Based on the holographic duality, we construct the new <italic>p</italic>-wave metal/superconductor phase transitions triggered by the electric and magnetic fields. Especially, using the axion field, we introduce simultaneously the spontaneous (SBT) and explicit (EBT) breaking of translation and then investigate how the SBT and EBT corrections influence on the critical temperature, vector condensate and the optical conductivity. Concretely, for the case with pure electric field, both the EBT correction with weak SBT correction and the SBT correction lower the critical temperature <math altimg='si1.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math> and soften the energy gap. Interestingly, for the strong enough SBT correction, the increasing EBT correction enhances firstly and then inhibits the phase transition. Meanwhile, the increasing EBT correction suppresses the SBT effect on <math altimg='si1.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>. At the lowest Landau energy level, the stronger SBT correction suppresses the phase transition for the weak magnetic field, whose inhibiting effect is finally eliminated by the strong enough magnetic field. The monotonic dependence of <math altimg='si1.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math> on the EBT correction only exists for the weak SBT correction. For the Landau energy level in the excited state, the monotonic dependence of <math altimg='si1.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math> on the EBT correction vanishes for the intermediate SBT correction with large magnetic field.

China

Bao-Ping Dong

Jun-Wang Lu

Ya-Bo Wu

Cheng-Yuan Zhang

Juan-Juan Luo

Jian-Xin Cheng

Hao Liao

Axion effects on new <italic>p</italic>-wave superconductors induced by electromagnetic fields

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

We investigate the Klein-Gordon (KG) oscillators in a global monopole (GM) spacetime in Eddington-inspired Born-Infeld (EiBI) gravity and a Wu-Yang magnetic monopole (WYMM). We discuss the gravitational effects in the presence of Ricci scalar curvature <math altimg='si1.svg'><mi>R</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>&#965;</mi></mrow><mrow><mi>&#965;</mi></mrow></msubsup></math>. It is observed that the presence of the Ricci scalar curvature, effectively and manifestly, introduces a force field that makes the corresponding quantum mechanical repulsive core more repulsive. Similar effect is also observed for the EiBI-gravitational field. We reiterate and report that the corresponding bosonic KG-oscillator quantum mechanical system admits a solution in the form of confluent Heun functions, the truncation of which into a physically admissible polynomial is shown to be associated with some parametric correlations/conditions. The use of such conditions/correlations is mandatory and yields a set of allowed/restricted quantum mechanical orbital <italic>&#8467;</italic>-excitations, for all radial quantum numbers <math altimg='si2.svg'><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>&#8805;</mo><mn>0</mn></math>. Our procedure is shown to be quite handy, in the sense that it allows one to retrieve results for KG-oscillators in GM-spacetime in different EiBI-gravity and Ricci scalar curvature settings.

Türkiye

Omar Mustafa

KG-oscillators in Eddington-inspired Born-Infeld gravity: Wu-Yang magnetic monopole and Ricci scalar curvature effects

In this paper, in the Starobinsky gravity (SG) model, the gravitational wave (GW) luminosity distance $$d_L^{GW}(z)$$ is analytically and numerically investigated by considering the dark matter as the two different kinds of shear viscous fluids in universe. Concretely, on the basis of the propagation equation of the metric perturbation derived by using transverse-traceless gauge for the linear perturbation of the metric in FRW background, we obtain the analytical expressions of the modified friction term $$\delta (z)$$ and the ratio $$d_L^{GW}(z)/d_L^{EM}(z)$$ of GW to electromagnetic (EM) wave luminosity distance, and find that they only depend on the SG model parameter $$\alpha $$ and the shear viscous coefficient $$\eta $$ , regardless of the bulk viscous coefficient $$\zeta $$ . Evidently, both of them are affected by $$\alpha $$ and $$\eta $$ . It worth stressing that the results given by us can reduce to ones in documents [13, 22, 30]. It follows that we can extend the previous results as the special cases in our model. Furthermore, by combining the latest observational data, we more tightly constrain the values of related parameters and numerically analyze the influence of both $$\alpha $$ and $$\eta $$ on $$\delta (z)$$ and $$d_L^{GW}(z)/d_L^{EM}(z)$$ . We observe that, in the range of $$0< z\le 8.2$$ , the evolutionary curves of $$\delta (z)$$ and $$d_L^{GW}(z)/d_L^{EM}(z)$$ exhibit that $$\delta (z)$$ ( $$d_L^{GW}(z)/d_L^{EM}(z)$$ ) monotonically decrease (increase) as redshift rises, moreover there are always $$\delta (z)<0$$ and $$d_L^{GW}(z)\ge d_L^{EM}(z)$$ , specially $$d_L^{GW}(0)=d_L^{EM}(0)$$ in the limit of $$z\rightarrow 0$$ , which means that detecting GW signals might represent a more efficient tool than detecting EM signals to test modified gravity model on the given scale of cosmic distances. It is worth noting that the numerical analyses to $$\delta (z)$$ and $$d_L^{GW}(z)/d_L^{EM}(z)$$ illustrate once again that the GW luminosity distance $$d_L^{GW}(z)$$ is indeed influenced by $$\alpha $$ and $$\eta $$ , in particular more sensitive to $$\alpha $$ than $$\eta $$ in our model. In addition, by comparing the GW and EM luminosity distances of SG model with $$d_{L(GR)}$$ of Einstein GR, we find that the GW and EM signals in SG1 and SG2 change from stronger to weaker than the ones in GR as redshift increases and more difficultly to be detected in the same distance and detection sensitivity. Meanwhile, the EM signals change from strong to weak earlier than GW signals do. Finally, we confirm that $$\delta (z)$$ and $$d_L^{GW}(z)$$ of our model meet the constraints imposed by the standard siren GW170817 and its electromagnetic companion GRB170817A.

Jia-nan Chi

Yu Sang

Xue Zhang

Yi-liang Hu

Wen-zhong Liu

Bo-hai Chen

Gravitational wave luminosity distance for Starobinsky gravity in viscous cosmological models

At the probe limit, the effects of three typical nonlinear corrections of Born-Infeld electrodynamics (BINE), logarithmic Lagrangian (LNE) and exponential Lagrangian (ENE) on the holographic ferromagnetic model under the four-dimensional Gauss-Bonnet gravity background are studied by numerical calculation. For comparison, the Gauss-Bonnet parameter <italic>&#945;</italic> is fixed in the article. In the absence of an external magnetic field, three different nonlinear electrodynamic corrections reduce the critical temperature respectively and make the spontaneous magnetic moment more difficult to form. In the case of opening the external magnetic field, the magnetic susceptibility density always satisfies the Curie-Weiss law, and the increase of the nonlinear parameters under the three corrections will prolong the period of the external magnetic field. Comparing the three corrections horizontally, the exponential form of nonlinear electrodynamics correction has a more significant effect on the parameters.

Ruo-Tong Wei

Te Huang

Jun-Ping Wang

Holographic ferromagnetic phase transitions with three typical nonlinear electrodynamics in Gauss-Bonnet gravity

At the probe level, we investigate the holographic p-wave conductor/superconductor phase transition by both numerical and analytical methods. Especially, due to the nonlinear axion correction, the translational symmetry in superconductor is broken spontaneously. We then study the effects of the axion correction (or disorder) and the mass of vector field on the superconductor phase transition. Concretely, as the disorder parameter and the scaling dimension of vector operator increase, the critical temperature decreases and the stable value of condensate at the low temperature as well as the energy gap increase, which suggests that the larger mass of vector field and the disorder correction inhibit the phase transition, and increase the strength of interaction in superconductor. Near the critical point, the system always undergoes a second-order phase transition, which is independent of the disorder strength and the mass of vector field. According to the behaviors of grand potential and conductivity, the hairy state is verified to be thermodynamical favored and indeed superconducting state. Meanwhile, the analytical results uphold the numerical ones in terms of the critical behavior of condensate.

Yu Tang

Hui Zhu

Holographic -wave Superconductor With Spontaneously Broken Translation

We consider Klein–Gordon (KG) particles in a global monopole (GM) spacetime within Eddington-inspired Born–Infeld gravity (EiBI-gravity) and in a Wu–Yang magnetic monopole (WYMM). We discuss a set of KG-oscillators in such spacetime settings. We propose a textbook power series expansion for the KG radial wave function that allows us to retrieve the exact energy levels for KG-oscillators in a GM spacetime and a WYMM without EiBI-gravity. We, moreover, report some conditionally exact, closed form, energy levels (through some parametric correlations) for KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity, and for massless KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity under the influence of a Coulomb plus linear Lorentz scalar potential. We report the effects of the Eddington parameter  $$\kappa $$  <math> <mi>κ</mi> </math>  , GM-parameter  $$\alpha $$  <math> <mi>α</mi> </math>  , WYMM strength  $$\sigma $$  <math> <mi>σ</mi> </math>  , KG-oscillators’ frequency  $$\Omega $$  <math> <mi>Ω</mi> </math>  , and the coupling parameters of the Coulomb plus linear Lorentz scalar potential, on the spectroscopic structure of the KG-oscillators at hand. Such effects are studied over a vast range of the radial quantum number  $$n_r\ge 0$$  <math> <mrow> <msub> <mi>n</mi> <mi>r</mi> </msub> <mo>≥</mo> <mn>0</mn> </mrow> </math>   and include energy levels clustering at  $$\kappa&gt;&gt;1$$  <math> <mrow> <mi>κ</mi> <mo>&gt;</mo> <mo>&gt;</mo> <mn>1</mn> </mrow> </math>   (i.e., extreme EiBI-gravity), and at  $$|\sigma |&gt;&gt;1$$  <math> <mrow> <mo>|</mo> <mi>σ</mi> <mo>|</mo> <mo>&gt;</mo> <mo>&gt;</mo> <mn>1</mn> </mrow> </math>   (i.e., extreme WYMM strength).

Brazil

A. Soares

C. Pereira

R. Vitória

On the Klein–Gordon oscillators in Eddington-inspired Born-Infeld gravity global monopole spacetime and a Wu–Yang magnetic monopole

The leading-order chiral Lagrangian for the baryon octet and decuplet states coupled to Goldstone bosons and external sources contains six low-energy constants. Five of them are fairly well-known from phenomenology, but the sixth one is practically unknown. This coupling constant provides the strength of the (p-wave) coupling of Goldstone bosons to decuplet states. Its size and even sign are under debate. Quark models and quantum chromodynamics (QCD) for a large number of colors provide predictions, but some recent phenomenological analyses even suggest an opposite sign for the Delta-pion coupling. The Goldberger-Treiman relation connects this coupling constant to the axial charge of the Delta baryon. This suggests a Wu-type experiment to determine the unknown low-energy constant. While this is not feasible in the Delta sector because of the large hadronic width of the Delta, there is a flavor symmetry related process that is accessible; the weak semileptonic decay of the Omega baryon to a spin <math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> cascade baryon. A broad research program is suggested that can pin down at least the rough size and the sign of the last unknown low-energy constant of the leading-order Lagrangian. It encompasses experimental measurements, in particular the forward-backward asymmetry of the semileptonic decay, together with a determination of the quark-mass dependences using lattice QCD for the narrow decuplet states and chiral perturbation theory to extrapolate to the Delta sector. Besides discussing the strategy of the research program, the present work provides a feasibility check based on a simple leading-order calculation.

Sweden

Magnus Bertilsson

Stefan Leupold

Goldberger-Treiman relation and Wu-type experiment in the decuplet sector

In this work, we construct a holographic antiferromagnetism model by introducing two real antisymmetric tensor fields coupling to the background gauge field strength and interacting with each other in the four-dimensional Lifshitz black hole, and investigate the effects of Lifshitz dynamical exponent z on the paramagnetism-antiferromagnetism phase transition in detail. Using the numerical shooting method, we find that there is still a phase transition in asymptotically Lifshitz space-time in the probe limit. In the absence of an external magnetic field and in low temperature, the magnetic moments condense spontaneously in antiparallel manner with the same magnitude. But the critical temperature and the staggered magnetization decrease with increasing z, which makes paramagnetism-antiferromagnetism phase transition harder to happen. In the presence of the weak external magnetic field, the magnetic susceptibility has a peak at the critical temperature and increasing values of z makes the peak higher. In the case of the strong external magnetic field, there exists a critical magnetic field <math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math> in the antiferromagnetic phase. When the magnetic field reaches <math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math>, the system turns into the paramagnetic phase. Besides, the increasing of z results in increasing of <math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math>.

Ting Zhang

Guang-Zhi Xu

Lifshitz scaling effects on the holographic model for paramagnetism-antiferromagnetism phase transition

With the numerical method, we research the properties of the holographic paramagnetism/ferromagnetism phase transition for the Power - Maxwell field in the background of a Schwarzschild-AdS black hole. When there is no external magnetic field, we work out the values of the critical temperature and the magnetic moment with the different power parameter q for the Power - Maxwell field. It can be seen that the larger power parameter q reduces the critical temperature and makes it harder for the magnetic moment to be formed. What is more, in the presence of an external magnetic field, we get the values of the magnetic susceptibility density with the different q, which satisfies the Cure-Weiss law. When the external magnetic field changes, the hysteresis loop appears for different q.

The influence of Power-Maxwell field on holographic paramagnetism model