Exotic exchanges: from braiding anyons to sliding rings
Perhaps the most useful bit of information one may have about a particle is whether it is a boson or a fermion.
Systems of fermions have wave functions which are antisymmetric under exchange while bosonic wave functions are symmetric. This difference
ensures that many particle systems have immensely different properties depending on whether they consist of bosons or fermions or
a mixture. Obviously it would be interesting to have more classes of particles with different exchange behaviours. In 2+1 dimensional
systems, this is possible and there are new types of particles, called anyons, which have exchange behavior described by braid groups. I will
say a bit about anyons and the current quest for experimental detection of their exchange properties. Then I will return to 3+1
dimensions and give an introduction to the "loop braid group". This group governs the exchange properties of ring or loop shaped
excitations. Loops can perform a number of nontrivial exchange motions including simple exchanges like those of point particles and
"leapfrogging" like smoke rings. I will introduce the concept of a local representation of the loop braid group, analyze a number of
examples of such representations and make a conjecture on their general structure.
Worldsheet Form Factors in the AdS/CFT correspondence
Form factors are matrix elements of local operators in the basis of scattering states. Said in experimentalist's terms, particles are scattered off
a target and thereby probe its "form". From these matrix elements, correlation functions and various observables can be constructed. In this talk, we
discuss worldsheet form factors in the context of the AdS/CFT correspondence, that is form factors in (a) the worldsheet theory of strings in Anti-de
Sitter space and (b) the spin-chain description of planar Super-Yang-Mills theory. As these theories
are integrable, we can formulate functional equations for the form factors.
These equations are generalisations of the known form factor axioms for general two-dimensional, integrable, relativistic theories. We check our proposed
equations in worldsheet perturbation theory and demonstrate that they naturally also hold for the Heisenberg spin-chain.
A Modern look at the Regge limit in QCD, SUSY and gravity
A pedagogical introduction to the Regge limit of scattering amplitudes will be given. Its role in collider physics will be explained, together
with its connections to integrability in QCD and SUSY theories. We will finish with a discussion on graviton scattering at high energies.
Backreaction of flavors in the Kuperstein-Sonnenschein model
In the framework of gauge/gravity duality, I will review some top-down approaches to large Nc holographic QCD, including the somewhat lesser
known models by Dymarsky, Kuperstein and Sonnenschein whose most prominent feature is a geometric realisation of chiral symmetry breaking. Then I
will briefly discuss the so-called smearing technique used to introduce a large number of flavour branes Nf ~ Nc into the background in order to
account for their backreaction, and (in principle) allowing to study the Veneziano limit of the dual gauge. Finally, I report on some recent
progress in applying this procedure to the Kuperstein-Sonnenschein background and discuss some of the novel physical features that emerge
compared to the original, undeformed model.
Quantifying Information in Baryon Spectroscopy
Experimental measurements always carry uncertainties, both
from finite detector resolution and a limited sample of counts.
Quantifying the information gained in experiments with information
theoretic measures should allow one to determine what new physical
insights can be inferred from a measurement. As an example, the N*
programme with the CLAS detector at Jefferson Lab will be presented,
including a survey of the latest results. The application of
information theory to amplitude extraction in baryon spectroscopy
will then be discussed.
Dielectric properties of surfaces
Surfaces are the window through which the interior of solid matter is
Dielectric properties of matter arise from polarisation induced by
fields via excitation of optical transitions, phonons, etc. Surfaces
dielectric response which is distinct from the bulk response because
structures and local fields are different at the surface. In this
will describe recent theoretical work on optical and phonon
semiconductor surfaces induced by light or electron beams.
New Superconformal Field Theories From Wrapped Branes
In string/M-theory, it is possible to engineer a wide variety
of interesting supersymmetric conformal field theories (SCFTs)
by wrapping branes on nontrivial manifolds. In this talk, I
will describe a new infinite set of theories which come from
M5-branes on Riemann surfaces. The corresponding supergravity
solutions interpolate between and extend beyond a famous pair
of solutions by Maldacena and Nuñez. Additionally, the
dual SCFTs are "non-Lagrangian" theories, which have no weakly
coupled UV descriptions, yet can (and will) be described explicitly.
Spontaneous symmetry breaking and topology: what lattice QCD can tell us
After a short review of the progress made in lattice QCD simulations,
I will introduce the so-called spectral projector method which allows
for an accurate determination of the chiral condensate and the
topological susceptibility. I will discuss the quark mass dependence
of both quantities and give a value of the chiral condensate for a
simulation of the first two fermion generations with quarks at (almost)
their physical values. In addition, I will present first results for
the Witten-Veneziano relation.
The Spin-1/2 Heisenberg Chain: Solved and Open Problems
The theory of integrable quantum chains is highly developed. Integrable
systems satisfy the Yang-Baxter equation and allow for more explicit
calculations than non-integrable systems.
In my talk I intend to review results relevant for understanding experimental
systems that were obtained by exact calculations. There are different
techniques for calculating thermodynamical potentials and derived quantities,
especially the logarithmic low-temperature singularities of the
susceptibility. Thanks to recent progress in the field of integrable lattice
systems there are exact data for the temperature dependent static correlation
functions yielding for instance the frequency moments of electron spin
resonance (ESR) lines.
Despite the integrability, many properties are unknown. A notorious problem is
posed by questions on transport. A very specific, but still difficult problem
is posed by the spin Drude weight at finite temperature. I will sketch the
different attempts of the literature to this problem by means of quantum Monte
Carlo, exact numerical diagonalisation of finite chains, Bethe ansatz, and
Mazur bounds applied to matrix product operators.
Implications of Poincare' symmetry for thermal field theories
The analytic continuation to an imaginary velocity of the canonical partition
function of a thermal system expressed in a moving frame has a natural
implementation in the Euclidean path-integral formulation in terms of shifted
boundary conditions. The Poincare' invariance underlying a relativistic theory
implies a dependence of the free-energy on the compact length L0 and the shift
xi only through the combination beta=L_0(1+xi^2)^(1/2). This in turn implies a
of Ward identities among the correlators of the energy-momentum tensor which
have also interesting applications in lattice field theory. In particular, they
offer identities to renormalize non-perturbatively the energy-momentum tensor
and novel ways to compute thermodynamic potentials. At fixed bare parameters
they also provide a simple method to vary the temperature in much smaller steps
than with the standard procedure.
String theory scattering, automorphic forms and Kac-Moody symmetries
At low energies, string theory can be well described by
supergravity field theory. Calculating scattering amplitudes at low
energies in lowest order therefore is a problem in field theory, but
string theory predicts very precise corrections to the supergravity
answer. These corrections can be calculated either explicitly from
string scattering calculations or indirectly by using constraints
from discrete duality symmetries. I will review how this leads to
automorphic forms and predictions for non-perturbative corrections
to the scattering amplitude. Terra incognita in mathematics is
explored by considering cases when the duality symmetry is of
A spectral parameter for scattering amplitudes in N=4 super Yang-Mills theory
Planar N=4 super Yang-Mills appears to be integrable. While this
allows to find this theory's exact spectrum, integrability has hitherto
been of no direct use for scattering amplitudes. To remedy this, we deform
all scattering amplitudes by a spectral parameter. The deformed tree-level
four-point function turns out to be essentially the one-loop R-matrix of
the integrable N=4 spin chain satisfying the Yang-Baxter equation.
Deformed on-shell three-point functions yield novel three-leg R-matrices
satisfying bootstrap equations. Finally, we supply initial evidence that
the spectral parameter might find its use as a novel symmetry-respecting
regulator replacing dimensional regularization. Its physical meaning is a
local deformation of particle helicity, a fact which might be useful for a
much larger class of non-integrable four-dimensional field theories.
Black holes beyond astrophysics
In the context of modifications of gravity, large extra dimensions,
and the AdS-CFT correspondence, there has been much interest
in black holes solutions in theories of gravity and matter that are
exotic - they might live in spacetime dimension other than 4, or
have exotic matter and boundary conditions. One common theme
is that traditional analytic methods to find solutions tend not to work
when confronted with these more exotic contexts and instead we are
increasingly forced to use numerical techniques. I will discuss a
numerical approach to finding static and stationary black hole
solutions, and give some example applications.
Strange Metals in One Spatial Dimension
We consider 1+1 dimensional SU(N) gauge theory coupled to a multiplet of
massive Dirac fermions transforming in the adjoint representation of the
gauge group. The high density limit is characterized by a deconfined
Fermi surface state with Fermi wavevector equal to that of free
gauge-charged fermions. Its low energy fluctuations are described by a
coset conformal field theory with central charge c=(N^2-1)/3. It displays
an emergent N=(2,2) supersymmetry as well as extensive higher spin
W-symmetries. We determine the exact scaling dimensions of the operators
associated with Friedel oscillations and pairing correlations.
Integrability and Scattering in N=4 SYM
We discuss how a spectral parameter, crucial for the quantum inverse scattering method (QISM) in 1+1 dimensions, makes its appearance in the
calculation of on-shell scattering amplitudes in N=4 Super Yang-Mills
theory. This opens the door for applying QISM techniques to spacetime
scattering in 1+3 dimensional quantum field theory. Excitingly, the
regulator seems to allow for the replacement of dimensional regularization
by what one might term spectral regularization.