Anomaly Induced Current in Boundary Lifshitz Field Theory
National Tsing-Hua University（国立清华大学）；Center for Theory-Computation-Data Science Research, National Tsing-Hua University（国立清华大学理论-计算-数据科学研究中心）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）；Department of Physics, College of Science, Kyung Hee University（庆熙大学理学院物理系）
Chong-Sun Chu, Himanshu Parihar
备注：
24 pages, no figures, appendix added; matches published JHEP version
We study quantum transport phenomena induced by anisotropic Lifshitz scale anomaly in a boundary Lifshitz field theory (BLFT) coupled to an external electromagnetic background. In this context, we obtain the anisotropic scale anomaly in Lifshitz field theories coupled to a background $U(1)$ gauge field and subsequently compute the anomaly induced near boundary current in a BLFT. Focusing on 5D BLFTs, we find that the temporal and spatial components of the induced current exhibit distinct power law dependencies on the distance from the boundary, reflecting the intrinsic time-space anisotropy of the theory. We further derive this anomalous current holographically from the bulk dual of BLFT and find that the temporal component is independent of the boundary conditions while the spatial component depends explicitly on them. The distance dependence is in exact agreement with the dual field theory result.
The main result of this paper is that the Weyl anomaly of a $z=2$ (1+1)-dimensional Lifshitz effective action can be derived from a (2+1)-dimensional non-relativistic Schr$\mathrm{\ddot{o}}$dinger-invariant Chern-Simons (NRSCS) action which was shown to be equivalent to a specific Weyl-invariant non-projectable Horava-Lifshitz action of gravity. On a manifold with a boundary, we will show that the (1+1)-dimensional Lifshitz Weyl anomaly can be derived from a specific term, the torsional CS (tCS) term, in the NRSCS action built from the gauge fields of the Weyl and special conformal symmetry ge…
We demonstrate the existence of a universal transition from a continuous scale invariant phase to a discrete scale invariant phase for a class of one-dimensional quantum systems with anisotropic scaling symmetry between space and time. These systems describe a Lifshitz scalar interacting with a background potential. The transition occurs at a critical coupling $λ_{c}$ corresponding to a strongly attractive potential.
We construct analytical Lifshitz massive black brane solutions in massive Einstein-Maxwell-dilaton gravity theory. We also study the thermodynamics of these black brane solutions and obtain the thermodynamical stability conditions. On the dual nonrelativistic boundary field theory with Lifshitz symmetry, we analytically compute the DC transport coefficients, including the electric conductivity, thermoelectric conductivity, and thermal conductivity. The novel property of our model is that the massive term supports the Lifshitz black brane solutions with $z\neq 1$ in such a way that the DC trans…
On a class of four-dimensional Lifshitz spacetimes with critical exponent $z=2$, including a hyperbolic and a spherical Lifshitz topological black hole, we consider a real Klein-Gordon field. Using a mode-decomposition, we split the equation of motion into a radial and into an angular component. As first step, we discuss under which conditions on the underlying parameters, we can impose to the radial equation boundary conditions of Robin type and whether bound state solutions do occur. Subsequently, we show that, whenever bound states are absent, one can associate to each admissible boundary c…
We analytically compute the thermoelectric conductivities at zero frequency (DC) in the holographic dual of a four dimensional Einstein-Maxwell-Axion-Dilaton theory that admits a class of asymptotically hyperscaling violating Lifshitz backgrounds with a dynamical exponent $z$ and hyperscaling violating parameter $θ$. We show that the heat current in the dual Lifshitz theory involves the energy flux, which is an irrelevant operator for $z>1$. The linearized fluctuations relevant for computing the thermoelectric conductivities turn on a source for this irrelevant operator, leading to several nov…
In this paper, we analyze the fermionic Casimir effects associated with a massless quantum field in the context of Lorentz symmetry violation approach based on Horava-Lifshitz methodology. In order to obtain these observables, we impose the standard MIT bag boundary condition on the fields on two large and parallel plates. Our main objectives are to investigate how the Casimir energy and pressure depend on the parameter associated with the breaking of Lorentz symmetry.
Boundary Conformal Field Theory and Entanglement Entropy in Two-Dimensional Quantum Lifshitz Critical Point
讨论了二维量子Lifshitz临界点，即Rokhsar-Kivelson型临界波函数中的von Neumann纠缠熵。我遵循B. Hsu et al. [Phys.Rev.B79，115421（2009）]，但是指出了关于副本玻色子场的紧化的微妙问题：尽管可以通过原始场的线性组合来定义一组新的玻色子场，但是新的场不是独立紧化的。为了系统地研究多分量自由玻色子的边界共形场论，我采用了一种基于紧化格的几何表述。边界共形场论的结果与J. M. Stephan等人[Phys.Rev.B80，184421（2009）]，证实了它的普遍性，正如B. Hsu等人
We investigate the Gauss-Bonnet dark energy model and its deformed version on Hořava-Lifshitz cosmology, which belongs to the class of cosmologies obtained from the so-called projectable version of Hořava-Lifshitz gravity. In particular, we investigate the bulk/boundary interaction in this scenario through the $Q$ function, which we interpret as a measure of the energy transference between the bulk and the spacetime boundary. Then we discuss whether the thermal equilibrium will be stable or not, once it is reached, and the validity of the generalized second law. We show that the $Q$ function c…
In the present article, Radiative Correction (RC) to the Casimir energy was computed for the self-interacting massive/massless Lifshitz-like scalar field, confined between a pair of plates with Dirichlet and Mixed boundary conditions in $3+1$ dimensions. Moreover, using the results obtained for the Dirichlet Casimir energy, the RC to the Casimir energy for Periodic and Neumann boundary conditions were also draw outed. To renormalize the bare parameters of the Lagrangian, a systematic perturbation expansion was used in which the counterterms were automatically obtained in a position-dependent m…
In the context of boundary conformal field theory, we derive a sum rule that relates two and three point functions of the displacement operator. For four dimensional conformal field theory with a three dimensional boundary, this sum rule in turn relates the two boundary contributions to the anomaly in the trace of the stress tensor. We check our sum rule for a variety of free theories and also for a weakly interacting theory, where a free scalar in the bulk couples marginally to a generalized free field on the boundary.
In quantum cosmology the DeWitt boundary condition is a proposal to set the wave function of the universe to vanish at the classical big-bang singularity. In this Letter, we show that in many gravitational theories including general relativity, the DeWitt wave function does not take a desired form once tensor perturbations around a homogeneous and isotropic closed universe are taken into account: anisotropies and inhomogeneities due to the perturbations are not suppressed near the classical singularity. We then show that Hořava-Lifshitz gravity provides a satisfactory DeWitt wave function. In …
We develop a new heat kernel method that is suited for a systematic study of the renormalization group flow in Horava gravity (and in Lifshitz field theories in general). This method maintains covariance at all stages of the calculation, which is achieved by introducing a generalized Fourier transform covariant with respect to the nonrelativistic background spacetime. As a first test, we apply this method to compute the anisotropic Weyl anomaly for a (2+1)-dimensional scalar field theory around a z=2 Lifshitz point and corroborate the previously found result. We then proceed to general scalar …
Matter one-loop logarithms and homogeneous TTNC scale response of Lifshitz black branes
Zhongtai Securities Institute for Financial Studies, Shandong University（山东大学）；Department of Physics, Southern Methodist University（南方卫理公会大学）；School of Statistics, Dongbei University of Finance and Economics（东北财经大学）
In this paper we obtain exact asymptotically anti-de Sitter black hole solutions and asymptotically Lifshitz black hole solutions with dynamical exponents $z=0$ and $z=4$ of four-dimensional conformal gravity coupled with a self-interacting conformally invariant scalar field. Then, we compute their thermodynamical quantities, such as the mass, the Wald entropy and the Hawking temperature. The mass expression is obtained by using the generalized off-shell Noether potential formulation. It is found that the anti-de Sitter black holes as well as the Lifshitz black holes with $z=0$ have zero mass …
