We construct a family of solutions of the holographic insulator/superconductor phase transitions with the excited states in the AdS soliton background by using both the numerical and analytical methods. The interesting point is that the improved Sturm-Liouville method can not only analytically investigate the properties of the phase transition with the excited states, but also the distributions of the condensed fields in the vicinity of the critical point. We observe that, regardless of the type of the holographic model, the excited state has a higher critical chemical potential than the corresponding ground state, and the difference of the dimensionless critical chemical potential between the consecutive states is around 2.4, which is different from the finding of the metal/superconductor phase transition in the AdS black hole background. Furthermore, near the critical point, we find that the phase transition of the systems is of the second order and a linear relationship exists between the charge density and chemical potential for all the excited states in both s-wave and p-wave insulator/superconductor models.

Holographic insulator/superconductor phase transitions with excited states

We study non-Abelian vortex strings in four-dimensional (4D) $\mathcal{N}=2$ supersymmetric QCD with the $\mathrm{U}(N=2)$ gauge group and ${N}_{f}=4$ flavors of quark hypermultiplets. It has recently been shown that these vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory was found and interpreted as a spectrum of hadrons in 4D $\mathcal{N}=2$ supersymmetric QCD. In particular, the lowest string state appears to be a massless Bogomol'nyi-Prasad-Sommerfield (BPS) ``baryon.'' Here we show the occurrence of this stringy baryon using a purely field-theoretic method. To this end we study the conformal world-sheet theory on the non-Abelian string---the so-called weighted $\mathcal{N}=(2,2)$ supersymmetric $\mathbb{C}\mathbb{P}$ model. Its target space is given by the six-dimensional noncompact Calabi-Yau space ${Y}_{6}$, the conifold. We use a mirror description of the model to study the BPS kink spectrum and its transformations on curves (walls) of marginal stability. Then we use the 2D-4D correspondence to show that the deformation of the complex structure of the conifold is associated with the emergence of a nonperturbative Higgs branch in 4D theory which opens up at strong coupling. The modulus parameter on this Higgs branch is the vacuum expectation value of the massless BPS baryon previously found in string theory.

https://link.aps.org/pdf/10.1103/PhysRevD.102.054026

String baryon in four-dimensional N =2 supersymmetric QCD from the 2D-4D correspondence

We study two-dimensional weighted $$ \mathcal{N} $$
 = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N, $$ \tilde{N} $$
 ) 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, 𝕎ℂℙ(N, $$ \tilde{N} $$
 ) has N charges +1 and $$ \tilde{N} $$
 charges −1 fields. As well-known, at $$ \tilde{N} $$
 = 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 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.

/pdf/long-way-to-ricci-flatness-k4xzd9g9tk.pdf

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.

/pdf/long-way-to-ricci-flatness-587b5ewhup.pdf

Long Way to Ricci Flatness

In this paper two issues are addressed. First, we discuss renormalization properties of a class of gauged linear sigma models (GLSM), which reduce to $\mathbb{W}\mathbb{C}\mathbb{P}(\mathbit{N},\stackrel{\texttildelow{}}{\mathbit{N}})$ nonlinear sigma models (NLSM) in the low-energy limit. Sometimes they are referred to as the Hanany-Tong models. If supersymmetry is $\mathcal{N}=(2,2)$ the ultraviolet-divergent logarithm in GLSM 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 $N=\stackrel{\texttildelow{}}{N}$ there is no UV logarithm in the parent GLSM, while they do appear in the corresponding NLSM. In the second part of the paper we discuss the same problem for a class of $\mathcal{N}=(0,2)$ GLSMs considered previously. In this case renormalization is not limited to one loop; all orders exact $\ensuremath{\beta}$ functions for GLSMs are known. We discuss logarithmically divergent loops at one- and two-loop levels.

https://link.aps.org/pdf/10.1103/PhysRevD.101.025007

From gauged linear sigma models to geometric representation of W C P ( N , N ˜ ) in 2D

The dispersion law of plasmons running along thin wires with radius a is known to be practically linear. We show that in wires with a dielectric constant [Formula: see text] much larger than that of its environment [Formula: see text], such dispersion law crosses over to a dispersionless three-dimensional-like law when the plasmon wavelength becomes shorter than the length [Formula: see text] 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.

/pdf/plasmons-in-semiconductor-and-topological-insulator-wires-1ctole5j.pdf

Plasmons in semiconductor and topological insulator wires with large dielectric constant

We study the pattern of chiral symmetry breaking ($\chi$SB) in the $\psi\chi\eta$ model (with the chiral fermion sector containing $ \psi^{\{ij\}}$, $\chi_{[ij]}$, and $\eta_{i}^{A}$, 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 $L(S^1)\ll \Lambda^{-1}$, i.e. at weak coupling, no phase transitions are expected in passing to large $L(S^1)\gg \Lambda^{-1}$ (here $\Lambda$ 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 $\langle \psi^{\{ij\}}\chi_{[jk]}\rangle \neq 0$ at weak coupling i.e. at $L(S^1)\ll \Lambda^{-1}$. Then adiabatic continuity tells us that $\langle \psi^{\{ij\}}\chi_{[jk]}\rangle \neq 0$ exists on $\mathbb{R}^4$, in full accord with the prediction [2]. Simultaneously with $\langle \psi^{\{ij\}}\chi_{[jk]}\rangle \sim \Lambda^3\delta^i_k$ the SU($N_c$) gauge symmetry is spontaneously broken at strong coupling down to its maximal Abelian subgroup.

Chao Hsiang Sheu

Papers

Long way to Ricci flatness

Long Way to Ricci Flatness

From gauged linear sigma models to geometric representation of W C P ( N , N ˜ ) in 2D

Plasmons in semiconductor and topological insulator wires with large dielectric constant

Consistency of chiral symmetry breaking in chiral Yang-Mills theory with adiabatic continuity