Scientific Series

We derive Born’s rule and the density-operator formalism for quantum systems with Hilbert spaces of finite dimension. Our extension of Gleason’s theorem only relies upon the consistent assignment of probabilities to the outcomes of projective measurements and their classical mixtures. This assumption is significantly weaker than those required for existing Gleason-type theorems valid in dimension two.

This talk is about a new type of string theory with a non-relativistic conformal field theory on the world-sheet, as well as a non-relativistic target space geometry. Starting with the relativistic Polyakov action with a fixed momentum along a non-compact null-isometry, we can take a scaling limit that gives the non-relativistic string, including an interesting intermediate step. This can in particular be applied to a string on AdS5 x S5. In this case the scaling limit realizes a limit of AdS/CFT that on the field theory side gives a quantum mechanical theory known as Spin Matrix theory. We review that Spin Matrix theory is a finite-N version of nearest neighbor spin chains, from which one can find a long-wavelength semi-classical description using sigma-model such as the Landau-Lifshitz sigma-model. Hence, we can show that both sides of the AdS/CFT gives, in this limit, equivalent non-relativistic sigma-models that we are able to write down in a fully covariant manner, and show that it has a non-relativistic local symmetry that realizes the Galilean Conformal Algebra (GCA). This suggests that one has a holographic duality between the quantum mechanical theory of Spin Matrix theory, and the non-relativistic string. This could provide a more tractable holographic duality in which one can study the emergence of non-relativistic strings, geometry and gravity.

We present the complete history of structure formation in a simple dissipative dark-sector model. The model has only two particles: a dark electron and a dark photon. Dark-electron perturbations grow from primordial overdensities, become non-linear, and form dense, dark galaxies. We show that asymmetric dark stars and black holes form within the Milky Way from the collapse of dark electrons. These exotic compact objects may be detected and their properties measured at new high-precision astronomical observatories, giving insight into the particle nature of the dark sector without the requirement of non-gravitational interactions with the visible sector.

Fundamental physics traditionally views the dynamical laws governing the world as time reversal invariant. The evident arrow of time of nature is then held to be an accident, emerging as we coarse grain and originating in the improbable choice of initial conditions. The main pillar which supports this time-symmetric lifestyle is the fluctuation-dissipation theorem, which connects purely time-symmetric microscopic equations to the emergence of a macroscopic arrow of thermodynamics. I will describe arguments from statistical physics claiming that existing proofs of this theorem are faulty and do not demonstrate the emergence of an arrow from time-symmetric laws. I will argue that, as a result of this assumption of time symmetry, we cosmologists stand to pay an unreasonable price concerning what we’re expected to explain. I argue for instead to turn this picture around and propose a fundamental theory of cosmology and quantum gravity which is fundamentally time asymmetric and based on time-irreversible laws. I will describe a new class of models of quantum space-time, energetic causal sets, in which space-time itself, as well as aspects of quantum theory, emerge under natural conditions. The framework is based on arXiv:1307.6167 and subsequent papers in collaboration with Lee Smolin.

Strominger-Yau-Zaslow explained mirror symmetry via duality between tori.  There have been a lot of recent developments in the SYZ program, focusing on the non-equivariant setting.  In this talk, I explain an equivariant construction and apply it to toric Calabi-Yau manifolds.  It has a close relation to the equivariant open GW invariants found by Aganagic-Klemm-Vafa and studied by Katz-Liu, Graber-Zaslow and many others.

2D CFTs have an infinite set of commuting conserved charges, known as the quantum KdV charges. There is a generalised Gibbs ensemble for these theories where we turn on chemical potentials for these charges. I will describe some partial results on calculating this partition function, both in the limit of large charges and perturbatively in the chemical potentials. 

The partition function of three-dimensional N=2 SCFTs on circle bundles of closed Riemann surfaces \Sigma_g was recently computed via supersymmetric localization. In this talk I will describe supergravity solutions having as conformal boundary such circle bundle. These configurations are solutions to N=2 minimal gauged supergravity in 4d and pertain to the class of AdS-Taub-NUT and AdS-Taub-Bolt preserving 1/4 of the supersymmetries. I will discuss the conditions for the uplift of these solutions to M-theory and I provide the expression for the on-shell action of the Bolt solutions, computed via holographic renormalization. I will show that, when the uplift condition is satisfied, the Bolt free energy matches with the large N limit of the partition function of the corresponding dual field theory. I will finally comment on possible subtleties that arise in our framework when a given boundary geometry admits multiple bulk fillings.

What is the black hole in quantum mechanics? We examine this problem in a self-consistent manner. First, we analyze time evolution of a 4D spherically symmetric collapsing matter including the back reaction of particle creation that occurs in the time-dependent spacetime. As a result, a compact high-density star with no horizon or singularity is formed and eventually evaporates. This is a quantum black hole. We can construct a self-consistent solution of the semi-classical Einstein equation showing this structure. In fact, we construct the metric, evaluate the expectation values of the energy momentum tensor, and prove the self-consistency under some assumptions. Large pressure appears in the angular direction to support this black hole, which is consistent with 4D Weyl anomaly. When the black hole is formed adiabatically in the heat bath, integrating the entropy density over the interior volume reproduces the area law. 

One of the central problems in the study of quantum resource theories is to provide a given resource with an operational meaning, characterizing physical tasks relevant to information processing in which the resource can give an explicit advantage over all resourceless states. We show that this can always be accomplished for all convex resource theories. We establish in particular that any resource state enables an advantage in a channel discrimination task, allowing for a strictly greater success probability than any state without the given resource. Furthermore, we find that the generalized robustness measure serves as an exact quantifier for the maximal advantage enabled by the given resource state in a class of subchannel discrimination problems, providing a universal operational interpretation to this fundamental resource quantifier. 

Next, we significantly extend the above consideration beyond "quantum" resource theories of "states"; we establish an operational characterization of general convex resource theories --- describing the resource content of not only states, but also measurements and channels, both within quantum mechanics and in general probabilistic theories (GPTs) --- in the context of state and channel discrimination. We find that discrimination tasks provide a unified operational description for quantification and manipulation of resources by showing that the family of robustness measures can be understood as the maximum advantage provided by any physical resource in several different discrimination tasks, as well as establishing that such discrimination problems can fully characterize the allowed transformations within the given resource theory. Our results establish a fundamental connection between the operational tasks of discrimination and core concepts of resource theories --- the geometric quantification of resources and resource manipulation --- valid for all physical theories beyond quantum mechanics with no additional assumptions about the structure of the GPT required.

References: 

[1] Ryuji Takagi, Bartosz Regula, Kaifeng Bu, Zi-Wen Liu, and Gerardo Adesso, "Operational Advantage of Quantum Resources in Subchannel Discrimination", Phys. Rev. Lett. 122.140402 (2019)

[2] Ryuji Takagi and Bartosz Regula, "General resource theories in quantum mechanics and beyond: operational characterization via discrimination tasks", arXiv: 1901.08127

Melonic tensor model is a new type of solvable model, where the melonic Feynman diagrams dominate in the large N limit. The melonic dominance, as well as the solvability of the model, relies on a special type of interaction vertex, which generically would not be preserved under renormalization group flow. I will discuss a class of 2d N=(2,2) melonic tensor models, where the non-renormalization of the superpotential protects the melonic dominance. Another important feature of our models is that they admit a novel type of deformations which gives a large IR conformal manifold. At generic point of the conformal manifold, all the flavor symmetries (including the O(N)^{q-1} symmetry) are broken and all the flat directions in the potential are lifted. I will also discuss how the operator spectrum and the chaos exponent depend on the deformation parameters.

In 1997, Kontsevich gave a universal solution to the "deformation quantization" problem in mathematical physics: starting from any Poisson manifold (the classical phase space), it produces a  noncommutative algebra of quantum observables by deforming the ordinary multiplication of functions.  His formula is a Feynma  expansion, involving an infinite sum over graphs, weighted by volume integrals on the moduli space of marked holomorphic disks. The precise values of these integrals are currently unknown.  I will describe recent joint work with Banks and Panzer, in which we develop a theory of integration on these moduli spaces via suitable sheaves of polylogarithms, and use it to prove that Kontsevich's integrals evaluate to integer-linear combinations of special transcendental constants called multiple zeta values, yielding the first algorithm for their calculation.

Kitaev materials — spin-orbit assisted Mott insulators, in which local, spin-orbit entangled j=1/2 moments form that are subject to strong bond-directional interactions — have attracted broad interest for their potential to realize spin liquids. Experimentally, a number of 4d and 5d systems have been widely studied including the honeycomb materials Na2IrO3, α-Li2IrO3, and RuCl3 as candidate spin liquid compounds — however, all of these materials magnetically order at sufficiently low temperatures. In this talk, I will discuss the physics of Kitaev materials that plays out when applying magnetic fields. Experiments on RuCl3 indicate the formation of a chiral spin liquid that gives rise to an observed quantized thermal Hall effect. Conceptually, this asks for a deeper understanding of the physics of the Kitaev model in tilted magnetic fields. I will report on our recent numerical studies that give strong evidence for a Higgs transition from the well known Z2 topological spin liquid to a gapless U(1) spin liquid with a spinon Fermi surface and put this into perspective of experimental studies.