Past Quantum Field Theory Seminar

We find a new duality  for form factors of lightlike Wilson loops
in planar N=4 super-Yang-Mills theory. The duality maps a form factor
involving a lightlike polygonal super-Wilson loop together with external
on-shell states, to the same type of object  but with the edges of the
Wilson loop and the external states swapping roles.  This relation can
essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace
where it is equivalent to planar graph duality.

In 1997, Maxim Kontsevich gave a universal formula for the
quantization of Poisson brackets.  It can be viewed as a perturbative
expansion in a certain two-dimensional topological field theory.  While the
formula is explicit, it is currently impossible to compute in all but the
simplest cases, not least because the values of the relevant Feynman
integrals are unknown.  In forthcoming joint work with Peter Banks and Erik
Panzer, we use Francis Brown's approach to the periods of the moduli space
of genus zero curves to give an algorithm for the computation of these
integrals in terms of multiple zeta values.  It allows us to calculate the
terms in the expansion on a computer for the first time, giving tantalizing
evidence for several open conjectures concerning the convergence and sum of
the series, and the action of the Grothendieck-Teichmuller group by gauge
transformations.

The "Weyl fermion" was discovered in a topological semimetal in
2015. Its mathematical characterisation turns out to involve deep and subtle
results in differential topology. I will outline this theory, and explain
some connections to Euler structures, torsion of manifolds,
and Seiberg-Witten invariants. I also propose interesting generalisations
with torsion topological charges arising from Kervaire semicharacteristics
and ``Quaternionic'' characteristic classes.

Quantization is the study of the interface between commutative and
noncommutative geometry. There are myriad approaches to it, mostly presented
as ad hoc recipes. I shall discuss the motivating ideas, and the relations
between some of the methods, especially the relation between 'deformation'
and 'geometric' quantization.

The talk will review the origins
of ambitwistor strings, and  recent progress in extending them to a
wider variety of theories and loop amplitudes.

In this talk, we discuss an ongoing calculation of the
four-loop form factors in massless QCD. We begin by discussing our
novel approach to the calculation in detail. Of particular interest
are a new polynomial-time integration by parts reduction algorithm and
a new method to algebraically resolve the IR and UV singularities of
dimensionally-regulated bare perturbative scattering amplitudes.
Although not all integral topologies are linearly reducible for the
more non-trivial color structures, it is nevertheless feasible to
obtain accurate numerical results for the finite parts of the complete
four-loop form factors using publicly available sector decomposition
programs and bases of finite integrals. Finally, we present first
results for the four-loop gluon form factor Feynman diagrams which
contain three closed fermion loops.

The $\phi^4$ model in statistical physics describes the
continous phase transition in the liquid-vapour system, transition to
the superfluid phase in helium, etc. Experimentally measured values in
this model are critical exponents and universal amplitude ratios.
These values can also be calculated in the framework of the
renormalization group approach. It turns out that the obtained series
are divergent asymptotic series, but it is possible to perform Borel
resummation of such a series. To make this procedure more accurate we
need as much terms of the expansion as possible.
The results of the recent six loop analitical calculations of the
anomalous dimensions, beta function and critical exponents of the
$O(N)$ symmetric $\phi^4$ model will be presented. Different technical
aspects of these calculations (IBP method, R* operation and parametric
integration in Feynman representation) will be discussed. The

numerical estimations of critical exponents obtained with Borel
resummation procedure are compared with experimental values and
results of Monte-Carlo simulations.

The big phase space is an infinite dimensional manifold which is the arena
for topological quantum field theories and quantum cohomology (or
equivalently, dispersive integrable systems). tt*-geometry was introduced by
Cecotti and Vafa and is a way to introduce an Hermitian structure on what
would be naturally complex objects, and the theory has many links with
singularity theory, variation of Hodge structures, Higgs bundles, integrable
systems etc.. In this talk the two ideas will be combined to give a
tt*-geometry on the big phase space.

(joint work with Liana David)

This talk will start with a brief historical review of the classification of solids by their symmetries, and the more recent K-theoretic periodic table of Kitaev. It will then consider some mathematical questions this raises, in particular about the behaviour of electrons on the boundary of materials and in the bulk. Two rather different models will be described, which turn out to be related by T-duality. Relevant ideas from noncommutative geometry will be explained where needed.

I'll explain the formalism of extended QFT, while
focusing on the cases of two dimensional conformal field theories,
and three dimensional topological field theories.

In this talk, I will review an inverse scattering construction of interacting integrable quantum field theories on two-dimensional Minkowski space and its ramifications. The construction starts from a given two-body S-matrix instead of a classical Lagrangean, and defines corresponding quantum field theories in a non-perturbative manner in two steps: First certain semi-local fields are constructed explicitly, and then the analysis of the local observable content is carried out with operator-algebraic methods (Tomita-Takesaki modular theory, split subfactor inclusions). I will explain how this construction solves the inverse scattering problem for a large family of interactions, and also discuss perspectives on extensions of this program to higher dimensions and/or non-integrable theories.

Amplitudes in quantum field theory have discontinuities when regarded as
functions of
the scattering kinematics. Such discontinuities can be determined from
Cutkosky rules.
We present a structural analysis of such rules for massive quantum field
theory which combines
algebraic geometry with the combinatorics of Karen Vogtmann's Outer Space.
This is joint work with Spencer Bloch (arXiv:1512.01705).

Hawking radiation and particle creation by an expanding Universe
are paradigmatic predictions of quantum field theory in curved spacetime.
Although the theory is a few decades old, it still awaits experimental
demonstration. At first sight, the effects predicted by the theory are too
small to be measured in the laboratory. Therefore, current experimental
efforts have been directed towards siumlating Hawking radiation and
studying quantum particle creation in analogue spacetimes.
In this talk, I will present a proposal to test directly effects of
quantum field theory in the Earth's spacetime using quantum technologies.
Under certain circumstances, real spacetime distortions (such as
gravitational waves) can produce observable effects in the state of
phonons of a Bose-Einstein condensate. The sensitivity of the phononic
field to the underlying spacetime can also be used to measure spacetime
parameters such as the Schwarzschild radius of the Earth.

[based on joint work with Li Guo and  Bin Zhang]

 We apply to  the study of exponential sums on lattice points in
convex rational polyhedral cones, the generalised algebraic approach of
Connes and Kreimer to  perturbative quantum field theory.  For this purpose
we equip the space of    cones   with a connected coalgebra structure.
The  algebraic Birkhoff factorisation of Connes and Kreimer   adapted  and
generalised to this context then gives rise to a convolution factorisation
of exponential sums on lattice points in cones. We show that this
factorisation coincides with the classical Euler-Maclaurin formula
generalised to convex rational polyhedral cones by Berline and Vergne by
means of  an interpolating holomorphic function.
We define  renormalised conical zeta values at non-positive integers as the
Taylor coefficients at zero of the interpolating holomorphic function.  When
restricted to Chen cones, this  yields yet another way to renormalise
multiple zeta values  at non-positive integers.

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.