Advancing New Frontiers of Lattice Field Theory
David Schaich
University of Liverpool --- www.davidschaich.net
ukri-flf-annual-cohort-event-2020.ipostersessions.com/?s=08-04-DD-3A-82-65-B7-D0-8B-62-90-DD-73-05-ED-91
Presented at:

Context: Lattice field theory

Quantum field theory (QFT)

  • Governs fundamental constituents of the universe and how they interact
  • Combines quantum mechanics + special relativity

Lattice formulation

  • Replaces continuous space & time with finite grid of discrete points
  • Enables formal mathematical definiton of QFT
  • Provides numerical predictions from supercomputing --- especially important for strongly interacting systems

Fellowship project

My research applies lattice field theory to advance three inter-related new frontiers

www.davidschaich.net

OPEN

Frontier: Composite Higgs and composite dark matter

Hypothesis: Higgs boson or dark matter arise as composite particles produced by as-yet unknown strongly interacting QFT

Can explain currently mysterious aspects of these particles

Goal: Predictions for future experiments at Large Hadron Collider, dark matter detectors, gravitational wave observatories, etc.

Recent achievements

  • arXiv:2006.16429 on gravitational waves from composite dark matter, featuring open data release
  • arXiv:2007.01810 on first study of novel composite Higgs model
  • DiRAC proposal for additional supercomputing access under review
  • PhD student Felix Springer hired to research composite dark matter
OPEN

Frontier: Supersymmetry and holography

Holographic duality conjecture

Quantum gravity equivalent to supersymmetric QFT ⇾ non-perturbative definition from lattice field theory

Challenge: Discrete lattice space-time breaks supersymmetry

Goal: Develop and apply new lattice methods to test holographic duality and investigate quantum gravity

Recent achievements

OPEN

Frontier: Sign problems and quantum computing

Problem: Algorithms encounter negative (or complex) numbers where they expect probabilities between 0% and 100% ⇾ exponentially increasing computational costs to study quantum systems with non-quantum methods

Goal: Develop and apply quantum methods to investigate quantum systems

Requires complicated reformulation in terms of entangled qubits

Will work with emerging UK quantum industry to support technological advances

Recent achievements

OPEN

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