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Solitonic sectors, alpha-induction and symmetry breaking boundaries
We develop a systematic approach to boundary conditions that break bulk
symmetries in a general way such that left and right movers are not necessarily
connected by an automorphism. In the context of string compactifications, such
boundary conditions typically include non-BPS branes. Our formalism is based on
two dual fusion rings, one for the bulk and one for the boundary fields. Only
in the Cardy case these two structures coincide. In general they are related by
a version of alpha-induction. Symmetry breaking boundary conditions correspond
to solitonic sectors. In examples, we compute the annulus amplitudes and
boundary states.Comment: 13 pages, LaTeX2e; v2: typos correcte
Does Integrated Information Lack Subjectivity
I investigate the status of subjectivity in Integrated Information Theory. This
leads me to examine if Integrated Information Theory can answer the hard problem of consciousness.
On itself, Integrated Information Theory does not seem to constitute an answer to
the hard problem, but could be combined with panpsychism to yield a more satisfying theory
of consciousness. I will show, that even if Integrated Information Theory employs the metaphysical
machinery of panpsychism, Integrated Information would still suffer from a different
problem, not being able to account for the subjective character of consciousness
Dualizability in Low-Dimensional Higher Category Theory
These lecture notes form an expanded account of a course given at the Summer
School on Topology and Field Theories held at the Center for Mathematics at the
University of Notre Dame, Indiana during the Summer of 2012. A similar lecture
series was given in Hamburg in January 2013. The lecture notes are divided into
two parts.
The first part, consisting of the bulk of these notes, provides an expository
account of the author's joint work with Christopher Douglas and Noah Snyder on
dualizability in low-dimensional higher categories and the connection to
low-dimensional topology. The cobordism hypothesis provides bridge between
topology and algebra, establishing important connections between these two
fields. One example of this is the prediction that the -groupoid of
so-called `fully-dualizable' objects in any symmetric monoidal -category
inherits an O(n)-action. However the proof of the cobordism hypothesis outlined
by Lurie is elaborate and inductive. Many consequences of the cobordism
hypothesis, such as the precise form of this O(n)-action, remain mysterious.
The aim of these lectures is to explain how this O(n)-action emerges in a range
of low category numbers ().
The second part of these lecture notes focuses on the author's joint work
with Clark Barwick on the Unicity Theorem, as presented in arXiv:1112.0040.
This theorem and the accompanying machinery provide an axiomatization of the
theory of -categories and several tools for verifying these axioms.
The aim of this portion of the lectures is to provide an introduction to this
material.Comment: 65 pages, 8 figures. Lecture Note
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