arXiv subjects

Chao-Hsiang Sheu

Publications and source records attributed to Chao-Hsiang Sheu.

10 recordsLinked to original sources

arXiv2026

Revisiting fermion bound states in baby Skyrme background with Dzyaloshinskii Moriya interaction

In this paper, we investigate a fermion coupled to a Skyrme model in $2+1$ dimensions, where the Skyrmion is stabilized by the Dzyaloshinskii-Moriya and Skyrme interactions under a quadratic potential. This framework interpolates between the magnetic Skyrmion at the critical coupling and the baby-Skyrme limit. The Dirac equation is studied both analytically in a non-relativistic reduction and numerically for the full relativistic spectrum, and the parameter region admitting states bound to the Skyrmion is determined. Localized solutions exist only for electrically charged fermions with positive charge and negative angular momentum, and are absent for neutral fermions. The lowest bound state in each angular momentum sector is characterized as a function of the fermion mass, charge, and the coupling $h$ to the Skyrmion isospin, and its behavior is compared across the magnetic, baby, and mixed Skyrmion backgrounds. The resulting fermion--Skyrmion composite constitutes an electrically charged state bound to a topological texture, providing concrete signatures for potential future transport and scattering measurements in chiral magnets.

hep-th↗

arXiv2026

More on Classical Stability of Hopf-like Solitons of the Toroidal-Twisted type

The Faddeev-Hopf model [1] supporting Hopfions was shown to emerge in the low-energy limit of four-dimensional scalar quantum electrodynamics (QED) with two charged scalar fields [2, 3]. Faddeev and Noemi conjectured that the Hopfions and Hopf-like solitons -- vortons -- can be based on a twisted toroidal structure inherent to QED [4-6]. This conjecture was discussed in detail in [2] in the approximation of negligibly small extrinsic curvature. Qualitative and semi-quantitative arguments were used to demonstrate the validity of the Faddeev-Noemi hypothesis. Here we further enhance the proof by applying a numerical analysis which confirms that large-size Hopf-like solitons exist as local energy minima in the full QED theory (in the Faddeev-Skyrme model they become topological solitons representing the global minima in the given topological sector).

hep-th↗

arXiv2024

Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions

We investigate the trans-series structure of a quantum mechanical system originating from a Lie-algebraic Kähler sigma model with multiple right-handed chiral fermions, extending previous results for the standard onecomplex projective ($\mathbb{CP}^1$) model [1],[2] to its deformed counterpart. We identify and analyze saddle point solutions and examine their contributions within the perturbative expansions of the ground state energy, revealing that the ambiguity structure observed in the $\mathbb{CP}^1$ model persists in the deformed model as well. Additionally, we explore the role of the elongation parameter and its potential impact on higher-loop corrections, and propose that it becomes relevant in shaping the system's quantum behavior from the three-loop level. This verifies that the trans-series framework provides a comprehensive approach to capturing the structure of quantum fluctuations and ambiguities in these deformed sigma models.

hep-th↗

arXiv2024

Lie-algebraic Kähler sigma models with the U(1) isotropy

We discuss various questions which emerge in connection with the Lie-algebraic deformation of $\mathbb{CP}^1$ sigma model in two dimensions. First we supersymmetrize the original model endowing it with the minimal ${\cal N}=(0,2)$ and extended ${\cal N}=(2,2)$ supersymmetries. Then we derive the general hypercurrent anomaly in the both cases. In the latter case this anomaly is one-loop but is somewhat different from the standard expressions one can find in the literature because the target manifold is non-symmetric. We also show how to introduce the twisted masses and the $θ$ term, and study the BPS equation for instantons, in particular the value of the topological charge. Then we demonstrate that the second loop in the $β$ function of the non-supersymmetric Lie-algebraic sigma model is due to an infrared effect. To this end we use a supersymmetric regularization. We also conjecture that the above statement is valid for higher loops too, similar to the parallel phenomenon in four-dimensional ${\cal N}=1$ super-Yang-Mills. In the second part of the paper we develop a special dimensional reduction -- namely, starting from the two-dimensional Lie-algebraic model we arrive at a quasi-exactly solvable quantum-mechanical problem of the Lamé type.

hep-th↗

arXiv2023

Remarks on Baby Skyrmion Lie-Algebraic Generalization

We discuss generalized baby Skyrmions emerging in a (1+2)-dimensional $σ$ model with a certain Lie-algebraic structure. The same result applies to the Polyakov-Belavin instantons in $D=1+1$. The O(3) symmetry of the target space is lost, but O(2) is preserved in the simplest model under consideration. Both the topological charge and the soliton mass (the instanton action) are determined. Of special interest are limiting cases of the deformation parameter $k$ (also referred to as the elongation parameter). If $|k-1|\ll 1$, we arrive at a model which is studied in condensed matter. If $k\gg1$, we obtain the so-called cigar, or sausage model, well-known in little string theory. If $k=1$, we return to CP(1). The deformed model under consideration interpolates between CP(1) and the cigar model. In $D=2$ we calculate the coupling constants renormalization at one loop. At $k\geq 1$ this class of models is asymptotically free in the ultraviolet limit and enters the strong coupling domain in the infrared. Also, in the infrared $k\to 1$ (i.e., we recover CP(1)).

hep-th↗

arXiv2023

Consistency of $χ$SB in chiral Yang-Mills theory with adiabatic continuity

We study the pattern of chiral symmetry breaking ($χ$SB) in the $ψχη$ model (with the chiral fermion sector containing $ ψ^{\{ij\}}$, $χ_{[ij]}$, and $η_{i}^{A}$, see [1]) on $\mathbb{R}^3 \times S^{1}_{L}$ and derive implications to $\mathbb{R}^4$ physics. Center-symmetric vacua are stabilized by a double-trace deformation. With the center symmetry maintained at small $L(S^1)\ll Λ^{-1}$, i.e. at weak coupling, no phase transitions are expected in passing to large $L(S^1)\gg Λ^{-1}$ (here $Λ$ is the dynamical Yang-Mills scale). Starting with the small $L$-limit, we find the leading-order nonperturbative corrections in the given theory. The instanton-monopole operators induce the adjoint chiral condensate $\langle ψ^{\{ij\}}χ_{[jk]}\rangle \neq 0$ at weak coupling i.e. at $L(S^1)\ll Λ^{-1}$. Then adiabatic continuity tells us that $\langle ψ^{\{ij\}}χ_{[jk]}\rangle \neq 0$ exists on $\mathbb{R}^4$, in full accord with the prediction [2]. Simultaneously with $\langle ψ^{\{ij\}}χ_{[jk]}\rangle \sim Λ^3δ^i_k$ the SU($N_c$) gauge symmetry is spontaneously broken at strong coupling down to its maximal Abelian subgroup.

hep-th↗

arXiv2022

Plasmons in semiconductor and topological insulator wires with large dielectric constant

The dispersion law of plasmons running along thin wires with radius $a$ is known to be practically linear. We show that in a wire with a dielectric constant $κ$ much larger than that of its environment $κ_e$, such dispersion law crosses over to a dispersionless three-dimensional-like law when the plasmon wavelength becomes shorter than the length $(a/2) \sqrt{(κ/κ_e)\ln(κ/2κ_e)}$ at which the electric field lines of a point charge exit from the wire to the environment. This happens both in trivial semiconductor wires and wires of three-dimensional topological insulators.

cond-mat.mes-hall↗

arXiv2021

Treating Divergent Perturbation Theory: Lessons from Exactly Solvable 2D Models at Large $N$

We consider the operator product expansion (OPE) of correlation functions in the supersymmetric $O(N)$ non-linear sigma model at sub-leading order in the large $N$ limit in order to study the cancellation between ambiguities coming from infrared renormalons and those coming from various operators in the OPE. As has been discussed in the context of supersymmetric Yang-Mills theory in four dimensions, supersymmetry presents a challenge to this cancellation. In a bid to solve this problem we consider $O(N)$ as a toy model. A background field method inspired by Polyakov's treatment of the renormalization of the bosonic $O(N)$ model is used to identify explicit operators in the OPE of the two-point functions of bosonic and fermionic fields in the model. In order to identify the coefficient functions in the OPE, the exact two-point functions at sub-leading order in large $N$ are expanded in powers of the natural infrared length scale. The ambiguities arising from renormalons in the coefficient functions and vacuum expectation values of operators in the OPE are shown to cancel to all orders. The question of supersymmetric Yang-Mills theory without matter remains open.

hep-th↗

arXiv2020

Long Way to Ricci Flatness

We study two-dimensional weighted ${\mathcal N}=2$ supersymmetric $\mathbb{CP}$ models with the goal of exploring their infrared (IR) limit. $\mathbb{WCP}(N,\widetilde{N})$ are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional ${\mathcal N}=2$ QCD. In the gauged linear sigma model (GLSM) formulation, $\mathbb{WCP} (N,\widetilde{N})$ has $N$ charges +1 and $\widetilde{N}$ charges $-1$ fields. As well-known, at $\widetilde{N}=N$ this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the $N=2$ case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the $\mathbb{WCP}$ model -- the so called $zn$ model -- which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this $zn$ model has similar RG properties.

hep-th↗

arXiv2019

From Gauged Linear Sigma Models to Geometric Representation of $\mathbb{WCP}(N,\tilde{N})$ in 2D

In this paper two issues are addressed. First, we discuss renormalization properties of a class of gauged linear sigma models (GLSM) which reduce to $\mathbb{WCP}(N,\tilde{N})$ non-linear sigma models (NLSM) in the low-energy limit. Sometimes they are referred to as the Hanany-Tong models. If supersymmetry is ${\cal N} =(2,2)$ the ultraviolet-divergent logarithm in LGSM appears, in the renormalization of the Fayet-Iliopoulos parameter, and is exhausted by a single tadpole graph. This is not the case in the daughter NLSMs. As a result, the one-loop renormalizations are different in GLSMs and their daughter NLSMs We explain this difference and identify its source. In particular, we show why at $N=\tilde N$ there is no UV logarithms in the parent GLSM, while they do appear on the corresponding NLSM does not vanish. In the second part of the paper we discuss the same problem for a class of ${\cal N} =(0,2)$ GLSMs considered previously. In this case renormalization is not limited to one loop; all-orders exact $β$ functions for GLSMs are known. We discuss divergent loops at one and two-loop levels.

hep-th↗