We extend earlier treatments of holographic superconductors by studying cases where operators of different dimension condense in both 2 þ 1 and 3 þ 1 superconductors. We also compute a correlation length. We find surprising regularities in quantities such as ! g =T c where ! g is the gap in the frequency dependent conductivity. In special cases, new bound states arise corresponding to vector normal modes of the dual near-extremal black holes.

We consider holographic superconductors whose bulk description consists of gravity minimally coupled to a Maxwell field and charged scalar field with general potential. We give an analytic argument that there is no "hard gap": the real part of the conductivity at low frequency remains nonzero (although typically exponentially small) even at zero temperature. We also numerically construct the gravitational dual of the ground state of some holographic superconductors. Depending on the charge and dimension of the condensate, the infrared theory can have emergent conformal or just Poincare symmetry. In all cases studied, the area of the horizon of the dual black hole goes to zero in the extremal limit, consistent with a nondegenerate ground state.1 Some early indications of emergent Poincare symmetry were found in [13]

Peri-operative SARS-CoV-2 infection increases postoperative mortality. The aim of this study was to determine the optimal duration of planned delay before surgery in patients who have had SARS-CoV-2 infection. This international, multicentre, prospective cohort study included patients undergoing elective or emergency surgery during October 2020. Surgical patients with pre-operative SARS-CoV-2 infection were compared with those without previous SARS-CoV-2 infection. The primary outcome measure was 30-day postoperative mortality. Logistic regression models were used to calculate adjusted 30-day mortality rates stratified by time from diagnosis of SARS-CoV-2 infection to surgery. Among 140,231 patients (116 countries), 3127 patients (2.2%) had a pre-operative SARS-CoV-2 diagnosis. Adjusted 30-day mortality in patients without SARS-CoV-2 infection was 1.5% (95%CI 1.4-1.5). In patients with a pre-operative SARS-CoV-2 diagnosis, mortality was increased in patients having surgery within 0-2 weeks, 3-4 weeks and 5-6 weeks of the diagnosis (odds ratio (95%CI) 4.1 (3.3-4.8), 3.9 (2.6-5.1) and 3.6 (2.0-5.2), respectively). Surgery performed ≥ 7 weeks after SARS-CoV-2 diagnosis was associated with a similar mortality risk to baseline (odds ratio (95%CI) 1.5 (0.9-2.1)). After a ≥ 7 week delay in undertaking surgery following SARS-CoV-2 infection, patients with ongoing symptoms had a higher mortality than patients whose symptoms had resolved or who had been asymptomatic (6.0% (95%CI 3.2-8.7) vs. 2.4% (95%CI 1.4-3.4) vs. 1.3% (95%CI 0.6-2.0), respectively). Where possible, surgery should be delayed for at least 7 weeks following SARS-CoV-2 infection. Patients with ongoing symptoms ≥ 7 weeks from diagnosis may benefit from further delay.

Motivated by the Kerr/CFT conjecture, we explore solutions of vacuum general relativity whose asymptotic behavior agrees with that of the extremal Kerr throat, sometimes called the Near-Horizon Extreme Kerr (NHEK) geometry. We argue that all such solutions are diffeomorphic to the NHEK geometry itself. The logic proceeds in two steps. We first argue that certain charges must vanish at all times for any solution with NHEK asymptotics. We then analyze these charges in detail for linearized solutions. Though one can choose the relevant charges to vanish at any initial time, these charges are not conserved. As a result, requiring the charges to vanish at all times is a much stronger condition. We argue that all solutions satisfying this condition are diffeomorphic to the NHEK metric.1 A more complete argument notes that the horizon-generating Killing field of a non-extreme Kerr black hole is timelike near the horizon, so that timelike observers sufficiently close to a nonextreme Kerr black hole can co-rotate with the black hole, out to the so-called velocity of light surface where such co-rotating observers must become null. For positive-energy matter, this timelike Killing field defines a positive conserved quantity for excitations in the near-horizon region, ruling out instabilities. In contrast, the horizon-generating Killing field of extreme Kerr is spacelike at all points near the equator outside the horizon, no matter how far one goes down the throat. As a result, the Frolov-Thorne vacuum [9] for linear fields discussed in [3] is not well-defined in the extreme Kerr throat [10,11,12].

Abstract:We study the effects of a superconducting condensate on holographic Fermi surfaces. With a suitable coupling between the fermion and the condensate, there are stable quasiparticles with a gap. We find some similarities with the phenomenology of the cuprates: in systems whose normal state is a non-Fermi liquid with no stable quasiparticles, a stable quasiparticle peak appears in the condensed phase.

There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativisitic symmetries which supports massive matter fields. In particular, one can not impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [1] we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of nonrelativistic fluids.Recently there has been a revival of interest in the Newton-Cartan description of nonrelativistic spacetimes in the condensed matter literature [2][3][4][5][6][7][8][9][10][11][12] where, it has been used with great effect to describe phenomena in the quantum Hall effect and various transport phenomena in condensed matter systems. Newton-Cartan spacetimes are used to describe matter fields and their interaction with general background geometries which are consistent with non-relativistic Galilean invariance. Newton-Cartan geometry also arises in the study of nonrelativistic holographic systems, where the boundary theory realizes a "twistless-torsionful" Newton-Cartan geometry [13][14][15][16][17][18][19]. On the other hand, in the gravitational physics literature (see [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] and also Ch.12 of [35] and Ch.4 of [36]) Newton-Cartan geometry has been well studied as a diffeomorphism-covariant, geometric way to describe Newtonian gravity. As such, the Newton-Cartan spacetimes considered there belong to a much more restricted class. This divergence of interests has lead to some conflicts in the construction (or at least in the interpretation) of Newton-Cartan spacetimes. One of the aims of this work is to alleviate these conflicts and set a clear stage for describing both Newtonian gravity and matter R I J := dω I J + ω I K ∧ ω K J (2.13b) 7Here we use the convention that the connection is a 1-form valued in the Lie algebra, instead of viewing it as 1-form components in a set of bases given by the generators of the Lie algebra.

Classical SU (2) Yang-Mills theory in 3+1 dimensional anti-de Sitter space is known to provide a holographic dual to a 2+1 system that undergoes a superconducting phase transition. We study the electrical conductivity and spectral density of an isotropic superconducting phase. We show that the theory exhibits a pseudogap at low temperatures and a nonzero Hall conductivity. The Hall conductivity is possible because of spontaneous breaking of time reversal symmetry.

We consider non-relativistic curved geometries and argue that the background structure should be generalized from that considered in previous works. In this approach the derivative operator is defined by a Galilean spin connection valued in the Lie algebra of the Galilean group. This includes the usual spin connection plus an additional "boost connection" which parameterizes the freedom in the derivative operator not fixed by torsion or metric compatibility. As an example we write down the most general theory of dissipative fluids consistent with the second law in curved non-relativistic geometries and find significant differences in the allowed transport coefficients from those found previously. Kubo formulas for all response coefficients are presented. Our approach also immediately generalizes to systems with independent mass and charge currents as would arise in multicomponent fluids. Along the way we also discuss how to write general locally Galilean invariant non-relativistic actions for multiple particle species at any order in derivatives. A detailed review of the geometry and its relation to non-relativistic limits may be found in a companion paper.