription of the refined geometric transition to proposing the stringy description of doubly quantized Seiberg--Witten curves called $qq$-characters in certain cases.

hep-th↗
arXiv2018

Quantum integrability from non-simply laced quiver gauge theory

We consider the compactifcation of 5d non-simply laced fractional quiver gauge theory constructed in arXiv:1705.04410. In contrast to the simply laced quivers, here two $Ω$-background parameters play different roles, so that we can take two possible Nekrasov-Shatashvili limits. We demonstrate how different quantum integrable systems can emerge from these two limits, using $BC_2$-quiver as the simplest illustrative example for our general results. We also comment possible connections with compactified 3d non-simply laced quiver gauge theory.

hep-th↗
arXiv2018

Fractional quiver W-algebras

We introduce quiver gauge theory associated with the non-simply-laced type fractional quiver, and define fractional quiver W-algebras by using construction of arXiv:1512.08533 and arXiv:1608.04651 with representation of fractional quivers.

hep-th↗
arXiv2018

Quiver W-algebras

For a quiver with weighted arrows we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al., and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds-Kac-Moody Lie algebras, their quantum affinizations and associated W-algebras.

hep-th↗
arXiv2018

Quiver elliptic W-algebras

We define elliptic generalization of W-algebras associated with arbitrary quiver using the formalism of arXiv:1512.08533 applied to six-dimensional quiver gauge theory compactified on elliptic curve.

hep-th↗
arXiv2018

Double quantization of Seiberg-Witten geometry and W-algebras

We show that the double quantization of Seiberg-Witten spectral curve for $Γ$-quiver gauge theory defines the generating current of W$(Γ)$-algebra in the free field realization. We also show that the partition function is given as a correlator of the corresponding W$(Γ)$-algebra, which is equivalent to the AGT relation under the gauge/quiver (spectral) duality.

hep-th↗
arXiv2017

Fermi/non-Fermi mixing in SU($N$) Kondo effect

We apply conformal field theory analysis to the $k$-channel SU($N$) Kondo system, and find a peculiar behavior in the cases $N > k > 1$, which we call Fermi/non-Fermi mixing: The low temperature scaling is described as the Fermi liquid, while the zero temperature IR fixed point exhibits the non-Fermi liquid signature. We also show that the Wilson ratio is no longer universal for the cases $N > k > 1$. The deviation from the universal value of the Wilson ratio could be used as an experimental signal of the Fermi/non-Fermi mixing.

cond-mat.str-el↗
arXiv2017

Edge-of-edge States

We study an exotic state which is localized only at an intersection of edges of a topological material. This "edge-of-edge" state is shown to exist generically. We construct explicitly generic edge-of-edge states in 5-dimensional Weyl semimetals and their dimensional reductions, such as 4-dimensional topological insulators of class A and 3-dimensional chiral topological insulators of class AIII. The existence of the edge-of-edge state is due to a topological charge of the edge states. The notion of the Berry connection is generalized to include the space of all possible boundary conditions, where Chern-Simons forms are shown to be nontrivial.

cond-mat.mes-hall↗
arXiv2017

Boundary Conditions of Weyl Semimetals

We find that generic boundary conditions of Weyl semimetal is dictated by only a single real parameter, in the continuum limit. We determine how the energy dispersions (the Fermi arcs) and the wave functions of edge states depend on this parameter. Lattice models are found to be consistent with our generic observation. Furthermore, the enhanced parameter space of the boundary condition is shown to support a novel topological number.

cond-mat.mes-hall↗
arXiv2016

Quantum Monte Carlo simulation of topological phase transitions

We study the electron-electron interaction effects on topological phase transitions by the ab-initio quantum Monte Carlo simulation. We analyze two-dimensional class A topological insulators and three-dimensional Weyl semimetals with the long-range Coulomb interaction. The direct computation of the Chern number shows the electron-electron interaction modifies or extinguishes topological phase transitions.

cond-mat.mes-hall↗
arXiv2016

Towards U(N|M) knot invariant from ABJM theory

We study U(N|M) character expectation value with the supermatrix Chern-Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives U(N|M) character expectation values in terms of U(1|1) averages for a particular type of character representations. This means that the U(1|1) character expectation value is a building block for all the U(N|M) averages, and in particular, by an appropriate limit, for the U(N) invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern-Simons matrix model. We obtain the Rosso-Jones-type formula and the spectral curve for this case.

hep-th↗
arXiv2016

Topological Number of Edge States

We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analogue of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a non-commutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.

cond-mat.mes-hall↗
arXiv2015

2d Partition Function in Omega-background and Vortex/Instanton Correspondence

We derive the exact vortex partition function in 2d $\mathcal{N}$ = (2,2) gauge theory on the Omega-background, applying the localization scheme in the Higgs phase. We show that the partition function at a finite Omega-deformation parameter $ε$ satisfies a system of differential equations, which can be interpreted as a quantized version of the twisted F-term equations characterizing the SUSY vacua. Using the differential equations derived in this paper, we show the correspondence between the partition function of the two-dimensional vortex string worldsheet theory and the Nekrasov partition function at the root of Higgs branch of the four-dimensional $\mathcal{N}$ = 2 theory with two Omega-deformation parameters $(ε_1,ε_2)$.

hep-th↗
arXiv2015

Domain-wall, overlap, and topological insulators

Topological insulators are a new class of materials which have gapped spectra in the bulk, but are accompanied by topologically protected gapless excitations at the surface (edge) of the system. These phenomena have a close relationship with symmetry and dimensionality of the system through quantum anomalies. We point out that such a surface state is a physical realization of the domain-wall/overlap fermion. From this point of view, we discuss its implications for experiments of topological insulators. We also discuss an unconventional overlap fermion, which is suggested by the "periodic table" of topological insulators and superconductors.

cond-mat.mes-hall↗
arXiv2015

Band spectrum is D-brane

We show that band spectrum of topological insulators can be identified as the shape of D-branes in string theory. The identification is based on a relation between the Berry connection associated with the band structure and the ADHM/Nahm construction of solitons whose geometric realization is available with D-branes. We also show that chiral and helical edge states are identified as D-branes representing a noncommutative monopole.

hep-th↗
arXiv2015

Linking loops in ABJM and refined theory

We consider the link average of the half-BPS Wilson loop operators in N = 6 superconformal Chern-Simons-matter theory, which is called ABJM theory. We show that this loop average is reduced to a (super)matrix integral by the localization method, in a similar way to the bosonic U(N) Chern-Simons theory. Using this matrix integral, we compute the two- and three-link averages with an operator formalism inspired by a three-dimensional topological field theory. We obtain a factorization of the link average, and the Verlinde formula in a sector of supergroup representations. We also propose a refined version of ABJM theory, and compute some refined link averages.

hep-th↗