Theory Seminar

Reggeized scattering, entanglement and chaos using AdS/CFT

Abstract: 
 
The eikonalized parton-parton scattering amplitude at large energy and large impact parameter, is dominated by the exchange of a hyperbolic surface in walled AdS. Its analytical continuation yields a worldsheet instanton that is at the origin of the Reggeization of the amplitude and a thermal-like quantum entropy. I will construct the entangled density matrix following from the exchanged surface, and show that its von-Neumann entanglement entropy coincides with its thermal-like entropy. The ratio of the entanglement entropy to the transverse growth of the exchanged surface is similar to the Bekenstein entropy ratio for a black-hole, with a natural definition of saturation and the onset of chaos in high energy collisions. The largest eigenvalues of the entangled density matrix obey a cascade equation in rapidity, reminiscent of non-linear QCD evolution of wee-dipoles at low-x and weak coupling. We suggest that the largest eigenvalues describe the probability distributions of wee-quanta at low-x and strong coupling that maybe measurable at present and future hadron-hadron and lepton-hadron colliders. 
 
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Quantum black holes on the lattice

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Holography apparently relates certain quantum field theories to quantum theories of gravity. The original instance of this is Maldacena's duality between maximally supersymmetric gauge theories and type II string theory in the presence of D-branes. In the ’t Hooft limit, and at appropriate temperatures, the dual to the gauge theory is described by certain black holes (or rather black p-branes). This allows the remarkable opportunity to perform calculations of quantum black holes through the equivalent gauge theory, and to check the consistency of holographic duality. I will discuss such calculations, and the progress that has been made over the last decade in showing that the predicted gravity behaviour does indeed emerge from thermal gauge theory.

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Hot qubits on the horizon

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Perturbation theory for gravitating quantum systems tends to fail at very late times (a type of perturbative breakdown known as secular growth). We argue that gravity is best treated as a medium/environment in such situations, where reliable late-time predictions can be made using tools borrowed from quantum optics. To show how this works, we study the explicit example of a qubit hovering just outside the event horizon of a Schwarzschild black hole (coupled to a real scalar field) and reliably extract the late-time behaviour for the qubit state. At very late times, the so-called Unruh-DeWitt detector is shown to asymptote to a thermal state at the Hawking temperature.

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Mean string field theory

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Just as conventional global symmetries result in a conserved particle number, higher-form global symmetries are associated with a conserved density of higher dimensional objects, such as strings or branes. Many well-known systems possess such symmetries. I will present an overview of the applications of such symmetries and discuss the prospect of using them to enlarge the usual Landau classification of the phases of matter. I will then describe the construction of a continuum Landau-Ginzburg theory to describe the spontaneous breaking of a higher-form symmetry. As the order parameter is an operator that creates a string, the framework can be thought of as a kind of "mean string field theory" that provides a non-perturbative description where effective strings can be created and destroyed. I will argue that many aspects of higher form symmetries — including the phase structure, the behavior of line operators, and the dynamics of Goldstone modes — can be transparently understood in this framework. 

Recording: https://uky.zoom.us/rec/share/zizGB74KnjUaF_IsrJSURWKLjXz_Slwm1VJ-1qCtK…

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Quantum eigenstates from classical Gibbs distributions

Abstract:

 
I will discuss how the language of wave functions (state vectors) and associated non-commuting Hermitian operators naturally emerges from classical mechanics by applying the inverse Wigner-Weyl transform to the phase space probability distribution and observables. In this language, the Schrödinger equation follows from the Liouville equation, with ℏ now a free parameter. Classical stationary distributions can be represented as sums over stationary states with discrete (quantized) energies, where these states directly correspond to quantum eigenstates. Interestingly, it is now classical mechanics which allows for apparent negative probabilities to occupy eigenstates. This correspondence is particularly pronounced for canonical Gibbs ensembles, where classical eigenstates satisfy an integral eigenvalue equation that reduces to the Schrödinger equation in a saddle-point approximation controlled by the inverse temperature. This correspondence by showing that some paradigmatic examples such as tunneling, band structures, Berry phases, Landau levels, level statistics and quantum eigenstates in chaotic potentials can be reproduced to a surprising precision from a classical Gibbs ensemble, without any reference to quantum mechanics. At the end I will mention some unpublished results on emergence of negative probabilities and associated doubling of the Hilbert space, which is similar to emergence of spin degrees of freedom.
 

 

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Unitarity for AdS Loops

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According to the AdS/CFT correspondence, Witten diagrams in Anti-de Sitter space (AdS) compute 1/N corrections to correlators in a large-N conformal field theory (CFT). Despite recent progress, loop Witten diagrams are far less understood than their flat-space counterparts. We present unitarity methods to study Witten diagrams - one Lorentzian method and one Euclidean. In both approaches, we perform cuts of Witten diagrams that factorize them onto on-shell sub-diagrams. In the Lorentzian method, cuts turn Feynman propagators into on-shell propagators (Wightman functions), as in the standard S-matrix approach. In the Euclidean approach, Witten diagrams are recast as boundary conformal diagrams, and then cuts localize the result onto the expected multi-trace conformal blocks. The Lorentzian and Euclidean methods compute the CFT double-commutator, from which the correlator can be reconstructed. We discuss similar structure in holographic CFTs at finite temperature. Finally, we comment briefly on how these unitarity methods extend tree-level properties of AdS/CFT to loop level for other observables.

 

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The information paradox for cosmology

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The information paradox demands a large departure from semiclassical physics at the black hole horizon. We will develop a similar paradox for cosmology, which will tell us that new physics has to emerge at the scale of the cosmological horizon. For the black hole, the novel effects emerge from the dynamics of vecros: virtual fluctuations of fuzzball-like configurations; the large action for these fluctuations is compensated by the large degeneracy of possible fluctuations. In cosmology, one finds a new variable required to define the spacetime: the vecro distribution function (VDF), which affects dynamics at the scale of the cosmological horizon. We speculate on how the VDF may address the cosmological constant problem, provide a source for inflaton energy and the dark energy today.

 
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Entanglement entropy of energy eigenstates follows a universal scaling function

We consider the entanglement entropies of energy eigenstates in quantum many-

body systems. For the typical models that allow for a field-theoretical

description of the long-range physics, we find that the entanglement entropy of

(almost) all eigenstates is described by a single scaling function. This is

predicated on the validity of the weak or strong eigenstate thermalization

hypothesis (ETH), which then implies that the scaling functions can be deduced

from subsystem entropies of thermal ensembles. The scaling functions describe

the full crossover from the groundstate entanglement regime for low energies

and small subsystem size (area or log-area law) to the extensive volume-law

regime for high energies or large subsystem size. For critical 1d systems, the

scaling function follows from conformal field theory (CFT). We use it to also

deduce the scaling function for Fermi liquids in d>1 dimensions. These

analytical results are complemented by numerics for large non-interacting

systems of fermions in d=1,2,3 and the harmonic lattice model in d=1,2.

Lastly, we demonstrate ETH for entanglement entropies and the validity of the

scaling arguments in integrable and non-integrable interacting spin chains. In

particular, we analyze the XXZ and transverse-field Ising models with and

without next-nearest-neighbor interactions.



References: arXiv:1905.07760, arXiv:1912.10045, arXiv:2010.07265

 

Recording: https://uky.zoom.us/rec/share/GutjuSkIJLS-UsSxmZ398q4iwfWDv9MGu4laXKP0arl0VZafKmv5N4TZDQfZcSJa.FukSni-Fex-uv3lI

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The Return of the String

Two applications of worldsheet string theory illustrate the structure of string theory near the threshold of black hole formation.  In the first, we consider string probes of horizonless microstate geometries and find that strong tidal forces cause infalling strings to become trapped, mimicking the absorptive properties of black holes.  In the second, we re-examine the structure of (near) BPS microstates and find a mechanism whereby the geometrical description breaks down. 

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Long Range Processes in QCD

A rich variety of phenomena in the Standard Model and its extensions manifest in long-range processes involving bound states of quantum chromodynamics (QCD), namely hadrons. These are processes where intermediate hadronic states propagate over a long distance, between electroweak interactions. Examples include virtual Compton scattering and double-beta decay. Such processes are at the cusp of what can be systematically studied given two challenges. First, these reactions involve hadrons, and as a result one must use a non-perturbative tool to access their amplitudes. Currently lattice QCD is the only systematically improvable way we have for doing just this. Second, lattice QCD is defined in a finite, Euclidean spacetime. This introduces its own specific challenges, time in purely imaginary in lattice QCD, and by truncating the space one looses the notion of asymptotic states. In this talk I explain how these issues can all be resolved systematically for a relatively large kinematic region. In presenting the necessary formalism for doing this, I will summarize recent progress in lattice QCD in order to argue that the community is up to the challenge. 
 
 
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