UEICMSNew Seminar Room
FIRST seminar
SECOND seminar
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DHTLG.062015-09-21Panagiota AdamopoulouHWODE/IM correspondence and classical integrability
We discuss a connection between classes of linear ODEs and quantum
integrable models, also known as the ODE/IM correspondence. We present
recent results concerning the extension of this connection to include
certain integrable PDEs, as well as other aspects of the correspondence.
Sergei GukovCaltechRenormalization and Morse theory
Abstract of the corresponding paper arXiv:1503.01474:
Interpreting renormalization group flows as solitons interpolating between
different fixed points, we ask various questions that are normally asked in
soliton physics but not in renormalization theory. Can one count RG flows? Are
there different "topological sectors" for RG flows? What is the moduli space of
an RG flow, and how does it compare to familiar moduli spaces of (supersymmetric)
domain walls? Analyzing these questions in a wide variety of contexts -- from
counting RG walls to AdS/CFT correspondence -- will not only provide favorable
answers, but will also lead us to a unified general framework that is powerful
enough to account for peculiar RG flows and predict new physical phenomena.
Namely, using Bott's version of Morse theory we relate the topology of conformal
manifolds to certain properties of RG flows that can be used as precise
diagnostics and "topological obstructions" for the strong form of the C-theorem
in any dimension. Moreover, this framework suggests a precise mechanism for
how the violation of the strong C-theorem happens and predicts "phase transitions"
along the RG flow when the topological obstruction is non-trivial. Along the way,
we also find new conformal manifolds in well-known 4d CFT's and point out
connections with the superconformal index and classifying spaces of
global symmetry groups.
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ICMSNew Seminar Room2015-09-30Vladislav KupriyanovUFABCPreseminar for PhD StudentsDeformation quantization and star productsÜmit ErtemUoEHigher-degree Dirac currents of twistor and Killing spinors with applications to supergravity
We show that higher-degree Dirac currents of twistor and Killing spinors
correspond to the hidden symmetries of the background. Hidden symmetries
are defined as the antisymmetric generalizations of Killing and conformal
Killing vectors and are called as Killing-Yano and conformal Killing-Yano
forms respectively. In the case of Killing spinors, we find that the equations
satisfied by the higher-degree Driac currents are related to the Maxwell-like
and Duffin-Kemmer-Petiau equations. We also analyze the supergravity twistor
and Killing spinor cases in ten and eleven dimensional supergravity theories
and find that although different inner product classes induce different
involutions on spinors, the higher-degree Dirac currents still correspond to
the hidden symmetries of the background. As a result, we discuss the possibilities
of the extension of Killing superalgebras of supergravity backgrounds
by adding Killing-Yano forms.
Vladislav KupriyanovUFABCNonassociative Weyl star products
Deformation quantization is a formal deformation of the algebra of
smooth functions on some manifold. In the classical setting, the Poisson bracket
serves as an initial conditions, while the associativity allows to proceed to
higher orders. Some applications to string theory require deformation in the
direction of a quasi-Poisson bracket (that does not satisfy the Jacobi identity).
This initial condition is incompatible with associativity, it is quite unclear
which restrictions can be imposed on the deformation. We show that for any
quasi-Poisson bracket the deformation quantization exists and is essentially
unique if one requires (weak) hermiticity and the Weyl condition. We also propose
an iterative procedure that allows to compute the star product up to
any desired order.
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7 Bristo SquareLecture Theatre 4, 7 Bristo Square2015-10-14Carlos ShahbaziCEA-SaclayPreseminar for PhD StudentsPreseminar for PhD StudentsSimone MurroRegensburg UA new construction of algebraic states for CAR algebrasWe give a functional analytic construction of algebraic states for
CAR algebras on a globally hyperbolic Lorentzian manifold. We show that in
Minkowski space we recover the vacuum state and when we couple the Dirac equation
to a time-dependent external potential, which is smooth and decays faster than
quadratically for large times, we obtain Hadamard states.Carlos ShahbaziCEA-SaclayComplex Non-geometric M-theory backgrounds
We study a particular class of supersymmetric M-theory eight-dimensional
non-geometric compactification backgrounds to three-dimensional Minkowski space-time,
proving that the global space of the non-geometric compactification is still a
differentiable manifold, although with very different geometric and topological
properties with respect to the corresponding standard M-theory compactification
background: it is a compact complex manifold admitting a K\"ahler covering with
deck transformations acting by holomorphic homotheties with respect to the K\"ahler
metric. We show that this class of non-geometric compactifications evade the
Maldacena-Nu\~nez no-go theorem by means of a mechanism originally developed
by Mario Garc\'ia-Fern\'andez and the author for Heterotic Supergravity, and
thus do not require lP-corrections to allow for a non-trivial warp factor or
four-form flux. We obtain an explicit compactification background on a complex
Hopf four-fold that solves all the equations of motion of the theory. We also
show that this class of non-geometric compactification backgrounds is equipped
with a holomorphic principal torus fibration over a projective K\"ahler base as
well as a codimension-one foliation with nearly-parallel G2-leaves, making thus
contact with the work of M. Babalic and C. Lazaroiu on the foliation structure
of the most general M-theory supersymmetric compactifications.
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ICMSNew Seminar Room2015-10-28Antonio PittelliSurrey UPreseminar for PhD StudentsPreseminar for PhD StudentsBrian DolanNUI MaynoothBlack Holes, Boyle's Law and the Quark-Gluon Plasma
The thermodynamics of a black hole in asymptotically anti-de Sitter
space-time can be generalised beyond the usual treatment by including
the cosmological constant as a thermodynamic variable with the physical
interpretation of pressure. New phases and phase transitions, analagous to
those of a van der Waals gas, have been uncovered in this picture. Recent
results will be summarised and their application to conformal field theory,
via the AdS/CFT correspondence, will be presented. Some consequences for the
physics of the quark-gluon plasma and the deconfining phase transition
in QCD will be discussed.
Antonio PittelliSurrey UT-Self Duality of AdS(d) x S(d) x S(d) Superstrings
Dual superconformal symmetry is a remarkable, hidden feature
of N=4 SYM in 4 dimensions. Via AdS/CFT, such a symmetry corresponds
to the invariance of the AdS(5) x S(5) superstring under specific
combinations of bosonic and fermionic T-dualities.
We show that AdS(d) x S(d) x S(d) superstrings with D(2,1;\alpha)
isometry supergroup are T-self-dual if additional T-dualities along
complexified S(d) directions are performed. This implies a new type of
dual superconformal symmetry for the CFTs dual to
AdS(d) x S(d) x S(d) x T(10-3d) superstrings.
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ICMSNew Seminar Room2015-11-11Klaus FredenhagenHamburg UPreseminar for PhD StudentsA brief introduction to quantum field theoryVishnu JejjalaUniversity of the Witwatersrand, JohannesburgHot Attractors
Non-extremal black holes, which emit thermal Hawking
radiation, have two horizons: the event horizon or outer horizon and
the Cauchy horizon or inner horizon. Surprisingly, for a broad class
of solutions to the Einstein equations, the product of the areas of
the inner and outer horizons is the square of the area of the horizon
of the zero temperature black hole obtained from taking the smooth
extremal limit. We use the attractor mechanism in supergravity to
motivate this result. We motivate these results in terms of CFT.
Klaus FredenhagenHamburg ULocality and Quantum Physics
Quantum physics shows nonlocal features, formally connected
with the so-called collapse of the wave function and most
evidently visible in the violation of Bell's inequalities. It is
argued that nevertheless, by an appropriate split between
observables and states, the principle of locality is fulfilled on
the side of the observables, whereas the non-localities are due
to correlations induced by states.
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ICMSNew Seminar Room2015-11-25Andrea SantiUoEOn Spencer cohomology and maximal supersymmetry
We recover the classification of the maximally supersymmetric bosonic
backgrounds of eleven-dimensional supergravity by purely Lie algebraic means,
our point of departure being the supertranslation ideal. Along the way
we compute some cohomological groups and recover exactly
the zeroth order terms of the supercovariant connection associated with
the four-form flux. This is a joint work with José Figueroa-O’Farrill.
Holger FrahmHannover UAnyonic quantum chains - a twist on strongly correlated systems
Starting from a given set of fusion rules one-dimensional lattice models
of interacting anyons can be constructed. For a system of particles
satisfying the fusion rules of $SO(5)_2$ fine-tuning of the coupling
constants leads to integrable anyon chains with commuting transfer
matrices of 'interactions round the face' (IRF) type. The conserved
topological charges of the anyon chain are recovered from the transfer
matrices in the limit of large spectral parameter. The properties of the
models in the thermodynamic limit and the low energy excitations are
studied using Bethe ansatz methods. We find two critical points which
are effectively described by rational conformal field theories invariant
under extensions of the Virasoro algebra related to the underlying
$SO(5)$ symmetry of the anyon chain. The modular partition function and
fusion rules of these RCFTs are derived.
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ICMSNew Seminar Room2015-12-02Bartek CzechStanford UPreseminar for PhD StudentsPreseminar for PhD StudentsJean AvanUniversity of Cergy-PontoiseSpace time duality in integrable hierarchies
Based on the example of the non-linear Schrodinger hierarchy
we define and explore the notion of dual classical integrable
hierarchies. The role of Lagrangian formulation is emphasized
in this framework, to be taken into account in addition to the
more familiar Hamiltonian approach to classically integrable
systems. Explicit dual hiererchies of Hamiltonians are built,
and a multidimensional procedure is evoked.
Bartek CzechStanford UTensor Networks from Kinematic Space
The analogy between Multi-scale Entanglement Renormalization
Ansatz (MERA) and the spatial slice of three-dimensional anti-de
Sitter space (AdS3) has motivated a great interest in tensor networks
among holographers. I discuss a way to promote this analogy to a
rigorous, quantitative, and constructive relation. A key quantitative
ingredient is the way the strong subadditivity of entanglement entropy
is encoded in MERA and in a holographic spacetime. The upshot is that
the map between MERA and the spatial slice of AdS3 is mediated through
an additional integral transform. Interpreted directly, MERA is a
discretization not of the spatial slice of AdS3, but of kinematic space--the
space of geodesics on the spatial slice of AdS3.
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ICMSNew Seminar Room2015-12-09Andrew HicklingImperial College LondonPreseminar for PhD StudentsPreseminar for PhD StudentsRogelio JanteHWSpin in Geometric Models of Matter
The Taub-NUT manifold coupled to an abelian gauge field
with self-dual curvature, is considered as a geometric model
for the electron in recently proposed Geometric Models of Matter.
In this model the spin degrees of freedom are proposed to be given
by the zero-modes of the Dirac operator. We compute the zero-modes
and show that the gauge field allows the existence
of classical bounded orbits and quantum bound states.
Andrew HicklingImperial College LondonEnergy Gaps and Casimir Energies in Holographic CFTs
Two interesting properties of static curved space QFTs are Casimir Energies,
and the Energy Gaps of fluctuations. We investigate what AdS/CFT has to say
about these properties by examining holographic CFTs defined on curved but
static spatially closed spacetimes. Being holographic, these CFTs have a dual
gravitational description under Gauge/Gravity duality, and these properties
of the CFT are reflected in the geometry of the dual bulk. We can turn this
on its head and ask, what does the existence of the gravitational bulk dual
imply about these properties of the CFTs? In this talk we will consider
holographic CFTs where the dual vacuum state is described by pure Einstein
gravity with negative cosmological constant. We will argue using the bulk
geometry first, that if the CFT spacetime's spatial scalar curvature is positive
there is a lower bound on the gap for scalar fluctuations, controlled by the
minimum value of the boundary Ricci scalar. In fact, we will show that it is
precisely the same bound as is satisfied by free scalar CFTs, suggesting that
this bound might be something that applies more generally than just in a
Holographic context. We will then show, in the case of 2+1 dimensional CFTs,
that the Casimir energy is non-positive, and is in fact negative unless
the CFT's scalar curvature is constant. In this case, there is no restriction
on the boundary scalar curvature, and we can even allow singularities in the bulk,
so long as they are 'good' singularities. If time permits, we will also describe
some new results about the Hawking-Page transition in this context.
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ICMSNew Seminar Room2016-01-20John BarrettNottingham UPreseminar for PhD StudentsPreseminar for PhD StudentsSergio InglimaHWDeformed Wave Equations in 3D gravity
We use results from 3D gravity to explore deformations of
relativistic wave equations for massive particles. In particular
we present a method for deriving standard wave equations using both
the representation theory of the Poincare group and a covariance
procedure leading to momentum space wavefunctions satisfying mass
and spin constraints. Following Fourier transform these constraints
become well known wave equations. This procedure is presented for both
half integer spin and more generally for anyonic particles, by working
with appropriate covering groups.
We then review the emergence of deformed symmetries in 3D gravity
where the role of the Quantum Double is briefly mentioned. We repeat
this procedure now with gravity in the picture, using the representation
theory of the Double, to show how this leads to deformed momentum space
constraints. Following a choice of momentum space co-ordinates and a formal
Group Fourier transform we see the emergence of a deformed spacetime together
with modified wave equations.
John BarrettNottingham URandom non-commutative geometries
Random non-commutative geometries are introduced by integrating
over the space of Dirac operators that form a spectral triple
with a fixed algebra and Hilbert space (arXiv:1502.05383). Lisa
Glaser and I have investigated the properties of simple cases of
this statistical system using Monte Carlo methods (arXiv:1510.01377).
Preliminary results indicate that some of the models have a phase
transition, with interesting behaviour near the transition.
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ICMSNew Seminar Room2016-02-03Rouven FrassekDurham UPreseminar for PhD StudentsPreseminar for PhD StudentsChristian SaemannHWLooking for the classical (2,0)-theory
I report on recent progress identifying a classical version of
six-dimensional superconformal field theory, the ``(2,0)-theory,''
with higher gauge theory. I start with a review of higher gauge
theory and how it overcomes naive no-go-theorems. I then explain
that many classical Lagrangians studied in the context of M-theory
are in fact higher gauge theories in disguise. Interesting
non-trivial solutions to higher gauge theory can be found, and
an underlying twistor description reduces the search for the
classical (2,0)-theory to a search for the appropriate gauge structure.
Finally, I show how to extend conventional higher gauge theory in
various ways to allow for more interesting solutions.
Rouven FrassekDurham UQ-operators for the open Heisenberg chain
After introducing the quantum inverse scattering method I will
review the construction of Baxter Q-operators for closed rational
spin chains. Subsequently, I will combine the ideas of the Q-operator
construction with Sklyanin's formulation of the quantum inverse scattering
method for systems with boundaries to construct Q-operators for the open
Heisenberg spin chains with diagonal boundary conditions.
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ICMSNew Seminar Room2016-02-17Roger BehrendCardiff UPreseminar for PhD StudentsPreseminar for PhD StudentsAlexander SchenkelHWAbelian S-duality: An algebraic perspective
Abelian S-duality is a generalization of electric-magnetic duality
of Maxwell's equations that takes into account important gauge-theoretic
aspects such as magnetic monopoles, the Dirac charge quantization condition
and Aharonov-Bohm phases. Using a combination of techniques from locally
covariant quantum field theory and Cheeger-Simons differential cohomology,
I show that Abelian S-dualities can be realized as natural isomorphisms
between certain Abelian quantum gauge theories. As a spin-off of our formalism,
I will also show how to quantize the self-duality equation F = * F for the field
strength of a higher Abelian gauge field. This talk is based on joint work
with C. Becker, M. Benini and R. J. Szabo ( arXiv:1511.00316 [hep-th]
and arXiv:1511.00324 [math.DG] ).
Roger BehrendCardiff UDiagonally and antidiagonally symmetric alternating sign matrices
An alternating sign matrix (ASM) is a square matrix in which each
entry is -1, 0 or 1, and along each row and column the nonzero
entries alternate in sign, starting and ending with a 1. It was
conjectured by Mills, Robbins and Rumsey in 1982 that the number of
ASMs of fixed size is given by a certain simple product formula.
A relatively short proof of this conjecture was obtained by Kuperberg
in 1996, using the Izergin-Korepin determinant formula for the partition
function of the six-vertex model on a square grid with domain-wall
boundary conditions, together with a bijection between ASMs and
configurations of that model. It was also conjectured by Robbins in
the mid 1980's that the number of ASMs of fixed odd size which are
invariant under diagonal and antidiagonal reflection is given by a
simple product formula. This conjecture has only recently been proved,
in my joint work with Ilse Fischer and Matjaz Konvalinka (see arXiv:1512.06030).
Our proof again uses connections with a particular case of the six-vertex model.
In the first part of this talk, I'll introduce ASMs, and review Kuperberg's
proof. In the second part, I'll outline the proof of the conjecture for the
enumeration of diagonally and antidiagonally symmetric ASMs, and present some
new results for the associated case of the six-vertex model.
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ICMSNew Seminar Room2016-03-02Jochen ZahnLeipzig UPreseminar for PhD StudentsPreseminar for PhD StudentsJosé Figueroa-O'FarrillUoEKilling superalgebras and their uses
I will report on ongoing work with Paul de Medeiros and
Andrea Santi concerning the algebraic structure of the Lie
superalgebra generated by the Killing spinors of a supergravity
background, as well as its applications to the classification of
supersymmetric supergravity backgrounds and the determination of
geometries admitting rigidly supersymmetric field theories.
Jochen ZahnLeipzig UGeneralised Wentzell boundary conditions and holography
We study a free scalar field subject to boundary conditions
involving second order derivatives, i.e., of generalised Wentzell type.
For the classical system, we establish well-posedness of the Cauchy
problem and causal propagation. We quantise the system canonically and
discuss the relation between the bulk and the boundary field.
Based on arXiv:1512.05512.
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ICMSNew Seminar Room2016-03-16Severin BunkHWThe prequantum 2-Hilbert spaces of bundle gerbes
We extend the theory of bundle gerbes along the lines of higher
geometric prequantisation. The 2-category of bundle gerbes as introduced
by Waldorf turns out to admit a monoidal structure on its morphism categories.
Further, we construct an internal hom functor on these morphism categories,
allowing us to obtain a 2-Hilbert space of sections of a bundle gerbe.
Finally, we provide an extension of the transgression functor to non-invertible
morphisms which is compatible with the above additional structures,
and comment on relations with earlier works on higher geometric quantisation.
Nick MantonDAMTP CambridgeSkyrmions as Models of Nuclei
The Skyrme model is one of the most realistic soliton models
for application to particle physics. Skyrmions have a topological
charge which is identified with baryon number. The nucleons
(proton and neutron) are different quantum states of the basic Skyrmion.
Although the Skyrme equations are not integrable, much is known about
the static and dynamic solutions, and we can study properties of nuclei
like Carbon-12 using Skyrmions. One gains a quite different perspective
from this field-theoretic model than from conventional point-nucleon models.
Bruce BartlettOxford UString-net description of TQFTs and the tube algebra
In quantum algebra, the notion of a spherical fusion category
plays an important role, and there are two interesting constructions
which take such a category C as input. The first is "string nets",
an elegant graphical description of the 3-dimensional Turaev-Viro TQFT
in terms of string diagrams drawn on surfaces. The second is the "tube
algebra" of C, a certain algebra whose category of representations is
equivalent to the Drinfeld centre of C. I will describe the relationship
between these two constructions.
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ICMSNew Seminar Room2016-03-30Andreas DeserITP Hannover
Graded Poisson manifolds and the structure and deformation of double
field theory
Originally used in the study of Dirac structures, Courant algebroids
are now of central intrest in string theory. In typical cases, an
underlying Lie bialgebroid exists and an elegant characterization of a
Courant algebroid is given by the existence of a homological vector
field on the cotangent bundle of the parity reversed version of the
starting Lie algebroid.
After reviewing this result, we show how the canonical Poisson
structure on the total space of this graded manifold can be used to
understand the gauge structure of "double field theory", a T-duality
invariant description of closed strings.
This is more than a beautiful coincidence: First it turns out that the
inclusion of string fluxes can be understood as fibre-translations
(originally described by Roytenberg). And second, by applying a
Moyal-Weyl deformation to the Poisson bracket, the resulting
corrections to the Courant bracket coincide with those found recently
in heterotic string theory.Mahdi GodazgarDAMTP Cambridge
Supergravity, consistent reductions and uplifts
I will explain the concept of consistent reductions and uplifts for gravitational theories and discuss recent progress in understanding consistent reductions in supergravity by exploiting duality symmetries.UE -->
ICMSNew Seminar Room2016-05-04Preseminar for PhD StudentsPreseminar for PhD StudentsChris HeunenUoEOperator algebras through commutative subalgebras If a noncommutative operator algebra models the observables of a quantum system, its empirical content given by classical measurement outcomes lies within the commutative subalgebras. I will survey a programme showing that the operator algebra is determined to a great extent by its partially ordered set of commutative subalgebras, and how adding dynamics leads to a noncommutative notion of configuration space.J.M. BismutOrsayHypoelliptic Laplacian, index theory and the trace formulaThis is a joint Topology and EMPG seminar. For details see: http://www.maths.ed.ac.uk/~aar/bismut.pdfUE -->
ICMSNew Seminar Room2016-05-18Getachew Alemu DemessieHWHigher gauge theory with String 2-groupsHigher gauge theory is a generalization of ordinary gauge theory. This requires categorifying the underlying mathematical structures in ordinary gauge theory. In this talk we will discuss the case with String 2-groups by defining smooth 2-group bundles as internal functors in the bicategory of finite dimensional Lie groupoids, right-principal bibundles and smooth bibundle maps. George PapamikosKent UDarboux-Dressing transformation for the vector sine-Gordon equation
We present the vector sine-Gordon (vSG) equation together with some of its integrability properties such as Lax representaion, Darboux and Backlund transformations. We use the Darboux transformation to
construct a related vector Yang-Baxter map and an integrable vector differential-difference equation
on the sphere. We will briefly discuss the dressing method and the construction of soliton solutions
for the vSG.
This is a joint work with Dr J.P. Wang (Kent) and Prof A.V. Mikhailov (Leeds)UE -->
TBA2016-07-27Anjan KunduSaha Institute for Nuclear Physics, KolkataTBA