Triangle Seminars

Abstract:
In recent years, the discovery of integrable sectors of string theory has expanded the range of models which are solvable by the techniques of the Bethe ansatz and by the general theory of quantum groups. In this talk, we will give an overview of the S-matrix theory involved in the solution of these models, with mention to the problem of massless particles emerging in a particular instance of the AdS/CFT correspondence.

Abstract:
The Riemann hypothesis asserts that the nontrivial zeros of the Riemann zeta function should be of the form 1/2 + i E_n, where the set of numbers {E_n} are real. The so-called Hilbert-Pólya conjecture assumes that {E_n} should correspond to the eigenvalues of an operator that is Hermitian. The discovery of such an operator, if it exists, thus amounts to providing a proof of the Riemann hypothesis. In 1999 Berry and Keating conjectured that such an operator should correspond to a quantisation of the classical Hamiltonian H = xp. Since then, the Berry-Keating conjecture has been investigated intensely in the literature, but its validity has remained elusive up to now. In this talk I will derive a "Hamiltonian" (a differential operator), whose classical counterpart is H = xp, having the property that with a suitable boundary condition on its eigenstates, the eigenvalues {E_n} correspond to the nontrivial zeros of the Riemann zeta function. This Hamiltonian is not Hermitian, but is symmetric under space-time reflection (PT symmetric) in a special way. A formal argument will be given for the construction of the metric operator to define an inner-product space for the eigenstates, and the formally "Hermitian" counterpart Hamiltonian. The talk is based on the work carried out in collaboration with Carl M. Bender (Washington University) and Markus P. Mueller (University of Western Ontario).

Abstract:
Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons, glueballs and exotic hadrons as strings in four dimensional flat space-time. The models are based on a “map” from stringy hadrons of curved holographic confining backgrounds. In the first part of the talk I will review the “derivation” of the models. I will start with a brief reminder of the passage from the original AdS/CFT correspondence to the string/gauge duality of certain favored confing holographic models. I will then describe the string configurations in these holographic backgrounds that correspond to Wilson lines, mesons, baryons, glueballs and exotics. Key ingredients of the four dimensional picture of hadrons are the “string end-point mass” and the “baryonic string vertex”. I will determine the classical trajectories of the HISH spectra. I will review the current understanding of the quantization of these hadronic strings. The computation of HISH decay width of hadrons will be described. In the last part of the talk I will sum-marize the comparison of the outcome of the HISH models with the PDG data about mesons and baryons. I will present the values of the tension, masses and intercepts extracted from best fits to hadron spectra and write down certain predictions for higher excited hadrons. I will present attempts to identify glueballs. The decay width of certain hadrons will be compared with the theoretical calculation. I will suggest a window to the landscape of tetra-quarks and other exotic hadrons.

Abstract:
One can easily be frustrated by the tremendous redundancy in possible physical description. By this I mean the freedom to choose gauge, make field redefinitions, add any amount of auxiliary spectator matter, and the such. Happily we can exploit such freedom to encourage the emergence of a new duality in gauge theories. The existence of a duality between color and kinematics exposes a hidden local double-copy structure inherent to prediction in many theories. This structure weaves its way between theories both formal and phenomenological, from QCD to Gravity, from Chiral Perturbation Theory to Born-Infeld and Volkov-Akulov, and from open to closed superstring theories. The duality is sharpest at the level of the perturbative S-matrix — so I will focus my talk there, although I will also mention some recent provocative work beyond scattering. I will mainly discuss progress and challenges to generically achieving color-dual kinematic representations at the multi-loop level. I present a path forward that introduces, at least temporarily, a redundancy of description that we can exploit to map a set of functional relations to linear ones. I will talk about this approach in terms of a geometric picture involving the graph of local graphs, discussing tradeoffs and applicability to long-standing problems.