# Past Quantum Field Theory Seminar

In a quantum quench, a system is prepared in some state

$|\psi_0\rangle$, usually the ground state of a hamiltonian $H_0$, and then

evolved unitarily with a different hamiltonian $H$. I study this problem

when $H$ is a 1+1-dimensional conformal field theory on a large circle of

length $L$, and the initial state has short-range correlations and

entanglement. I argue that (a) for times $\ell/2<t<(L-\ell)/2$ the

reduced density matrix of a subinterval of length $\ell$ is exponentially

close to that of a thermal ensemble; (b) despite this, for a rational CFT

the return amplitude $\langle\psi_0|e^{-iHt}|\psi_0\rangle$ is $O(1)$ at

integer multiples of $2t/\ell$ and has interesting structure at all rational

values of this ratio. This last result is related to the modular properties

of Virasoro characters.

Axions are ubiquitous in string theory compactifications. They are

pseudo goldstone bosons and can be extremely light, contributing to

the dark sector energy density in the present-day universe. The

mass defines a characteristic length scale. For 1e-33 eV<m< 1e-20

eV this length scale is cosmological and axions display novel

effects in observables. The magnitude of these effects is set by

the axion relic density. The axion relic density and initial

perturbations are established in the early universe before, during,

or after inflation (or indeed independently from it). Constraints

on these phenomena can probe physics at or beyond the GUT scale. I

will present multiple probes as constraints of axions: the Planck

temperature power spectrum, the WiggleZ galaxy redshift survey,

Hubble ultra deep field, the epoch of reionisation as measured by

cmb polarisation, cmb b-modes and primordial gravitational waves,

and the density profiles of dwarf spheroidal galaxies. Together

these probe the entire 13 orders of magnitude in axion mass where

axions are distinct from CDM in cosmology, and make non-trivial

statements about inflation and axions in the string landscape. The

observations hint that axions in the range 1e-22 eV<m<1e-20 eV may

play an interesting role in structure formation, and evidence for

this could be found in the future surveys AdvACT (2015), JWST, and

Euclid (>2020). If inflationary B-modes are observed, a wide range

of axion models including the anthropic window QCD axion are

excluded unless the theory of inflation is modified. I will also

comment briefly on direct detection of QCD axions.

We treat the problem of geometric interpretation of the formalism

of algebraic quantum mechanics as a special case of the general problem of

extending classical 'algebra - geometry' dualities (such as the

Gel'fand-Naimark theorem) to non-commutative setting.

I will report on some progress in establishing such dualities. In

particular, it leads to a theory of approximate representations of Weyl

algebras

in finite dimensional "Hilbert spaces". Some calculations based on this

theory will be discussed.

Topological phases of matter exhibit Bott-like periodicity with respect to

time-reversal, charge conjugation, and spatial dimension. I will explain how

the non-commutative topology in topological phases originates very generally

from symmetry data, and how operator K-theory provides a powerful and

natural framework for studying them.

We will discuss the relation between perturbative gauge theory and

perturbative gravity, and look at how this relation extends to some exact

classical solutions. First, we will review the double copy prescription that

takes gauge theory amplitudes into gravity amplitudes, which has been

crucial to progress in perturbative studies of supergravity. Then, we will

see how the relation between the two theories can be made manifest when we

restrict to the self-dual sector, in four dimensions. A key role is played

by a kinematic algebraic structure mirroring the colour structure, which can

be extended from the self-dual sector to the full theory, in any number of

dimensions. Finally, we will see how these ideas can be applied also to some

exact classical solutions, namely black holes and plane waves. This leads to

a relation of the type Schwarzschild as (Coulomb charge)^2.