Emergent properties of space-time

20 Jun 2016, 09:00 → 1 Jul 2016, 18:00 Europe/Zurich

TH Theory Conference Room (CERN)

Agostino Patella (CERN and University of Plymouth (GB)), David Zueco (University of Zaragoza), Diego Blas Temino (CERN), Kyriakos Papadodimas (CERN), Oriol Pujolas (IFAE, Spain), Sergey Sibiryakov (CERN & EPFL & INR RAS)

The low-energy dynamics of physical systems often exhibit nontrivial emergent phenomena. Among them, those related to the properties of space-time, such as enhanced symmetries and emergent geometry, have a special status. 

Recently there has been a lot of interest in their systematic study. This is largely due to the development of tools to handle strong dynamics, where these phenomena occur most efficiently. The different methods range from lattice theory and quantum simulation to non-perturbative characterization of scale invariant field theories (relativistic and non-relativistic) and gauge/gravity duality. 

The purpose of the TH Institute is to bring together researchers in the fields of Quantum
field theory (FT), Conformal FT, Lattice FT, Holography, Condensed Matter and Quantum Mechanics interested in the following broad topics:

• Emergence of space-time symmetries (Poincarè, SUSY, conformal...) in the context of Lattice Field Theories, Quantum Gravity, Condensed Matter Systems and Quantum Simulators
• Renormalization group flows in non-relativistic theories
• Quantum and classical simulations for generic RG flows
• Emergent geometry in the context of Holography and Discrete Systems
• Emergent phenomena at zero and nonzero density/temperature

We plan to have a fairly relaxed daily schedule (two or three talks per day), in order to have plenty of time for discussions.

Key-speakers include:

• John Donoghue
• Ben Freivogel
• Leonardo Giusti
• Igor Herbut
• Diego Hofman
• Petr Hořava
• Etsuko Itou
• Jared Kaplan 
• Jose Ignacio Latorre
• Sunk-Sik Lee
• Stefano Liberati
• Renata Loll 
• Juan Maldacena
• Yannick Meurice
• Javier Molina-Vilaplana
• Román Orús
• Fernando Patawski
• Joao Penedones
• Jörg Schmiedmayer 
• Marco Serone
• Dam Than Son
• Julian Sonner
• Xiao-Gang Wen 
• Cenke Xu

* TBC

Cern_2016.pdf

Cern_2016.pptx

Monday 20 June

Registration

1 On the metric theory of gravity

I plan to use the introduction to review some past work on emergent symmetries. But then in the spirit of the workshop I will describe some ongoing work on a pathway to describe why general relativity appears as a metric theory, without initially making that assumption.

Speaker: John Donoghue (Unknown)

CERN Emergent - Donoghue.pdf

15:00 Coffee break

2 Causal Dynamical Triangulations: The emergence of spacetime

Causal Dynamical Triangulations (CDT) is a candidate theory for quantum gravity, formulated nonperturbatively as scaling limit of a lattice theory in terms of triangulated spacetimes. I will describe briefly the rationale behind this approach and its ingredients, and will then summarize the status quo of what we have learned so far about its phase structure and dynamical behaviour, focusing mostly on the physical case of four spacetime dimensions.

Speaker: Renata Loll

CERN2016.pdf

16:30 Discussion

Tuesday 21 June

3 Emergent stable (2+1)d conformal field theory at the boundary of a class of (3+1)d symmetry protected topological phases

By definition, a d-dimensional symmetry protected topological (SPT) phase must have nontrivial d-1 dimensional boundary states. The boundary of a large class of (3+1)d SPT phases can be described by a (2+1)d nonlinear sigma model (NLSM) with a topological Wess-Zumino-Witten (WZW) term. We will demonstrate that a stable strongly interacting (2+1)d conformal field theory (CFT) could emerge in the quantum disordered phase in this boundary system, due to the existence of the WZW term. This CFT is stable in the sense that any symmetry allowed perturbation will be irrelevant. In order to perform a controlled calculation, we choose to study the NLSM whose target manifold is the Grassmannian U(N)/[U(n) x U(N-n)], which permits a WZW term in (2+1)d for any N and fixed n, and hence permits a large-N generalization. Through a large-N, large-k, and epsilon generalization of this model, we indeed identify a stable CFT fixed point in the quantum disordered phase through a (quasi) controlled renormalization group calculation.

Speaker: Cenke Xu

Cern_2016.pdf

Cern_2016.pdf

Cern_2016.pptx

11:00 Coffee break

4 A Higher­-Spin Theory of the Magneto­-Rotons

Fractional quantum Hall liquids exhibit a rich set of excitations, the
lowest-energy of which are the magneto-rotons with dispersion minima
at finite momentum. We propose a theory of the magneto-rotons on the
quantum Hall plateaux near half filling, namely, at filling fractions
$\nu=N/(2N+1)$ at large $N$. The theory involves an infinite number
of bosonic fields arising from bosonizing the fluctuations of the
shape of the composite Fermi surface. At zero momentum there are
$O(N)$ neutral excitations, each carrying a well-defined spin that
runs integer values 2, 3,... The mixing of modes at nonzero momentum
$q$ leads to the characteristic bending down of the lowest excitation
and the appearance of the magneto-roton minima. A purely algebraic
argument show that the magneto-roton minima are located at
$q\ell_B=z_i/(2N+1)$, where $\ell_B$ is the magnetic length and $z_i$
are the zeros of the Bessel function $J_1$, independent of the
microscopic details.

Speaker: Dam Than Son

cern-all.pdf

14:00 Discussion

18:30 Reception

Wednesday 22 June

5 Overview: from qubits to space­-time

In this talk I will make an overview of how space-time properties emerge from the entanglement structure of many-body wavefunctions. I will mainly focus on the connection between Entanglement Renormalization and AdS/CFT, but I will mention briefly other topics such as the appearance of spin networks in symmetric tensor networks, and the definition of "entanglement Hamiltonians" through a bulk-boundary correspondence for Projected Entangled Pair States. I will also discuss several open questions along these directions.

Speaker: Román Orús

CERN2016_Orus.pdf

11:00 Coffee break

6 Emergence of bulk locality in the gauge/gravity duality

Speaker: Ben Freivogel (University of California at Berkeley)

7 Emergence of Symmetries from Entanglement

Maximal Entanglement appears to be a key ingredient for the emergence
of symmetries. We first illustrate this phenomenon using two examples:
the emergence of conformal symmetry in condensed matter systems
and the relation of tensor networks to holography. We further present
a Principle of Maximal Entanglement that seems to dictate to a large
extend the structure of gauge symmetry.

Speaker: José Ignacio Latorre (Universitat Barcelona)

15:00 Coffee break

15:30 Discussion

Thursday 23 June

8 Quantum Quenches and Black Hole Formation at large c

Holography allows us to formulate questions about quantum gravity in terms of more ordinary quantum field theories without gravity. A natural and long-standing goal has been to understand the physics of black holes using holographic duality. I will report on some recent progress on this question formulating the spherical collapse of an in-falling shell of null matter in three dimensions in terms of a first-principles CFT calculation. I will argue that the apparent loss of information in the CFT can be traced back to late-time non-perturbative effects in an expansion in large central charge.

Speaker: Julian Sonner (Universite de Geneve (CH))

BHCollapseCERNtheoryinstitute.pdf

11:00 Coffee break

9 On Information Loss in Two-­Dimensional CFT

We discuss information loss from black hole physics
in AdS_3, focusing on two sharp signatures infecting CFT_2 correlators
at large central charge c: 'forbidden singularities' arising from
Euclidean-time periodicity due to the effective Hawking temperature,
and late-time exponential decay in the Lorentzian region. We study an
infinite class of examples where forbidden singularities can be
resolved by non-perturbative effects at finite c, and we show that the
resolution has certain universal features that also apply in the
general case. Analytically continuing to the Lorentzian regime, we
find that the non-perturbative effects that resolve forbidden
singularities qualitatively change the behavior of correlators at
times t~S_BH, the black hole entropy. This may resolve the exponential
decay of correlators at late times in black hole backgrounds. By Borel
resumming the 1/c expansion of exact examples, we explicitly identify
'information-restoring' effects from heavy states that should
correspond to classical solutions in AdS_3. Our results suggest a line
of inquiry towards a more precise formulation of the gravitational
path integral in AdS_3.

Speaker: Jared Kaplan (SLAC)

TALKInformationLossAdS3CFT2CERNOfficial.pdf

10 Nonrelativistic Naturalness and the Higgs

Speaker: Petr Horava (University of California, Berkeley)

15:00 Coffee Break

15:30 Discussion

Friday 24 June

11 S­-matrix from the Conformal Bootstrap

We consider QFT in hyperbolic space and study correlation functions of operators inserted at the conformal boundary. By construction, these observables transform like correlation functions of a lower dimensional Conformal Field Theory. We then apply conformal bootstrap techniques to find universal bounds on the mass spectrum and scattering amplitudes of the QFT. The AdS/CFT correspondence extends this holographic description of QFT to quantum gravity. We comment on how the conformal bootstrap can been used to derive universal properties of quantum gravity.

Speaker: Joao Miguel Penedones (Universidade do Porto (PT))

11:00 Coffee break

12 Horizon as critical phenomenon

We show that renormalization group flow can be viewed as a gradual wave
function collapse, where an initial state associated with the action of
field theory evolves toward a final state that describes an IR fixed
point. The process of collapse is described by the radial evolution in
the dual holographic theory. If the theory is in the same phase as the
assumed IR fixed point, the initial state is smoothly projected to the
final state. On the other hand, the initial state can not be smoothly
projected to the final state, if the system is in a different phase.
Obstructions to smooth projection appear as dynamical phase transitions,
which in turn give rise to horizons in the bulk geometry. We demonstrate
the connection between critical behavior and horizon in an example, by
deriving the bulk metrics that emerge in various phases of the U(N)
vector model in the large N limit based on the holographic dual
constructed from quantum renormalization group.

Speaker: Sunk-Sik Lee

Horizon_CERN_2016.pdf

Celebrating Supergravity at 40: TBA

https://indico.cern.ch/event/527162/

Monday 27 June

13 Entanglement Renormalization and Two Dimensional String Theory

Recently, new tools coming from quantum information theory have been used to understand the way spacetime could emerge from underlying microscopic building blocks. These tools allow to systematically analyze the structure of the quantum correlations in the quantum states of quantum many body systems in condensed matter and quantum field theories. Remarkably, it has been hypothesized that they could provide relevant insights into the physics of black holes, horizons and emergent spacetimes.
In this talk, I will first briefly review on one of these tools known as Entanglement Renormalization Tensor Networks, in both its discrete and continuous versions. Then I will present some recent results in which the entanglement renormalization flow of a (1+1) free boson is formulated as a path integral over some auxiliary scalar fields. It will be shown how the resulting effective theory for these fields amounts to the dilaton term of non-critical string theory in two spacetime dimensions. A connection between the scalar fields in these two theories will be provided. The results might help to understand how spacetimes may emerge from distributions of quantum states, or more concretely, from the structure of the quantum entanglement concomitant to those distributions, allowing to acquire novel insights into how a theory of gravity emerges from the entanglement structure of another one without gravity.
I will conclude mentioning a list of relevant challenges in the field.

Speaker: Javier Molina-Vilaplana

CERN_EMERGENT16_Molina.pdf

11:00 Coffee break

14 Classical and Quantum Computing near Conformality

We reformulate the O(2) model with a chemical potential and the Abelian Higgs model using the
Tensor Renormalization Group method (both on a 1+1 space-time lattice).
The reformulation allows exact blocking, is manifestly gauge invariant and connects smoothly the classical Lagrangian formulation
used by lattice gauge theorists to the quantum Hamiltonian method commonly used in condensed matter.
We calculate the entanglement entropy in the superfluid phase of the O(2) model and show that it obeys the Cardy scaling (c/3)*Ln(L).
We calculate the Polyakov loop in the Abelian Higgs model and discuss the possibility of a deconfinement transition at finite volume.
We propose to use Bose-Hubbard (BH) Hamiltonians with two species as quantum simulators for these models.
Using degenerate perturbation theory, we obtain effective Hamiltonians resembling those relevant for the two models discussed above.
We propose optical lattice implementations of these BH Hamiltonians.

Speaker: Yannick Meurice (University of Iowa)

MeuriceCern16.pdf

15 Relaxation and the emergence of thermalization in an isolated many body quantum systems

Speaker: Jörg Schmiedmayer

15:00 Coffee Break

15:30 Discussion

Tuesday 28 June

16 Emergent symmetries and lack thereof at quantum critical points in semimetals

I will review recent work on quantum criticality in three-dimensional gapless semiconductors, which feature quadratic band crossing at the fermi level. These rather ubiquitous systems, such as gray tin and mercury telluride, feature only a Galilean (z=2) invariance at low energies, and should exhibit interesting new phases and transitions as a result of electron-electron and electron-phonon interactions. I will discuss how the phenomenon of fixed point collision replaces the putative Abrikosov's scale-invariant phase with a nematic insulator at low energies, with the former phase leaving a trace in the characteristic separation of scales that ensues. A sufficiently strong electron-phonon interaction, on the other hand, leads to a quantum critical point with emergent particle-hole and rotational symmetries, but also with a non-integer dynamical critical exponent, at which the system develops s-wave superconducting order.

Speaker: Igor Herbut (Simon Fraser University)

CERN12016.pdf

11:00 Coffee break

17 A unification of information and matter and a solution of chiral fermion problem

Speaker: Xiao-Gang Wen

16Cern.pdf

15:15 Discussion

Wednesday 29 June

18 Quantum error correction and the information structure of holography

In this talk I will take a quantum information perspective of static holography motivated by AdS/CFT yet agnostic of the underlying theory.
This approach follows the recent trend of deriving the geometry of space from the entanglement structure of a critical boundary theory.
I will provide explicit examples of how these properties may be realized by QECCs obtained from tensor network constructions.
A particular driving principle for these constructions will be the subregion-subregion duality and the entanglement wedge hypothesis.

Speaker: Fernando Pastawski

Pastawski.pdf

11:00 Coffee break

19 Proof of central charge bounds

I will discuss a proof of bounds for central charges in unitary CFTs using crossing symmetry and its implication for the average null energy condition.

Speaker: Diego Hofman (Princeton University)

20 Emergent conformal symmetry in quantum mechanics and black holes

Speaker: Juan Maldacena (Unknown)

EmergenceCern2016.pdf

15:00 Coffee break

15:30 Discussion

18:30 Good bye drinks

Thursday 30 June

21 Non­-perturbative definition of the energy­-momentum tensor on the lattice

By enforcing suitable relations associated to the Poincar\'e invariance
of the continuum theory, it is possible to define an energy-momentum
tensor on the lattice which satisfies the appropriate Ward Identites and
has the right trace anomaly in the continuum limit. The renormalization
conditions come forth when the length of the box in the temporal direction
is finite, and they take a particularly simple form if the coordinate and
the periodicity axes of the lattice are not aligned. I show an implementation
of these ideas for the SU(3) Yang--Mills theory discretized with the standard
Wilson action in the presence of shifted boundary conditions in the (short)
temporal direction. By carrying out extensive numerical simulations, the
renormalization constants of the traceless components of the tensor are
determined with a precision of roughly half a percent for values of the bare
coupling constant in the useful range 0<g<1.

Speaker: Leonardo Giusti (Universita & INFN, Milano-Bicocca (IT))

lgiusti_CERN.pdf

11:00 Coffee break

22 Conformal field theory and energy­-momentum tensor on the lattice

Some non-abelian gauge theories coupled with many massless fermions show the conformal behavior in the low energy limit.
The range of the number of fermions, where the theory has the nontrivial infrared fixed point, is called “conformal window".
Recent lattice studies confirm the existence of the conformal window from the first-principle calculation, and clarify those conformal properties, e.g. the scaling behavior, the values of the anomalous dimension and the other critical exponents.
In this talk, I briefly review of these recent lattice works.
Next, one of the important tasks is to determine the central charge of the conformal field theory nonperturbatively.
An approach to this aim is give by the calculation of the multi-point function of the energy-momentum tensor.
However, to calculate EMT using the lattice simulations is a nontrivial task due to the explicit breaking of the Poincaré invariance on the lattice.
I also introduce the recent challenges to calculate the energy-momentum tensor using the lattice gauge theory on the basis of the Yang-Mills gradient flow is proposed.
Furthermore, I may show alternative trial to determine the central charge, namely the measurement of the entanglement within the lattice simulations, if I have a time.

Speaker: Etsuko Itou (Kyoto University, YITP)

EtsukoItou.pdf

14:00 Discussion

Friday 1 July

23 The Effective Bootstrap

We study the numerical bounds obtained using a conformal-bootstrap method where different points in the plane of conformal cross ratios are sampled. In contrast to previous methods, we can consistently integrate out" higher-dimensional operators and get a reduced simpler, and faster to solve, set of bootstrap equations. We test theeffective" bootstrap by studying the 3D Ising and O(n) vector models and bounds on generic 4D CFTs,
for which extensive results are available in the literature.

Speaker: Marco Serone (SISSA)

Serone.pdf

11:00 Coffee break

24 Emergent gravity: From Condensed matter analogues to Phenomenology

Analogue models of gravity have proved in the past formidable tool for testing quantum field theory in curved spacetime and the robustness of its phenomenology against UV physics.
However, they can be also used as toy models for emergent gravity scenarios. In this talk I will discuss a few lessons which can be learned from these models and consider some of their phenomenological implications amenable to observational or experimental tests in the near future.

Speaker: Stefano Liberati (SISSA)

CERN-EG-2016.pdf