In physical theories where the energy (action) is localized near a submanifold of Euclidean (Minkowski) space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite number of terms, and depends on intrinsic geometric invariants of the submanifold and extrinsic invariants of the embedding of the submanifold. This universal expression is a generalization of an exact formula of Hermann Weyl for the volume of a tube. We describe when our result is applicable, when our generalization gives an exact result, and when there are corrections (often exponentially small) to our formula. In special situations, dictated by spherical symmetry, the expression is a generalized Lovelock lagrangian for gravity, a class of theories that are interesting because they have no negative metric states. We discuss whether these results represent a true theory of emergent gravity by discussing simple models where a higher dimensional quantum field theory without a fundamental graviton leads to a gravity-like theory on a submanifold where all or some of the dynamical degrees of freedom are fluctuations of the metric on the submanifold.
The Fermi liquid has an emergent low-energy symmetry that corresponds to charge conservation at each momentum on the Ferm surface. Recently Else, Thorngren and Senthil (ETS) argued that the emergent symmetry had a specific t'Hooft anomaly. We give a simple derivation of the ETS anomaly using the chiral anomaly of Weyl fermions.
We consider the tight-binding model with cubic symmetry that may be relevant for the description of a certain class of Weyl semimetals. We take into account elastic deformations of the semimetal through the modification of hopping parameters. This modification results in the appearance of emergent gauge field and the coordinate dependent anisotropic Fermi velocity. The latter may be interpreted as emergent gravitational field.
Supersymmetry (SUSY) interchanges bosons and fermions but no direct evidences of it have been revealed in nature yet. In this letter, we observe that fluctuating pair density waves (PDW) consist of two complex order parameters which can be superpartners of the unavoidably-doubled Weyl fermions in three-dimensional lattice models. We construct explicit fermionic lattice models featuring 3D Weyl fermions and show that PDW is the leading instability via a continuous phase transition as short-range interactions exceed a critical value. Using renormalization group, we theoretically show that N=2 sp…
We present emergent ergosurfaces (ES) in a transition layer between type-I and type-II Weyl semimetals (WSMs). The Hawking temperature defined by the surface gravity at the acoustic event horizon which coincides with the ES when the tangent velocity $v_{\parallel}$ is small is in a measurable interval. On the type-II WSM side, i.e., inside the {ES when $v_{\parallel}$ is large}, the motion of the quasiparticles may be chaotic {after} a critical surface as they are governed by an effective inverted oscillator potential induced by the mismatch between the type-I and type-II Weyl nodes. In a rele…
Supersymmetry plays a crucial role in superstring theory and high-energy physics, but has never been observed in experiments. Recently, an effective space-time supersymmetry was argued to emerge in the low-energy region by tuning Dirac or Weyl semimetal to approach a superconducting quantum critical point, at which the Dirac or Weyl fermion and the bosonic order parameter are both massless. Here, we study under what circumstances can space-time supersymmetry be realized at a quantum critical point. We demonstrate that the Yukawa-type coupling between the massless fermion and massless boson can…
Momentum transport is anomalous in chiral $p+ip$ superfluids and superconductors in the presence of textures and superflow. Using the gradient expansion of the semi-classical approximation, we show how gauge and Galilean symmetries induce an emergent curved spacetime with torsion and curvature for the quasirelativistic low-energy Majorana-Weyl quasiparticles. We explicitly show the emergence of the spin-connection and curvature, in addition to torsion, using the superfluid hydrodynamics. The background constitutes an emergent quasirelativistic Riemann-Cartan spacetime for the Weyl quasiparticl…
In Ref. \cite{Horava2005} Hořava suggested, that the multi - fermion many-body system with topologically stable Fermi surfaces may effectively be described (in a vicinity of the Fermi surface) by the theory with coarse-grained fermions. The number of the components of these coarse-grained fermions is reduced compared to the original system. Here we consider the $3+1$ D system and concentrate on the particular case when the Fermi surface has co-dimension $p=3$, i.e. it represents the Fermi point in momentum space. First we demonstrate explicitly that in agreement with Hořava conjecture, in the …
Emergent Weyl Nodes and Berry Curvature in Bose Polarons via $p$-Wave Feshbach Coupling
The University of Tokyo（东京大学）；RIKEN Nishina Center（理化学研究所西村中心）；Quark Nuclear Science Institute, The University of Tokyo（东京大学夸克核科学研究所）；Kochi University（高知大学）；The Open University of Japan（日本开放大学）
We study inflation in Weyl gravity. The original Weyl quadratic gravity, based on Weyl conformal geometry, is a theory invariant under Weyl symmetry of (gauged) local scale transformations. In this theory Planck scale ($M$) emerges as the scale where this symmetry is broken spontaneously by a geometric Stueckelberg mechanism, to Einstein-Proca action for the Weyl "photon" (of mass near $M$). With this action as a "low energy" broken phase of Weyl gravity, century-old criticisms of the latter (due to non-metricity) are avoided. In this context, inflation with field values above $M$ is natural, …
Pursuing complementary field-theoretic and numerical methods, we here paint the global phase diagram of a three-dimensional dirty Weyl system. The generalized Harris criterion, augmented by a perturbative renormalization-group (RG) analysis shows that weak disorder is an irrelevant perturbation at the Weyl semimetal(WSM)-insulator quantum critical point (QCP). But, a metallic phase sets in through a quantum phase transition (QPT) at strong disorder across a multicritical point (MCP). The field theoretic predictions for the correlation length exponent $ν=2$ and dynamic scaling exponent $z=5/4$ …
We propose a correspondence between the description of emergent Lorentz symmetry in condensed-matter systems and the established general effective field theory for Lorentz violation in fundamental theories of spacetime and matter. This correspondence has potential implications in both directions. We illustrate the proposal by investigating its consequences for the spectral and transport properties of Dirac and Weyl semimetals. Particular realizations of this framework give rise to Dirac nodal spectra with nodal lines and rings. We demonstrate a bulk-boundary correspondence between bulk topolog…
We present a simple method for determining the shape of fundamental domains of generalized modular groups related to Weyl groups of hyperbolic Kac-Moody algebras. These domains are given as subsets of certain generalized upper half planes, on which the Weyl groups act via generalized modular transformations. Our construction only requires the Cartan matrix of the underlying finite-dimensional Lie algebra and the associated Coxeter labels as input information. We present a simple formula for determining the volume of these fundamental domains. This allows us to re-produce in a simple manner the…
In physical theories where the energy (action) is localized near a submanifold of a constant curvature space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite number of terms, and depends on intrinsic geometric invariants of the submanifold and extrinsic invariants of the embedding of the submanifold. This is the second of a pair of articles in which we try to develop a theory of emergent gravity arising from the embedding of a submanifold into an ambient space equipped with a quantum field theory. Our theoretical …
In this work, a clear connection is made between E. Verlinde's recent theory of emergent gravity in de Sitter space and the earlier work that described emergent gravity using holographic screens. A modified (non)holographic screen scenario is presented, wherein the screen fails to encode an emergent mass in the bulk "unemerged" part of space for sufficiently large length-scales, where the volume-law of the non-holographic bulk degrees of freedom overtakes the area-law scaling of the entropy of the screen. Within this framework, we can describe both an emergent dark gravitational force, which s…
The action of Weyl scale invariant p=2 brane which breaks the target super Weyl scale symmetry in the N=1, D=4 superspace down to the lower dimensional Weyl symmetry W(1,2) is derived by the approach of nonlinear realization. The dual form action for the Weyl scale invariant supersymmetric D2 brane is also constructed. The interactions of localized matter fields on the brane with the Nambu-Goldstone fields associated with the breaking of the symmetries in the superspace and one spatial translation directions are obtained through the Cartan one-forms of the Coset structures. The covariant deriv…
We analyze the Weyl invariance constraints on higher spin vertex operators in open superstring theory describing massless higher spin gauge field excitations in d-dimensional space-time. We show that these constraints lead to low-energy equations of motion for higher spin fields in AdS space, with the leading order beta-function for the higher spin fields producing Fronsdal's operator in $AdS_{d+1}$, despite that the higher spin vertex operators are originally defined in flat background. The correspondence between the $β$-function in string theory and $AdS_{d+1}$ Fronsdal operators in space-ti…
We derive manifestly locally supersymmetric extensions of the Born-Infeld action with $p=2$. The construction is based on a first order bosonic action for $Dp$-branes with a generalized Weyl invariance.
Large-N volume independence in circle-compactified QCD with N_f \geq 1 adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories are believed to possess a Hagedorn density of hadronic states. It turns out that these properties are in apparent tension with each other, because a Hagedorn density of states typically implies a phase transition at some finite radius. This tension is resolved if there are degeneracies between the spectra of bosonic and fermionic states, as happens in the N_f=1 supersymmetric case. R…
Alternative scenarios to the Big Bang singularity have been subject of intense research for several decades by now. Most popular in this sense have been frameworks were such singularity is replaced by a bounce around some minimal cosmological volume or by some early quantum phase. This latter scenario was devised a long time ago and referred as an "emergent universe" (in the sense that our universe emerged from a constant volume quantum phase). We show here that within an improved framework of canonical quantum gravity (the so called Quantum Reduced Loop Gravity) the Friedmann equations for co…
We study classical solutions in the Weyl-transverse (WTDiff) gravity coupled to an electro-magnetic field in four space-time dimensions. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeormorphisms (transverse diffeomorphisms) and is known to be equivalent to general relativity at least at the classical level (perhaps even in the quantum regime). In particular, we find that only in four space-time dimensions, the charged Reissner-Nordstrom black hole metric is a classical solution when it is expressed in the Cartesian coordinat…
We study the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology in the Weyl-transverse (WTDiff) gravity in a general space-time dimension. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeormorphisms (transverse diffeomorphisms) and is believed to be equivalent to general relativity at least at the classical level (perhaps, even in the quantum regime). It is explicitly shown by solving the equations of motion that the FLRW metric is a classical solution in the WTDiff gravity only when the spatial metric is flat, that is, the …
Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the ar…
Weyl conformal geometry may play a role in early cosmology where effective theory at short distances becomes conformal. Weyl conformal geometry also has a built-in geometric Stueckelberg mechanism: it is broken spontaneously to Riemannian geometry after a Weyl gauge transformation (of "gauge fixing") while Stueckelberg mechanism re-arranges the degrees of freedom, conserving their number ($n_{df}$). The Weyl gauge field ($ω_μ$) of local scale transformations acquires a mass after absorbing a compensator (dilaton), decouples, and Weyl connection becomes Riemannian. Mass generation has thus a dy…
The standard model is a remarkably consistent and complete quantum field theory but its coupling to gravity and the Higgs field remain problematic, as reflected in the cosmological constant problem, the Weyl anomaly, and the hierarchy puzzle. We point out that 36 conformally-coupled dimension-zero scalar fields can simultaneously cancel the vacuum energy and both terms in the Weyl anomaly, if the Higgs field is emergent. The cancellation is highly non-trivial: given the standard model gauge group $SU(3)\times SU(2)\times U(1)$, it requires precisely $48$ Weyl fermions, {\it i.e.}, three genera…
