We numerically construct static localized black holes in five and six spacetime dimensions which are solutions to Einstein's vacuum field equations with one compact periodic dimension. In particular, we investigate the critical regime in which the poles of the localized black hole are about to merge. A well adapted multi-domain pseudo-spectral scheme provides us with accurate results and enables us to investigate the phase diagram of those localized solutions within the critical regime, which goes far beyond previous results. We find that in this regime the phase diagram possesses a spiral structure adapting to the one recently found for non-uniform black strings. When approaching the common endpoint of both phases, the behavior of physical quantities is described by complex critical exponents giving rise to a discrete scaling symmetry. The numerically obtained values of the critical exponents agree remarkably well with those derived from the double-cone metric.

We study the effects of quenched one-dimensional disorder on the holographic Weyl semimetal quantum phase transition (QPT), with a particular focus on the quantum critical region. We observe the smearing of the sharp QPT linked to the appearance of rare regions at the horizon where locally the order parameter is non-zero. We discuss the role of the disorder correlation and we compare our results to expectations from condensed matter theory at weak coupling. We analyze also the interplay of finite temperature and disorder. Within the quantum critical region we find indications for the presence of log-oscillatory structures in the order parameter hinting at the existence of an IR fixed point with discrete scale invariance.

We study the surface states of a strongly coupled Weyl semimetal within holography. By explicit numerical computation of an inhomogeneous holographic Weyl semimetal, we observe the appearance of an electric current restricted to the surface in presence of an electric chemical potential. The integrated current is universal in the sense that it only depends on the topology of the phases showing that the bulk-boundary correspondence holds even at strong coupling. The implications of this result are subtle and may shed some light on anomalous transport at weak coupling. INTRODUCTIONWeyl semimetals (WSMs) are novel gapless topological states of matter with electronic low-energy excitations behaving as left-and right-handed Weyl fermions [1][2][3][4][5][6][7]. These quasiparticles are localized around Weyl nodes in the Brillouin zone, points where, in band theory, valence and conduction bands touch at the Fermi energy. The Nielsen-Ninomiya theorem [1] states that left-and right-handed Weyl nodes appear in pairs. The existence of these nodes requires either inversion or time reversal symmetry to be broken. In the latter case, Weyl nodes of opposite chirality are separated spatially in the Brillouin zone. Weyl nodes can be characterized as monopoles of Berry flux with charge ±1 which reflects the chirality of the excitations. As such, Weyl nodes represent topological objects in the Brillouin zone and are stable under most perturbations, including interactions. As in topological insulators, the existence of surface states is guaranteed by topology. Moreover, it has been shown [2] that the surface states of a WSM form so-called Fermi arcs connecting the projections of the Weyl nodes onto the surface Brillouin zone.The transport properties of WSMs are tightly bound to the axial anomaly of quantum field theories with Weyl fermions. This leads to anomaly-related phenomena in WSMs such as the anomalous Hall effect [8][9][10][11][12], the chiral magnetic effect [13,14] and related effects like the negative magnetoresistance [15,16]. Furthermore, it has been predicted that lattice deformations couple to the fermionic low-energy excitations with different signs, giving rise to effective axial gauge fields [17,18]. Such lattice deformations naturally arise at the surfaces of a WSM, inducing localised axial magnetic fields in their vicinity. Moreover, it was shown that the Fermi arcs can be understood from this perspective as zeroth Landau levels generated by these fields [19].It is important to remark that in the strong coupling regime the description in terms of bands, or even correlation functions, cannot be applied and therefore it is compelling to study to which extent the weak coupling intuitions can be extrapolated. In Refs. [20,21], the authors addressed the question whether the properties of a (homogeneous and infinite) WSM can be found in the strong coupling regime. To this end, they presented a holographic model which exhibits a topological phase transition from a trivial phase to a non-trivial WSM phase. In this letter...

We numerically construct static localized black holes in ten spacetime dimensions with one compact periodic dimension. In particular, we investigate the critical regime in which the poles of the localized black hole are about to merge. When approaching the critical region, the behavior of physical quantities is described by a single real valued exponent giving rise to a logarithmic scaling of the thermodynamic quantities, in agreement with the theoretical prediction derived from the double-cone metric. As a peculiarity, the localized black hole solution in ten dimensions can be related to the spatially deconfined phase of two dimensional N = (8, 8) super Yang-Mills theory (SYM) on a spatial circle. We use the localized black hole solutions to determine the SYM phase diagram. In particular, we compute the location of the first order phase confinement/deconfinement transition and the related latent heat to unprecedented accuracy.

A new hyperelliptic solution class for the hyperbolic Ernst equation is obtained by transforming the regarding solution of the elliptic Ernst equation. Furthermore, a nontrivial way for obtaining general polarized colliding wave solutions from this hyperelliptic family of solutions is presented. The explicit form of the solutions for a Riemann surface of genus n = 1 is given. In addition, an explicit example in terms of a Khan-Penrose seed is provided, emphasizing the importance of the presented procedure for generating general polarized colliding plane-wave space times from space-times with a collinear polarization of the colliding waves.