The CTP Lunch Club meets at 12noon in the CTP Cosman seminar room every Friday (provided that there are sufficient speakers). A light lunch will be provided (usually pizza, however some other options may be explored).
The seminars are designed for graduate students and should be accessible to all students. First year students are particularly encouraged to attend so that they may learn about research being performed in the CTP.
Email notification of the club will be sent to the ctp-all, ctp-postdocs and ctp-students email lists as appropriate. If you wish to speak, or have suggestions about speakers and/or possible workshop topics, please contact the organizers: Asmund Folkestad, Stella Schindler and Yitian Sun.
Every function possesses an inherent topological property: the number of times it links about the x-axis in the three-dimensional space of its complex solution range crossed with its real domain. The up-and-down oscillations of entirely real-valued functions are a degenerate signature of this winding.
The eigenfunctions of Hermitian and unbroken PT-symmetric Schrodinger equations possess winding numbers that are well-ordered with respect to their eigenvalue number. As a system passes through PT-symmetry-breaking singular points, this order breaks down in a characteristic manner. Non-Hermitian systems lacking symmetries do not exhibit well-defined eigenfunction winding order.
Similarly, it is possible to map the relationship between an initial-value or parameter space of a differential-equation system to the winding numbers of the solutions to which each parameter gives rise. This topological structure aids in the understanding of certain nonlinear and partial differential equations.
Lattice QCD calculation of the proton charge radius
The proton charge radius has been measured experimentally using both muons and electrons as probes. The muonic measurements yield a smaller radius than electronic measurements, and the discrepancy is about five standard deviations — the threshold for new physics. Some have speculated about new beyond-the-Standard-Model muon-proton interactions that violate lepton universality.
To shed some light on this problem, it would be useful to have a Standard Model prediction for what the radius of the proton should be. While the equations that govern the strong interaction between quarks and gluons in the proton are known, they are computationally very difficult to solve. The strong coupling constant is too large to allow perturbation theory to work, and the only known non-perturbative method, lattice QCD, requires large supercomputers to perform a brute-force solution of the equations in a finite box.
For the past two years, I worked on a project to use lattice QCD to compute the proton charge radius from first principles. I will discuss my specific work as well as the broader theoretical and experimental context for the proton radius puzzle.
Modular conformal bootstrap
The modular conformal bootstrap is a technique to constrain CFT data defined on the torus in order to obtain universal bounds in the AdS_3 bulk. In this talk he will review basic facts about the conformal bootstrap approach, discuss recent progress by Dyer et al. in constraining theories with a U(1) conserved current, and describe ongoing work to improve on the results from Dyer et al. by endowing the modular partition function with an additional parity symmetry, as suggested by Anous et al..
*This week's seminar will start 1 hour earlier.
Variational Quantum Factoring
Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the capabilities of today's noisy intermediate-scale quantum (NISQ) devices. In this work, we revisit the problem of factoring, developing an alternative to Shor's algorithm, which employs established techniques to map the factoring problem to the ground state of an Ising Hamiltonian. The proposed variational quantum factoring (VQF) algorithm starts by simplifying equations over Boolean variables in a preprocessing step to reduce the number of qubits needed for the Hamiltonian. Then, it seeks an approximate ground state of the resulting Ising Hamiltonian by training variational circuits using the quantum approximate optimization algorithm (QAOA). We benchmark the VQF algorithm on various instances of factoring and present numerical results on its performance.
Recently there has been increased interest in so-called global higher-form symmetries. These are symmetries that act on objects supported on higher-dimensional manifolds. In the one-form case, these charged objects are line operators and there is an associated two-form conserved current. Using the recently developed formalism for effective field theories of hydrodynamics of Crossley, Glorioso, and Liu, we construct an effective action that describes a fluid of line operators. The hydrodynamic mode turns out to be a one-form gauge field. We study the system described by this effective action, both in the symmetry-preserving and symmetry-broken phases. In the symmetry broken phase, the effective action reduces to Maxwell theory and the photon emerges naturally as the Goldstone boson of the broken symmetry. In the symmetry-preserving phase, due to the vector nature of the charges, there are rich diffusion phenomena for the one-form symmetry including complex diffusion constants.
Memory effects in non-Abelian gauge theory
We review the color memory effect which is the non-abelian gauge theoretic analog of the gravitational memory effect, in which the passage of color radiation induces a net relative SU(3) color rotation of a pair of nearby quarks. Then, we show how the color memory effect arises in Regge limit scattering processes and propose that this effect can be measured in the Regge limit of deeply inelastic scattering at electron-ion colliders.
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