A bstract A two-dimensional CFT dual to a semiclassical theory of gravity in three dimensions must have a large central charge c and a sparse low energy spectrum. This constrains the OPE coefficients and density of states of the CFT via the conformal bootstrap. We define an ensemble of CFT data by averaging over OPE coefficients subject to these bootstrap constraints, and show that calculations in this ensemble reproduce semiclassical 3D gravity. We analyze a wide variety of gravitational solutions, both in pure Einstein gravity and gravity coupled to massive point particles, including Euclidean wormholes with multiple boundaries and higher topology spacetimes with a single boundary. In all cases we find that the on-shell action of gravity agrees with the ensemble-averaged CFT at large c . The one-loop corrections also match in the cases where they have been computed. We also show that the bulk effective theory has random couplings induced by wormholes, providing a controlled, semiclassical realization of the mechanism of Coleman, Giddings, and Strominger.
more »
« less
Averaging over Narain moduli space
A bstract Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT’s to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain’s family of two-dimensional CFT’s obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like U(1) 2 D Chern-Simons theory than like Einstein gravity.
more »
« less
- Award ID(s):
- 1911298
- NSF-PAR ID:
- 10233809
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2020
- Issue:
- 10
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract A central problem in any quantum theory of gravity is to explain the emergence of the classical spacetime geometry in some limit of a more fundamental, microscopic description of nature. The gauge/gravity-correspondence provides a framework in which this problem can, in principle, be addressed. This is a holographic correspondence which relates a supergravity theory in five-dimensional Anti-deSitter space to a strongly coupled superconformal gauge theory on its 4-dimensional flat Minkowski boundary. In particular, the classical geometry should therefore emerge from some quantum state of the dual gauge theory. Here we confirm this by showing how the classical metric emerges from a canonical state in the dual gauge theory. In particular, we obtain approximations to the Sasaki-Einstein metric underlying the supergravity geometry, in terms of an explicit integral formula involving the canonical quantum state in question. In the special case of toric quiver gauge theories we show that our results can be computationally simplified through a process of tropicalization.more » « less
-
BACKGROUND Landau’s Fermi liquid theory provides the bedrock on which our understanding of metals has developed over the past 65 years. Its basic premise is that the electrons transporting a current can be treated as “quasiparticles”—electron-like particles whose effective mass has been modified, typically through interactions with the atomic lattice and/or other electrons. For a long time, it seemed as though Landau’s theory could account for all the many-body interactions that exist inside a metal, even in the so-called heavy fermion systems whose quasiparticle mass can be up to three orders of magnitude heavier than the electron’s mass. Fermi liquid theory also lay the foundation for the first successful microscopic theory of superconductivity. In the past few decades, a number of new metallic systems have been discovered that violate this paradigm. The violation is most evident in the way that the electrical resistivity changes with temperature or magnetic field. In normal metals in which electrons are the charge carriers, the resistivity increases with increasing temperature but saturates, both at low temperatures (because the quantized lattice vibrations are frozen out) and at high temperatures (because the electron mean free path dips below the smallest scattering pathway defined by the lattice spacing). In “strange metals,” by contrast, no saturation occurs, implying that the quasiparticle description breaks down and electrons are no longer the primary charge carriers. When the particle picture breaks down, no local entity carries the current. ADVANCES A new classification of metallicity is not a purely academic exercise, however, as strange metals tend to be the high-temperature phase of some of the best superconductors available. Understanding high-temperature superconductivity stands as a grand challenge because its resolution is fundamentally rooted in the physics of strong interactions, a regime where electrons no longer move independently. Precisely what new emergent phenomena one obtains from the interactions that drive the electron dynamics above the temperature where they superconduct is one of the most urgent problems in physics, attracting the attention of condensed matter physicists as well as string theorists. One thing is clear in this regime: The particle picture breaks down. As particles and locality are typically related, the strange metal raises the distinct possibility that its resolution must abandon the basic building blocks of quantum theory. We review the experimental and theoretical studies that have shaped our current understanding of the emergent strongly interacting physics realized in a host of strange metals, with a special focus on their poster-child: the copper oxide high-temperature superconductors. Experiments are highlighted that attempt to link the phenomenon of nonsaturating resistivity to parameter-free universal physics. A key experimental observation in such materials is that removing a single electron affects the spectrum at all energy scales, not just the low-energy sector as in a Fermi liquid. It is observations of this sort that reinforce the breakdown of the single-particle concept. On the theoretical side, the modern accounts that borrow from the conjecture that strongly interacting physics is really about gravity are discussed extensively, as they have been the most successful thus far in describing the range of physics displayed by strange metals. The foray into gravity models is not just a pipe dream because in such constructions, no particle interpretation is given to the charge density. As the breakdown of the independent-particle picture is central to the strange metal, the gravity constructions are a natural tool to make progress on this problem. Possible experimental tests of this conjecture are also outlined. OUTLOOK As more strange metals emerge and their physical properties come under the scrutiny of the vast array of experimental probes now at our disposal, their mysteries will be revealed and their commonalities and differences cataloged. In so doing, we should be able to understand the universality of strange metal physics. At the same time, the anomalous nature of their superconducting state will become apparent, offering us hope that a new paradigm of pairing of non-quasiparticles will also be formalized. The correlation between the strength of the linear-in-temperature resistivity in cuprate strange metals and their corresponding superfluid density, as revealed here, certainly hints at a fundamental link between the nature of strange metallicity and superconductivity in the cuprates. And as the gravity-inspired theories mature and overcome the challenge of projecting their powerful mathematical machinery onto the appropriate crystallographic lattice, so too will we hope to build with confidence a complete theory of strange metals as they emerge from the horizon of a black hole. Curved spacetime with a black hole in its interior and the strange metal arising on the boundary. This picture is based on the string theory gauge-gravity duality conjecture by J. Maldacena, which states that some strongly interacting quantum mechanical systems can be studied by replacing them with classical gravity in a spacetime in one higher dimension. The conjecture was made possible by thinking about some of the fundamental components of string theory, namely D-branes (the horseshoe-shaped object terminating on a flat surface in the interior of the spacetime). A key surprise of this conjecture is that aspects of condensed matter systems in which the electrons interact strongly—such as strange metals—can be studied using gravity.more » « less
-
A bstract We revisit the proposal that the ensemble average over free boson CFTs in two dimensions — parameterized by Narain’s moduli space — is dual to an exotic theory of gravity in three dimensions dubbed U(1) gravity. We consider flavored partition functions, where the usual genus g partition function is weighted by Wilson lines coupled to the conserved U(1) currents of these theories. These flavored partition functions obey a heat equation which relates deformations of the Riemann surface moduli to those of the chemical potentials which measure these U(1) charges. This allows us to derive a Siegel-Weil formula which computes the average of these flavored partition functions. The result takes the form of a “sum over geometries”, albeit with modifications relative to the unflavored case.more » « less
-
null (Ed.)Is change missing in Hamiltonian Einstein–Maxwell theory? Given the most common definition of observables (having weakly vanishing Poisson bracket with each first-class constraint), observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive electromagnetism with gauge freedom (‘Stueckelberg’) are inequivalent to those of massive electromagnetism without gauge freedom (‘Proca’). The alternative Pons–Salisbury–Sundermeyer definition of observables, aiming for Hamiltonian–Lagrangian equivalence, uses the gauge generator G, a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent observables for equivalent massive electromagnetisms. For General Relativity, G generates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time versus 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that G must generate the 4-dimensional Lie derivative (not 0) for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein–Maxwell theory? Pons, Salisbury and Shepley have studied G for Einstein–Yang–Mills. For Einstein–Maxwell, both 𝐹𝜇𝜈 and 𝑔𝜇𝜈 are invariant under electromagnetic gauge transformations and covariant (changing by a Lie derivative) under 4-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP10(2020)187
