We employ gauge/gravity duality to study the effects of Lifshitz scaling on the holographic p-wave superconductors in the presence of Born–Infeld nonlinear electrodynamics. By using the shooting method in the probe limit, we calculate the relation between critical temperature \(T_\mathrm{{c}}\) and \(\rho ^{z/d}\) numerically for different values of mass, nonlinear parameter b and Lifshitz critical exponent z in various dimensions. We observe that critical temperature decreases by increasing b, z or the mass parameter m which makes conductor/superconductor phase transition harder to form. In addition, we analyze the electrical conductivity and find the behavior of the real and the imaginary parts as a function of frequency, which depend on the model parameters. However, some universal behaviors are seen. For instance at low frequencies, the real part of conductivity shows a delta function behavior, while the imaginary part has a pole, which means that these two parts are connected to each other through the Kramers–Kronig relation. The behavior of the real part of the conductivity in the large frequency regime can be achieved by \(\mathrm{{Re}}[\sigma ]=\omega ^{D-4}\). Furthermore, with increasing the Lifshitz scaling z, the energy gap and the minimum values of the real and imaginary parts become unclear.

在存在Born-Infeld非线性电动力学的情况下，我们采用规范/重力对偶性来研究Lifshitz缩放对全息p波超导体的影响。通过使用探测极限中的射击方法，我们针对不同的质量值（非线性）计算临界温度\（T_ \ mathrm {{c}} \）和\（\ rho ^ {z / d} \）之间的关系参数b和Lifshitz临界指数z在各个维度上。我们观察到临界温度通过增加b，z或质量参数m降低这使得导体/超导体相变难以形成。此外，我们分析电导率并找到实部和虚部的行为与频率的关系，这取决于模型参数。但是，可以看到一些通用行为。例如，在低频时，电导率的实部表现出δ函数行为，而虚部具有极点，这意味着这两个部分通过Kramers-Kronig关系相互连接。可以通过\（\ mathrm {{Re}} [\ sigma] = \ omega ^ {D-4} \）来实现大频率范围内电导率实部的行为。此外，随着Lifshitz缩放z，能隙和实部和虚部的最小值变得不清楚。