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Register a new userBound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field
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We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent ($lambda_L$) and butterfly velocity ($v_B$), independently of the symmetry breaking patterns. We show that the diffusion constant ($D$) is bounded by $D ,geqslant, v_{B}^2/lambda_{L}$, where $D$ is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit.
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We study the pole-skipping phenomenon of the scalar retarded Greens function in the rotating BTZ black hole background. In the static case, the pole-skipping points are typically located at negative imaginary Matsubara frequencies $omega=-(2pi T)ni$ with appropriate values of complex wave number $q$. But, in a $(1+1)$-dimensional CFT, one can introduce temperatures for left-moving and right-moving sectors independently. As a result, the pole-skipping points $omega$ depend both on left and right temperatures in the rotating background. In the extreme limit, the pole-skipping does not occur in general. But in a special case, the pole-skipping does occur even in the extreme limit, and the pole-skipping points are given by right Matsubara frequencies.
In this paper we discuss a disordered $d$-dimensional Euclidean $lambdavarphi^{4}$ model. The dominant contribution to the average free energy of this system is written as a series of the replica partition functions of the model. In each replica partition function, using the saddle-point equations and imposing the replica symmetric ansatz, we show the presence of a spontaneous symmetry breaking mechanism in the disordered model. Moreover, the leading replica partition function must be described by a large-$N$ Euclidean replica field theory. We discuss finite temperature effects considering periodic boundary condition in Euclidean time and also using the Landau-Ginzburg approach. In the low temperature regime we prove the existence of $N$ instantons in the model.
We investigate the pole-skipping phenomenon in holographic chaos. According to the pole-skipping, the energy-density Greens function is not unique at a special point in complex momentum plane. This arises because the bulk field equation has two regular near-horizon solutions at the special point. We study the regularity of two solutions more carefully using curvature invariants. In the upper-half $omega$-plane, one solution, which is normally interpreted as the outgoing mode, is in general singular at the future horizon and produces a curvature singularity. However, at the special point, both solutions are indeed regular. Moreover, the incoming mode cannot be uniquely defined at the special point due to these solutions.
We study the spontaneous Lorentz symmetry breaking in a field theoretical model in (2+1)-dimension, inspired by string theory. This model is a gauge theory of an anti-symmetric tensor field and a vector field (photon). The Nambu-Goldstone (NG) boson for the spontaneous Lorentz symmetry breaking is identified with the unphysical massless photon in the covariant quantization. We also discuss an analogue of the equivalence theorem between the amplitudes for emission or absorption of the physical massive anti-symmetric tensor field and those of the unphysical massless photon. The low-energy effective action of the NG-boson is also discussed.
Holographic CFTs and holographic RG flows on space-time manifolds which are $d$-dimensional products of spheres are investigated. On the gravity side, this corresponds to Einstein-dilaton gravity on an asymptotically $AdS_{d+1}$ geometry, foliated by a product of spheres. We focus on holographic theories on $S^2times S^2$, we show that the only regular five-dimensional bulk geometries have an IR endpoint where one of the sphere shrinks to zero size, while the other remains finite. In the $Z_2$-symmetric limit, where the two spheres have the same UV radii, we show the existence of a infinite discrete set of regular solutions, satisfying an Efimov-like discrete scaling. The $Z_2$-symmetric solution in which both spheres shrink to zero at the endpoint is singular, whereas the solution with lowest free energy is regular and breaks $Z_2$ symmetry spontaneously. We explain this phenomenon analytically by identifying an unstable mode in the bulk around the would-be $Z_2$-symmetric solution. The space of theories have two branches that are connected by a conifold transition in the bulk, which is regular and correspond to a quantum first order transition. Our results also imply that $AdS_5$ does not admit a regular slicing by $S^2times S^2$.
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