Thesis

Chasing the Veneziano ghost via lattice QCD spectroscopy in the Landau gauge

• Call:

  IDPASC Portugal - PHD Programme 2016

• Academic Year:

  2016 / 2017

• Domain:

  Theoretical Particle Physics

• Supervisor:

  Orlando Oliveira

• Co-Supervisor:

  David Dudal

• Institution:

  Universidade de Coimbra

• Host Institution:

  Universidade de Coimbra

• Abstract:

  In general, correlation functions of a quantum field theory describing observable excitations are subject to several constraints in terms of their momenta. The analytical properties are encoded in the so-called spectral representation. Though, the standard inversion tools to convert incomplete and yet unphysical lattice QCD data into physically relevant spectral functions are inapplicable when probing spectral properties of unphysical degrees of freedom such as confined gluons or quarks, since those standard tools explicitly rely on the expected positivity of the spectral function, a feature not necessarily true for gluons. In fact, negativity of e.g. a gluon spectral function is sometimes interpreted as an avatar for color confinement by part of the community. In specific, we will develop an alternative (novel) strategy to study the so-called (gauge invariant) topological susceptibility. The latter quantity serves as a measure of the topological nature of the QCD vacuum (related to instantons, theta angle, large N, etc). It is a notoriously difficult quantity to compute, even using nonperturbative lattice gauge theory, related to subtleties in its definition to make it finite. On the other hand, Veneziano postulated the existence of a gauge non-invariant ghost (scalar particle with negative and thus unphysical norm); nowadays known as the Veneziano ghost, based on earlier work of Witten. This ghost's existence is necessary to recover a nonzero topological susceptibility. Interest in it was recently revived by Kharzeev-Levin, where a nonzero topological susceptibility was related via the Veneziano ghost to a violation of positivity in the gluon two-point function, that is again interpreted as a signal of confinement. The major goal of this PhD project will be to study, via lattice techniques, the underlying Veneziano ghost correlator, to verify it's a ghost to begin with (via its spectral function), and to find traces of its massless nature. Our attention will be devoted to the Landau gauge (transverse gauge field), as this gauge is well-studied and under control in both continuum and discrete lattice setting.