We provide a framework for non-relativistic holography so that a covariant action principle ensuring the Galilean symmetry for dual conformal field theory is given. This framework is based on the Bargmann lift of the Newton-Cartan gravity to the one-dimensional higher Einstein gravity, or reversely, the null-like Kaluza-Klein reduction. We reproduce the previous zero temperature results, and our framework provides a natural explanation about why the holography is co-dimension 2. We then construct the black hole solution dual to the thermal CFT, and find the horizon is curvature singular. However, we are able to derive the sensible thermodynamics for the dual non-relativistic CFT with correct thermodynamical relations. Besides, our construction admits a null Killing vector in the bulk such that the Galilean symmetry is preserved under the holographic RG flow. Finally, we evaluate the viscosity and find it zero if we neglect the back reaction of the singular horizon, otherwise, it could be nonzero.
Recently it was proposed that asymptotically flat spacetimes have a holographic dual which is an ultra-relativistic conformal field theory. In this paper, we obtain the conformal anomaly for such a theory via the flat-space holography technique. Furthermore, using flat-space holography we obtain a C-function for this theory which is monotonically decreasing from the UV to the IR by employing the null energy condition in the bulk.
Department of Space Science and Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学空间科学与彭桓武研究中心）；Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院斐泽克量子中心）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）
We investigate the standard and dual Bondi-Metzner-Sachs (BMS) supertranslation generators on a black hole horizon and draw some conclusions about black hole physics. Recently, it has been shown that in addition to conventional BMS supertranslation symmetries, there exists an additional infinite set of magnetic asymptotic symmetries, dual BMS supertranslations, again parametrized by a function on the two-sphere. We show that the Dirac bracket between these generators exhibits an anomalous central term when one parameter function exhibits a singularity in the complex stereographical coordinates…
We consider the holographic computation of two dimensional conformal field theory partition functions on non-orientable surfaces. We classify the three dimensional geometries that give bulk saddle point contributions to the partition function, and find that there are fewer saddles than in the orientable case. For example, for the Klein bottle there is a single smooth saddle and a single additional saddle with an orbifold singularity. We argue that one must generally include singular bulk saddle points in order to reproduce the CFT results. We also discuss loop corrections to these partition fu…
Placing D3-branes at conical Calabi-Yau threefold singularities produces many AdS$_5$/CFT$_4$ duals. Recent progress in differential geometry has produced a technique (called K-stability) to recognize which singularities admit conical Calabi-Yau metrics. On the other hand, the algebraic technique of non-commutative crepant resolutions, involving matrix factorizations, has been developed to associate a quiver to a singularity. In this paper, we put together these ideas to produce new AdS$_5$/CFT$_4$ duals, with special emphasis on non-toric singularities.
We study the ground state instability of a strongly coupled QFT with the $z=2$ Schrödinger symmetry in a constant electric field using probe branes holography. The system is $N_f$ $\mathcal{N}=2$ hypermultiplet fermions at zero charge density in the supergravity Schrödinger background. We show that the instability occurs due to Schwinger-like effect and an insulator state will undergo a transition to a conductor state. We calculate the decay rate of instability and pair production probability by using the $gauge/gravity$ duality. At zero temperature for massive fermions, we suggest that the in…
We study generic types of holographic matter residing in Lifshitz invariant defect field theory as modeled by adding probe D-branes in the bulk black hole spacetime characterized by dynamical exponent $z$ and with hyperscaling violation exponent $θ$. Our main focus will be on the collective excitations of the dense matter in the presence of an external magnetic field. Constraining the defect field theory to 2+1 dimensions, we will also allow the gauge fields become dynamical and study the properties of a strongly coupled anyonic fluid. We will deduce the universal properties of holographic mat…
We examine non-relativistic holographic RG flows by working with Einstein-Maxwell-scalar theories which support geometries that break Lorentz invariance at some energy scale. We adopt the superpotential formalism, which helps us characterize the radial flow in this setup and bring to light a number of generic features. In particular, we identify several quantities that behave monotonically under RG flow. As an example, we show that the index of refraction is generically monotonic. We also construct a combination of the superpotentials that flows monotonically in Einstein-scalar theories suppor…
We show how causal relativistic Navier-Stokes equations arise from the relativistic Boltzmann equation: the causality is preserved via a judicious choice of the zero modes of the collision operator. A completely analogous procedure may be used to extract causal hydrodynamics from the fluid-gravity correspondence: again, causality of the hydrodynamic equations is preserved by a suitable choice of zero modes of the corresponding differential operators in the bulk. We give examples of zero modes which give rise to causal hydrodynamic equations for non-conformal fluids with a conserved U(1) global…
In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional CFT for singular entangling surface. We observe that in addition to the universal term due to the entangling surface, there is a new logarithmic term which corresponds to a relevant perturbation of the conformal field theory with a coefficient depending on the scaling dimension of the relevant operator. We also find a new power law divergence in the holograph…
Trinity College Dublin（都柏林三一学院）；Hamilton Mathematics Institute, Trinity College Dublin（汉密尔顿数学研究所，都柏林三一学院）；II. Institut für Theoretische Physik, Universität Hamburg（汉堡大学理论物理第二研究所）
It is shown that the correspondence principle and the holographic principle are incompatible in the background of an eternal Schwarzschild-anti-de Sitter geometry. The argument is based on the observation that algebraic structures of local quantum field and CFT operators are not equivalent. This implies, in particular, the bulk CFT must be singular near the black-hole horizon. A CFT Hilbert space representation is elaborated which may correspond to the AdS black hole in the dual theory.
We study chaos in non-Lorentzian field theories, specifically Galilean and Carrollian conformal field theories in two dimensions. In a large central charge limit, we find that the Lyapunov exponent saturates the bound on chaos, conjectured originally for relativistic field theories. We recover the same Lyapunov exponent holographically by a shock-wave calculation in three-dimensional flat space cosmologies, providing further evidence for flat space holography.
Schrödinger Holography with and without Hyperscaling Violation
研究了一般动力学指数z和超标度破坏指数θ的薛定谔型非相对论全息的性质。标量关联函数由于广义z和θ的存在而具有更一般的形式，其效果也修改了标量算子的标度维数。我们提出了这种“余维2全息”的最小表面的处方，并证明了（d+3）维薛定谔背景的纠缠熵的（d-1）维面积定律。令人惊讶的是，即使没有超标度破坏，d+1 < z < d+2也违反了面积定律，这介于对数破坏和纠缠熵的广泛体积依赖性之间。在超尺度违反的情况下也发现了类似的违反。他们的双场论有望在包括费米面在内的参数范围内有新的相。我们还分析了使用非相对论膜的弦论嵌入。
We analytically obtain a new charged Lifshtitz solution by adding a non-relativistic Maxwell field in Horava-Lifshitz gravity. The black hole exhibits an anisotropic scaling between space and time (Lifshitz scaling) in the UV limit, while in the IR limit, the Lorentz invariance is recovered. We introduce the probed Lorentz-violation fermions into the background and holographically investigate the spectral properties of the dual fermionic operator. The Lorentz-violation of fermions will enhance the peak and corresponds larger fermi momentum, which compensates the non-relativistic bulk effect of…
We expand the holographic studies of momentum relaxation to include non-relativistic scaling symmetries in the ultraviolet. We do so by constructing black branes with Lifshitz asymptotics dressed with axions which explicitly depend on the boundary directions. Such configurations arise as analytic solutions of the Einstein-Proca theory coupled to massless scalar fields in arbitrary dimensions. Studying linear perturbations on these backgrounds, we conclude that there is a dual Ward identity which accounts for the dissipation of momentum in the system. In addition, we numerically compute the fre…
Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk - 2d boundary case and then focus on the 4d bulk - 3d boundary example, where the symmetry in question is the infinite dimensional BMS4 algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of …
