arXiv subjects

Se-Jin Kim

Publications and source records attributed to Se-Jin Kim.

At least 19 recordsLinked to original sources

arXiv2026

On the embeddings of selfadjoint operator spaces

We investigate when a map on a selfadjoint operator space $E$ is an embedding, i.e., when its unitisation in the sense of Werner is completely isometric. Combining with results of Russell, of Ng, and of Dessi, the second and the last author, it is shown that this is equivalent to: (a) extending bounded positive functionals on each matrix level with the same norm; (b) extending quasistates to quasistates in each matrix level; (c) extending completely bounded completely positive maps with the same cb-norm; and (d) the map being a gauge maximal isometry in the sense of Russell. If $E$ is approximately positively generated and $\mathrm{C}^*(E)$ is unital, or if $E_{sa}$ is singly generated, then completely positive maps on $E \subseteq \mathcal{B}(H)$ have completely positive extensions on $\mathrm{C}^*(E)$, but possibly not with the same cb-norm; and this is not enough for the inclusion $E \subseteq \mathrm{C}^*(E)$ to be an embedding. We show that the inclusion $E \subseteq \mathrm{C}^*(E)$ is always an embedding when $E$ is completely approximately 1-generated, and we fully resolve the case when $E_{sa}$ is singly generated. Combining with the works of Salomon, Humeniuk--Kennedy--Manor, and previous work of the third author, we show that if the inclusion $E \subseteq \mathrm{C}^*(E)$ is an embedding, then rigidity at zero, in the sense of Salomon, coincides with $E$ being approximately positively generated. Consequently, we show that $E$ is approximately positively generated if and only if $M_n(E)$ is approximately positively generated for all $n\in \mathbb{N}$, thus extending a previous result of Humeniuk--Kennedy--Manor to the approximation setting. As an application we show that hyperrigidity of $E$ in $\mathrm{C}^*(E)$ allows to identify $\mathrm{C}^*(E)$ as the C*-envelope of $E$ in several (non-unital) contexts.

math.OA↗

arXiv2024

Factoriality of groupoid von Neumann algebras

We give a characterisation of factoriality of the groupoid von Neumann algebra $L(\mathcal{G})$ associated to a discrete measured groupoid $(\mathcal{G},μ)$. We introduce the notion of groupoids with `infinite conjugacy classes' and show that this property together with ergodicity of the groupoid is equivalent to factoriality of $L(\mathcal{G})$.

math.OA↗

arXiv2024

The ideal intersection property for essential groupoid C*-algebras

We characterise, in several complementary ways, étale groupoids with locally compact Hausdorff space of units whose essential groupoid C*-algebra has the ideal intersection property, assuming that the groupoid is topologically transitive and either Hausdorff or $σ$-compact. This leads directly to a characterisation of the simplicity of this C*-algebra which, for Hausdorff groupoids, agrees with the reduced groupoid C*-algebra. Specifically, we prove for topologically transitive groupoids that the ideal intersection property is equivalent to the absence of essentially confined amenable sections of isotropy groups. For topologically transitive groupoids with compact space of units we moreover show that this is equivalent to the uniqueness of equivariant pseudo-expectations. A key technical idea underlying our results is a new notion of groupoid action on C*-algebras including the essential groupoid C*-algebra itself. For minimal groupoids, we further obtain a relative version of Powers averaging property. Examples arise from suitable group representations into simple groupoid \Cstar-algebras. This is illustrated by the example of the quasi-regular representation of Thompson's group $\mathrm{T}$ with respect to Thompson's group $\mathrm{F}$, which satisfies the relative Powers averaging property in the Cuntz algebra $\mathcal{O}_2$.

math.OA↗

arXiv2024

On the Completely Positive Approximation Property for Non-Unital Operator Systems and the Boundary Condition for the Zero Map

The purpose of this paper is two-fold: firstly, we give a characterization on the level of non-unital operator systems for when the zero map is a boundary representation. As a consequence, we show that a non-unital operator system arising from the direct limit of C*-algebras under positive maps is a C*-algebra if and only if its unitization is a C*-algebra. Secondly, we show that the completely positive approximation property and the completely contractive approximation property of a non-unital operator system is equivalent to its bidual being an injective von Neumann algebra. This implies in particular that all non-unital operator systems with the completely contractive approximation property must necessarily admit an abundance of positive elements.

math.OA↗

arXiv2024

The Choquet-Deny Property for Groupoids

A countable discrete group is called Choquet-Deny if for any non-degenerate probability measure on the group, the corresponding space of bounded harmonic functions is trivial. Building on the previous work of Jaworski, a complete characterization of Choquet-Deny groups was recently achieved by Frisch, Hartman, Tamuz, and Ferdowski. In this article, we extend the study of the Choquet-Deny property to the framework of discrete measured groupoids. Our primary result offers a complete characterization of this property in terms of the isotropy groups and the equivalence relation associated with the given groupoid. Additionally, we use the implications derived from our main theorem to classify the Choquet-Deny property of transformation groupoids.

math.FA↗

arXiv2022

Holographic two-point functions in medium

We study two-point correlation function in a medium composed of two kinds of matter, which is the dual of a three-dimensional generalized $p$-brane gas geometry. Following the holographic prescription, we calculate temporal and spatial two-point functions in the medium. In general, the screening effect of the medium makes two-point functions decrease more rapidly than the CFT's two-point function. In the extremal limit, however, we find that a temporal two-point function is still conformal. This indicates that a two-dimensional UV CFT flows into a one-dimensional quantum mechanics in the IR limit. This is consistent with the fact that the near horizon geometry in the extremal limit reduces to AdS$_2$. We also investigate holographic mutual information representing the correlation between two subsystems. We show that a critical distance in the IR region, where the mutual information vanishes, leads to a similar behavior to the correlation length of a two-point function.

hep-th↗

arXiv2022

Dual Geometry of Entanglement Entropy via Deep Learning

For a given entanglement entropy of QFT, we investigate how to reconstruct its dual geometry by applying the Ryu-Takayanagi formula and the deep learning method. In the holographic setup, the radial direction of the dual geometry is identified with the energy scale of the dual QFT. Therefore, the holographic dual geometry can describe how the QFT changes along the RG flow. Intriguingly, we show that the reconstructed geometry only from the entanglement entropy data can give us more information about other physical properties like thermodynamic quantities in the IR region.

hep-th↗

arXiv2021

Nonunital operator systems and noncommutative convexity

We establish the dual equivalence of the category of (potentially nonunital) operator systems and the category of pointed compact nc (noncommutative) convex sets, extending a result of Davidson and the first author. We then apply this dual equivalence to establish a number of results about operator systems, some of which are new even in the unital setting. For example, we show that the maximal and minimal C*-covers of an operator system can be realized in terms of the C*-algebra of continuous nc functions on its nc quasistate space, clarifying recent results of Connes and van Suijlekom. We also characterize "C*-simple" operator systems, i.e. operator systems with simple minimal C*-cover, in terms of their nc quasistate spaces. We develop a theory of quotients of operator systems that extends the theory of quotients of unital operator algebras. In addition, we extend results of the first author and Shamovich relating to nc Choquet simplices. We show that an operator system is a C*-algebra if and only if its nc quasistate space is an nc Bauer simplex with zero as an extreme point, and we show that a second countable locally compact group has Kazhdan's property (T) if and only if for every action of the group on a C*-algebra, the set of invariant quasistates is the quasistate space of a C*-algebra.

math.OA↗

arXiv2020

The Hamilton-Jacobi Equation and Holographic Renormalization Group Flows on Sphere

We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holographic renormalization group flows when the field theory is put on the sphere and mass terms are turned on. Although the system is supersymmetric and it is described by a superpotential, Hamilton's characteristic function is not readily given by the superpotential when the boundary of AdS is curved. We propose a method to construct the solution as a series expansion in scalar field degrees of freedom. The coefficients are functions of the warp factor to be determined by a differential equation one obtains when the ansatz is substituted into the Hamilton-Jacobi equation. We also show how the solution can be derived from the BPS equations without having to solve differential equations. The characteristic function readily provides information on holographic counterterms which cancel divergences of the on-shell action near the boundary of AdS.

hep-th↗

arXiv2020

On the progenitor quark mass matrix

We determined the quark mass matrix in terms of a small expansion parameter $\sqrt{\varepsilon}$, which gives correctly all the quark masses and the CKM matrix elements at the electroweak (EW) scale, and obtain a progenitor form at the GUT scale by running the EW scale mass matrix. Finally, a possible texture form for the progenitor quark mass matrix is suggested.

hep-ph↗

arXiv2020

Tetrahedral Symmetry A$_{\bf 4}$ in Anti-SU(5) GUT

We construct a flavor model in an anti-SU(5) GUT with a tetrahedral symmetry $A_4$. We choose a basis where $Q_{text{em}}=-\frac13$ quarks and charged leptons are already mass eigenstates. This choice is possible from the $A_4$ symmetry. Then, matter representation $\overline{10}_{-1}^{\rm\, matter}$ contains both a quark doublet and a heavy neutrino $N$, which enables us to use the $A_4$ symmetry to both $Q_{text{em}}=+\frac23$ quark masses and neutrino masses (through the see-saw via $N$). This is made possible because the anti-SU(5) breaking is achieved by the Higgs fields transforming as anti-symmetric representations of SU(5), $\overline{10}_{-1}^H\oplus 10_{+1}^H$, reducing the rank-5 anti-SU(5) group down to the rank-4 standard model group \smg. For possible mass matrices, the $A_4$ symmetry predictions on mass matrices at field theory level are derived. Finally, an illustration from string compactification is presented.

hep-ph↗

arXiv2020

Re-visiting Supersymmetric Janus Solutions: A Perturbative Construction

We construct holographic Janus solutions, which describe a conformal interface in the theory of M2-branes, in four-dimensional gauged supergravities using a perturbative method. In particular, we study three Einstein-scalar systems and their BPS equations, which are derived by Bobev, Pilch, and Warner (2014). The actions of our interest are all consistent truncations of $D=11$ supergravity chosen to be invariant under $SO(4)\times SO(4)$, $SU(3)\times U(1)\times U(1)$, and $G_2$ symmetry subgroups of $SO(8)$ respectively. The utility of our semi-analytic result is illustrated by the calculation of minimal area surface and the associated holographic entanglement entropy.

hep-th↗

arXiv2020

Hyperrigidity of C*-correspondences

We show that hyperrigidity for a C*-correspondence $(A,X)$ is equivalent to non-degeneracy of the left action of the Katsura ideal $\mathcal{J}_X$ on $X$. Due to the work of Katsoulis and Ramsey, our result shows that if $G$ is a locally compact group acting on $(A,X)$ and the Katsura ideal $\mathcal{J}_X$ acts on $X$ non-degenerately then the Hao-Ng isomorphism problem for reduced crossed products has a positive solution and the Hao-Ng isomorphism problem for full crossed products has a partial solution.

math.OA↗

arXiv2019

Jarlskog determinant and data on flavor matrices

The essences of the weak CP violation, the quark and lepton Jarlskog invariants, are determined toward future model buildings beyond the Standard Model (SM). The equivalence of two calculations of Jarlskog invariants gives a bound on the CP phase in some parametrization. Satisfying the unitarity condition, we obtain the CKM and MNS matrices from the experimental data, and present the results in matrix forms. The Jarlskog determinant $J^q$ in the quark sector is found to be $\sim 3.11\times 10^{-5}|\sin\delks|$ while $J^\ell$ in the leptonic sector is $\sim 2.96\times 10^{-2}|\sin\delksl|$ in the normal hierarchy parametrization.

hep-ph↗

arXiv2019

Perturbative solutions of ${\cal N}=1^*$ holography on $S^4$

We apply the recently proposed perturbative technique to solve the supergravity BPS equations of ${\cal N}=1^*$ theories put on $S^4$. In particular, we have calculated the coefficients of the leading quartic terms exactly, in the expression of the universal part for the holographic free energy as a function of the mass parameters. We also report on the coefficients of higher order terms upto 10th order, which are computed numerically.

hep-th↗

arXiv2019

A perturbative study of holographic mABJM theory

Recently the calculation of holographic free energy for mass-deformed ABJM model (mABJM) with ${\cal N}=2$ supersymmetry and $SU(3)\times U(1)$ global symmetry was tackled by Bobev et al. in arXiv:1812.01026. We solve the associated BPS equations, requiring IR regularity, using a perturbative method proposed by one of us recently in axXiv:1902.00418. In particular, we provide an analytic proof of a crucial conjecture made in arXiv:1812.01026 based on numerical solutions: that the R-charge values of three chiral multiplets in mABJM should be independent of the IR values of a hypermultiplet scalar, which is holographically dual to the superpotential mass term.

hep-th↗

arXiv2019

"Invisible" axion rolling through the QCD phase transition

The origin of `invisible' axion in four dimensional effective beyond-standard models from string compactification is discussed and its refined passover through the QCD phase transition is presented toward a reliable estimate of the current axion energy density in terms of the initial misalignment angle $\barθ_1$. The explicit examples are presented in a flipped SU(5) GUT model. This allows to introduce a flavor symmetry through string compactification, and hence we also comment on the source of flavor symmetries from string compactification and attempts to fit the resulting Yukawa couplings to the observed Cabibbo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakata matrices.

hep-ph↗

arXiv2018

Flavor mixing inspired by flipped SU(5) GUT

We obtain a phenomenologically acceptable Cabibbo-Kobayashi-Maskawa matrix in a flipped SU(5) model inspired by the compactification of heterotic string $E_8\times E_8'$.

hep-ph↗