Running in conjunction with the upcoming STP Board meetings a number of lectures will be hosted at DIAS, Burlington Road on 16 & 17 May. These talks are open to the all. No prior booking is required.

Schedule:

Monday May 16th
10:00-11:00 A. P. Balachandran
11:00-12:00 Ian Jubb

Tuesday May 17th
10:00-11:00 Giandominico Palumbo
11:00-12:00 Neetu
12:00-13:00 Takaki Matsumoto

Titles and Abstracts

Speaker: A.P. Balachandran
Title: Spin 1/2 from Colour and a Little More
Abstract: The theta vacuum in QCD is the standard vacuum, twisted by
the exponential of the Chern-Simons term. But what is the quantum
operator U(g) for winding number 1? We construct U(g) in this
talk. The Poincare’ generators commute with it only if they are
augmented by a spin 1/2 representation of the Lorentz group coming
from large gauge transformations. This result is analogous to the
‘spin-isospin ‘ mixing result due to Jackiw and Rebbi, and Hasenfratz
and ’t Hooft and a similar result in fuzzy physics. (See ‘Lectures on
Fuzzy and Fuzzy SUSY Physics’ by Balachandran, S. Kurkcuoglu and
S.Vaidya, chapters 5.4.1, 8.4.1).
Hence states can drastically affect representations of
observables. This fact is further shown by charged states dressed by
infrared clouds. Following Mund, Rehren and Schroer(arXiv:2109.10342),
we find that Lorentz invariance is spontaneously broken in these
sectors. This result is extended to QCD where even the global QCD
group is shown to be broken.
It is argued that the escort fields of Mund et al. are the Higgs
fields for Lorentz and colour breaking. They are string-localised
fields where the strings live in a union of de Sitter spaces. Their
oscillations and those of the infrared clouds generate the Goldstone
modes.

Speaker: Ian Jubb
Title: Causal Operations in Quantum Field Theory
Abstract: While Quantum Field Theory is the most accurate theory we
have for predicting the microscopic world, there are still open
problems regarding its mathematical description. In particular, the
usual quantum mechanical description of measurements, unitary kicks,
and other local operations has the potential to produce pathological
causality violations. Not all local operations lead to such
violations, but any that do cannot be physically realisable. It is an
open question whether a given local operation in the theory respects
causality, and hence whether a given local operation is physical. In
this talk I will work toward a general condition that distinguishes
causal and acausal local operations.

Speaker: Giandomenico Palumbo
Title: Non-Abelian and tensor gauge fields in topological phases of matter
Abstract: Non-Abelian Berry connections naturally emerge from the
degenerate band structure of multi-band topological systems and can be
seen as non-Abelian vector gauge fields in momentum space. In the
first part of my talk, I will show a unique topological effect that
manifests in the Bloch oscillations of higher-order topological
insulators through the interplay of non-Abelian Berry curvature and
quantised Wilson loops. In the second part of my talk, I will present
a general construction to identify momentum-space Higgs fields,
i.e. non-Abelian complex scalar fields that emerge from the degenerate
band structure of suitable topological phases that are protected by
certain symmetries. I will show that the topological invariants of
several two- and three-dimensional systems can be derived from the
winding numbers associated with the complex scalar fields. Through
these non-Abelian Higgs fields, I will then construct non-Abelian
tensor Berry connections, namely momentum-space tensor gauge fields
and show that their corresponding higher-form Berry-Zak phases give
rise to topological invariants that characterise novel gapped and
gapless phases in three and higher dimensions.

Speaker Neetu
Title: Asymptotics of Young diagrams through Matrix Models
Abstract: We will talk about a matrix model description of growth
processes of Young diagrams. In particular, we will see that the
Plancherel growth process and its generalisations can be described
through unitary matrix models. The classical solutions of unitary
matrix models capture the asymptotic behaviour of Young diagrams
growing according to (q-deformed) Plancherel probability. We will also
talk about a Hilbert space description of unitary matrix models and
Young diagrams.

Speaker: Takaki Matsumoto
Title: On the Berezin-Toeplitz quantization as a matrix regularization
Abstract: The matrix regularization is a regularization of the world
volume theory of a membrane and plays an important role in the
matrix-model formulation of M-theory. In this regularization,
functions on a membrane are replaced by matrices in such a way that a
Poisson bracket of functions corresponds to a commutator of
matrices. In other words, a membrane is replaced by a fuzzy
surface. In this talk, as a systematic method of constructing the
matrix regularization, I will introduce the so-called Berezin-Toeplitz
quantization, which is developed in the context of the geometric
quantization. Based on the idea of this method, I will show that we
can generalize the matrix regularization such that it can be applied
to not only globally defined scalar fields, but also various other
kinds of fields. I will also show a construction of a commutator-like
operation for matrices corresponding to a generalized  Poisson bracket
for the fields.