Scientific Series

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.

Tensor Models provide one of the calculationally simplest approaches to defining a partition function for random discrete geometries. The continuum limit of these discrete models then provides a background-independent construction of a partition function of continuum geometry, which are candadates for quantum gravity. The blue-print for this approach is provided by the matrix model approach to two-dimensional quantum gravity. The past ten years have seen a lot of progress using (un)colored tensor models to describe state sums if discrete geometries in more than two dimensions. However, so far one has not yet been able to find a continuum limit of these models that corresponds geometries with more than two continuum dimensions. This problem can be studied systematically using exact renormalization group techniques. In this talk I will report on joint work with Astrid Eichhorn, Antonio Perreira, Joseph Ben Geloun, Daniele Oriti, Johannes Lumma, Alicia Castro and Victor Mu\~noz in this direction. In a separate part of the talk I will explain that the renormalization group is not only a tool to help investigating the continuum limit, but that it in fact also provides a stand-alone approach to quantum gravity. In particular, I will show how scaling relations follow from cylidrical consistency relations.

We study the eigenstate properties of a nonintegrable spin chain that was recently realized experimentally in a Rydberg-atom quantum simulator. In the experiment, long-lived coherent many-body oscillations were observed only when the system was initialized in a particular product state. This pronounced coherence has been attributed to the presence of special "scarred" eigenstates with nearly equally-spaced energies and putative nonergodic properties despite their finite energy density. In this paper we uncover a surprising connection between these scarred eigenstates and low-lying quasiparticle excitations of the spin chain. In particular, we show that these eigenstates can be accurately captured by a set of variational states containing a macroscopic number of magnons with momentum π. This leads to an interpretation of the scarred eigenstates as finite-energy-density condensates of weakly interacting π-magnons. One natural consequence of this interpretation is that the scarred eigenstates possess long-range order in both space and time, providing a rare example of the spontaneous breaking of continuous time-translation symmetry. We verify numerically the presence of this space-time crystalline order and explain how it is consistent with established no-go theorems precluding its existence in ground states and at thermal equilibrium.

In string backgrounds with flux and branes, there are subtleties in identifying the independent, globally-defined degrees of freedom due to required gauge patching, which we illustrate with background flux. Work by Cariglia and Lechner (extending Dirac and Teitelboim) allows separation of D-brane and flux degrees of freedom without doubling the gauge sector in a democratic formalism. We review the Cariglia-Lechner formalism and adapt it for compactifications, point out some previously unremarked features, and give alternate derivations of some new terms in the 10D (and 11D) supergravity actions in the presence of branes. Along the way, we will discuss how to integrate gauge potentials that are only locally defined. Finally, we show how to find the independent degrees of freedom and derive their equations of motion.

In this talk, I will detail two ways to search for low-mass axion dark matter using cosmic microwave background (CMB) polarization measurements. These appear, in particular, to be some of the most promising ways to directly detect fuzzy dark matter. Axion dark matter causes rotation of the polarization of light passing through it. This gives rise to two novel phenomena in the CMB. First, the late-time oscillations of the axion field today cause the CMB polarization to oscillate in phase across the entire sky. Second, the early-time oscillations of the axion field wash out the polarization produced at last-scattering, reducing the polarized fraction (TE and EE power spectra) compared to the standard prediction. Since the axion field is oscillating, the common (static) ‘cosmic birefringence’ search is not appropriate for axion dark matter. These two phenomena can be used to search for axion dark matter at the lighter end of the mass range, with a reach several orders of magnitude beyond current constraints. I will present a limit from the washout effect using existing Planck results, and discuss the significant future discovery potential for CMB detectors searching in particular for the oscillating effect.

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