Scientific Series

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The Bose-Hubbard model is QMA-complete

David Gosset
Institute for Quantum Computing (IQC)
December 18, 2013

PIRSA:13120067
Quantum Information
(0,4) sigma models and K3

Sarah Harrison
Stanford University
December 18, 2013

PIRSA:13120071
Quantum Fields and Strings
A lattice non-perturbative definition of chiral fermion/gauge theory from Topological Order

Juven Wang
Harvard University
December 13, 2013

PIRSA:13120069
Condensed Matter
Integrability (and Near Integrability) in Matrix-valued Field Theories

Axel Cortes Cubero
City University of New York (CUNY) - Department of Physics
December 13, 2013

PIRSA:13120068
Quantum Fields and Strings
Curvature in terms of entanglement

Achim Kempf
University of Waterloo
December 12, 2013

PIRSA:13120064
Quantum Gravity
holographic path to the turbulent side of gravity
- Adam Brown
  Stanford University
- Stephen Green
  University of Nottingham
December 12, 2013

PIRSA:13120066
Cosmology
Partially Massless Gravity
December 11, 2013

PIRSA:13120005
Cosmology
Rebuilding Mathematics on a Quantum Logical Foundation

Richard deJonghe
University of Illinois at Chicago
December 10, 2013

PIRSA:13120060
Quantum Foundations
Consistency of Massive Gravity

Lavinia Heisenberg
ETH Zurich
December 10, 2013

PIRSA:13120061
Cosmology
(0,2) Trialities

Abhijit Gadde
Stony Brook University
December 10, 2013

PIRSA:13120062
Quantum Fields and Strings
Compactifying de Sitter

Alex Dahlen
Princeton University
December 10, 2013

PIRSA:13120049
Cosmology
No GUTs, All Glory: Charge Quantization and the Standard Model from Nonlinear Sigma Models

John Kehayias
University of Tokyo
December 06, 2013

PIRSA:13120056
Particle Physics

The Bose-Hubbard model is QMA-complete

David Gosset
Institute for Quantum Computing (IQC)
December 18, 2013

PIRSA:13120067
Quantum Information
The Bose-Hubbard model is a system of interacting bosons that live on the vertices of a graph. The particles can move between adjacent vertices and experience a repulsive on-site interaction. The Hamiltonian is determined by a choice of graph that specifies the geometry in which the particles move and interact. We prove that approximating the ground energy of the Bose-Hubbard model on a graph at fixed particle number is QMA-complete. In our QMA-hardness proof, we encode the history of an n-qubit computation in the subspace with at most one particle per site (i.e., hard-core bosons). This feature, along with the well-known mapping between hard-core bosons and spin systems, lets us prove a related result for a class of 2-local Hamiltonians defined by graphs that generalizes the XY model. By avoiding the use of perturbation theory in our analysis, we circumvent the need to multiply terms in the Hamiltonian by large coefficients. This is joint work with Andrew Childs and Zak Webb.
(0,4) sigma models and K3

Sarah Harrison
Stanford University
December 18, 2013

PIRSA:13120071
Quantum Fields and Strings
TBA
A lattice non-perturbative definition of chiral fermion/gauge theory from Topological Order

Juven Wang
Harvard University
December 13, 2013

PIRSA:13120069
Condensed Matter
A non-perturbative definition of anomaly-free chiral fermions and bosons in 1+1D spacetime as finite quantum systems on 1D lattice is proposed. In particular, any 1+1D anomaly-free chiral matter theory can be defined as finite quantum systems on 1D lattice with on-site symmetry, if we include strong interactions between matter fields. Our approach provides another way, apart from Ginsparg-Wilson fermions approach, to avoid the fermion-doubling challenge. In general, using the defining connection between gauge anomalies and the symmetry-protected topological orders, we propose that any truly anomaly-free chiral gauge theory can be non-perturbatively defined by putting it on a lattice in the same dimension. As an additional remark, we conjecture/prove the equivalence relation between 't Hooft anomaly matching conditions and the boundary fully gapping rules.
Integrability (and Near Integrability) in Matrix-valued Field Theories

Axel Cortes Cubero
City University of New York (CUNY) - Department of Physics
December 13, 2013

PIRSA:13120068
Quantum Fields and Strings
The principal chiral sigma model (PCSM) in 1+1 dimensions is asymptotically free and has as SU(N)-valued field with massive excitations. We have found all the exact form factors and two-point function of the Noether-current operators at large N using the integrable bootstrap program. At finite N, only the first non-trivial form factors are found, which give a good long distance approximation for the two-point function. We show how to use these new exact results to study non-integrable deformations. One example is the PCSM coupled to a Yang-Mills field. One can approximate the spectrum of the meson-like bound states using our form factors. We also examine an anisotropic version of (2+1)-dimensional Yang-Mills theory, which can be interpreted as an array of coupled PCSM’s.
Curvature in terms of entanglement

Achim Kempf
University of Waterloo
December 12, 2013

PIRSA:13120064
Quantum Gravity
The entanglement of the quantum field theoretic vacuum state is affected by curvature. I ask if or under which conditions the curvature of spacetime can be expressed entirely in terms of the spatial entanglement structure of the vacuum. This would open up the prospect that general relativity could be formulated in quantum theoretic terms, which should then be helpful for studies in quantum gravity.
holographic path to the turbulent side of gravity
- Adam Brown
  Stanford University
- Stephen Green
  University of Nottingham
December 12, 2013

PIRSA:13120066
Cosmology
We study the dynamics of a 2+1 dimensional relativistic viscous conformal fluid in Minkowski spacetime. Such fluid solutions arise as duals, under the "gravity/fluid correspondence", to 3+1 dimensional asymptotically anti-de Sitter (AAdS) black brane solutions to the Einstein equation. We examine stability properties of shear flows, which correspond to hydrodynamic quasinormal modes of the black brane. We find that, for sufficiently high Reynolds number, the solution undergoes an inverse turbulent cascade to long wavelength modes. We then map this fluid solution, via the gravity/fluid duality, into a bulk metric. This suggests a new and interesting feature of the behavior of perturbed AAdS black holes and black branes, which is not readily captured by a standard quasinormal mode analysis. Namely, for sufficiently large perturbed black objects (with long-lived quasinormal modes), nonlinear effects transfer energy from short to long wavelength modes via a turbulent cascade within the metric perturbation. As long wavelength modes have slower decay, this lengthens the overall lifetime of the perturbation. We also discuss various implications of this behavior, including expectations for higher dimensions, and the possibility of predicting turbulence in more general gravitational scenarios."
Partially Massless Gravity
December 11, 2013

PIRSA:13120005
Cosmology
On de Sitter space, there exists a special value for the mass of a graviton for which the linear theory propagates 4 rather than 5 degrees of freedom. If a fully non-linear version of the theory exists and can be coupled to known matter, it would have interesting properties and could solve the cosmological constant problem. I will describe evidence for and obstructions to the existence of such a theory.
Rebuilding Mathematics on a Quantum Logical Foundation

Richard deJonghe
University of Illinois at Chicago
December 10, 2013

PIRSA:13120060
Quantum Foundations
It is not unnatural to expect that difficulties lying at the foundations of quantum mechanics can only be resolved by literally going back and rethinking the quantum theory from first principles (namely, the principles of logic). In this talk, I will present a first-order quantum logic which generalizes the propositional quatum logic originated by Birkhoff and von Neumann as well as the standard classical predicate logic used in the development of virtually all of modern mathematics. I will then use this quantum logic to begin to build the foundations of a new ``quantum mathematics'' --- in particular a quantum set theory and a quantum arithmetic --- which has the potential to provide a completely new mathematical framework in which to develop the theory of quantum
mechanics.
Consistency of Massive Gravity

Lavinia Heisenberg
ETH Zurich
December 10, 2013

PIRSA:13120061
Cosmology
Recently there has been a successful non-linear covariant ghost-free generalization of Fierz-Pauli massive gravity theory, the dRGT theory. I will explore the cosmology in the decoupling limit of this theory. Furthermore, I will construct a Proxy theory to dRGT from the decoupling limit and study the cosmology there as well and compare the results. Finally, I will discuss the quantum consistency of the theory.
(0,2) Trialities

Abhijit Gadde
Stony Brook University
December 10, 2013

PIRSA:13120062
Quantum Fields and Strings
Motivated by the connection between 4-manifolds and 2d N=(0,2) theories, we study the dynamics of a fairly large class of 2d N=(0,2) gauge theories. We see that physics of such theories is very rich, much as the physics of 4d N=1 theories. We discover a new type of duality that is very reminiscent of the 4d Seiberg duality. Surprisingly, the new 2d duality is an operation of order three. We study the low energy physics and use elliptic genus to detect dynamical supersymmetry breaking.
Compactifying de Sitter

Alex Dahlen
Princeton University
December 10, 2013

PIRSA:13120049
Cosmology
TBA
No GUTs, All Glory: Charge Quantization and the Standard Model from Nonlinear Sigma Models

John Kehayias
University of Tokyo
December 06, 2013

PIRSA:13120056
Particle Physics
I will present recent and ongoing work in collaboration with Tsutomu Yanagida and Simeon Hellerman (arXiv:1309.0692 and 1312.xxxx) on a new way to obtain charge quantization, without a GUT or monopole solution. In the CP^1 model, SU(2)_G/U(1)_H, consistency conditions for a charged field and its transformation properties over the entire group manifold lead to a charge quantization condition. By gauging the U(1)_H and identifying it with hypercharge, we find charge quantization in the SM without a monopole or GUT, purely from the structure and dynamics of the nonlinear sigma model. This is easily extended to CP^2 and general CP^k models. Phenomenologically, the CP^1 model has a fractionally charged stable Nambu-Goldstone boson (NGB), which has intriguing applications to nuclear physics and dark matter. The CP^2 model has the Higgs as the NGB. With some additional minor assumptions, anomaly freedom then leads to the matter content of a generation in the SM.

Title	Speaker(s)	Date	Talk Type	Info link
The Bose-Hubbard model is QMA-complete	David Gosset	2013-12-18	Scientific Series	View details
(0,4) sigma models and K3	Sarah Harrison	2013-12-18	Scientific Series	View details
A lattice non-perturbative definition of chiral fermion/gauge theory from Topological Order	Juven Wang	2013-12-13	Scientific Series	View details
Integrability (and Near Integrability) in Matrix-valued Field Theories	Axel Cortes Cubero	2013-12-13	Scientific Series	View details
Curvature in terms of entanglement	Achim Kempf	2013-12-12	Scientific Series	View details
holographic path to the turbulent side of gravity	Adam Brown, Stephen Green	2013-12-12	Scientific Series	View details
Partially Massless Gravity		2013-12-11	Scientific Series	View details
Rebuilding Mathematics on a Quantum Logical Foundation	Richard deJonghe	2013-12-10	Scientific Series	View details
Consistency of Massive Gravity	Lavinia Heisenberg	2013-12-10	Scientific Series	View details
(0,2) Trialities	Abhijit Gadde	2013-12-10	Scientific Series	View details
Compactifying de Sitter	Alex Dahlen	2013-12-10	Scientific Series	View details
No GUTs, All Glory: Charge Quantization and the Standard Model from Nonlinear Sigma Models	John Kehayias	2013-12-06	Scientific Series	View details

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