We construct a quasi-local formalism for conserved charges in a theory of gravity in the presence of matter fields which may have slow falloff behaviors at the asymptotic infinity. This construction depends only on equations of motion and so it is irrespective of ambiguities in the total derivatives of the Lagrangian. By using identically conserved currents, we show that this formalism leads to the same expressions of conserved charges as those in the covariant phase space approach. At the boundary of the asymptotic AdS space, we also introduce an identically conserved boundary current which has the same structure as the bulk current and then show that this boundary current gives us the holographic conserved charges identical with those from the boundary stress tensor method. In our quasi-local formalism we present a general proof that conserved charges from the bulk potential are identical with those from the boundary current. Our results can be regarded as the extension of the existing results on the equivalence of conserved charges by the covariant phase space approach and by the boundary stress tensor method.
We study the magnetic effect in strongly interacting system with two conserved currents near the quantum critical point (QCP). For this purpose, we introduce the hyper-scaling violation geometry with the blackhole. Considering the perturbation near the background geometry, we compute the transport coefficients using holographic methods. We calculated the magneto-transport for general QCP and discuss the special point $(z,θ)=(3/2,1)$ where the data of Dirac material were well-described previously.
This thesis is devoted to the study of 3-dimensional quantum gravity as a spin foam model and group field theory. In the first part of this thesis, we review some general physical and mathematical aspects of 3-dimensional gravity, focusing on its topological nature. Afterwards, we review some important aspects of the Ponzano-Regge spin foam model for 3-dimensional Riemannian quantum gravity and explain in some details how it is related to the discretized path integral of general relativity in its first-order formulation. Furthermore, we discuss briefly some related spin foam models and review …
We calculate the transport of a theory with two conserved currents by holographic method and compare it with graphene data to determine its dynamical exponents $(z,θ)$ which characterizes a QCP. As a result, we find that the electric and the thermal conductivity data can be fit much more naturally if we assume $(z,θ)=(3/2,1)$ rather than $(1,0)$. Furthermore, we find that thermoelectric power data at high temperature can be fit if we use $(3/2,1)$ but not at all by $(1,0)$. The $θ=1$ result can be interpreted as taking into account the fermionic nature of the electrons and $z=3/2$ can be inter…
An effective action for diffusion of a conserved $U(1)$ charge is derived to all orders in the derivative expansion within a holographic model dual to the Schwinger-Keldysh closed time path. A systematic approach to solution of the 5D Maxwell equations in a doubled Schwarzschild-AdS$_5$ black brane geometry is developed. Constitutive relation for the stochastic charge current is shown to have a term induced by thermal fluctuations (coloured noise). All transport coefficient functions parameterising the effective action and constitutive relations are computed analytically in the hydrodynamic ex…
In this thesis we investigate some aspects of quantum field theories from a holographic perspective. In the first chapters we examine in detail a one-paremeter family of three-dimensional gauge theories by means of their type IIA gravity duals. We analyse features such as their confinement nature, spectrum, entanglement properties or thermal phase transitions. This family interpolates between quasi-conformal and quasi-confining physics. In the last two chapters, we use bottom-up models to study complex conformal field theories and transport properties of dense QCD respectively.
We discuss the physics of momentum diffusion in a charged plasma. Following the holographic strategy outlined in arXiv:2012.03999 we construct an open effective field theory for the low-lying modes of the conserved currents. The charged plasma is modeled holographically in terms of a Reissner-Nordstrom-AdS black hole. We analyze graviton and photon fluctuations about this background, decoupling in the process the long-lived momentum diffusion mode from the short-lived charged transport mode. Furthermore, as in the aforementioned reference, we argue that the dynamics of these modes are captured…
We consider the charged moments in $SL(3,\mathbb{R})$ higher spin holography, as well as in the dual two-dimensional conformal field theory with $W_3$ symmetry. For the vacuum state and a single entangling interval, we show that the $W_3$ algebra of the conformal field theory induces an entanglement $W_3$ algebra acting on the quantum state in the entangling interval. The algebra contains a spin 3 modular charge which commutes with the modular Hamiltonian. The reduced density matrix is characterized by the modular energy and modular charge, hence our definition of the charged moments is also w…
Space-based next-generation interferometers propose to measure the Lyapunov exponents of the nearly bound geodesics that comprise the photon ring surrounding the black hole M87*. We argue that these classical Lyapunov exponents equal the quantum Ruelle resonances describing the late-time approach to thermal equilibrium of the quantum microstate holographically dual to any Kerr black hole such as M87*. Moreover, we identify "near-ring regions" in the phase space of fields propagating on Kerr that exhibit critical behavior, including emergent conformal symmetries. These are analogues for sub-ext…
