Unless otherwise stated, seminars
will take place in Room 7.18 of the
at
the University of Edinburgh.

Please contact the organisers Tim Adamo (UoE) or Richard Davison (HW)
with any questions regarding the seminars.

Wednesday,
30 May 2012
at
16:00

Appleton Tower Room 2.11

Nils Carqueville
(LMU Munich)

Two-dimensional topological quantum field theories with defects are on general grounds expected to be described by bicategories with adjoints and further structures. I shall explain what this means and then turn to the rich example of Landau-Ginzburg models where we can turn these expectations into a constructive theorem. This result allows for numerous applications among which are a new proof of the Cardy condition (a generalisation of the Hirzebruch-Riemann-Roch theorem), and a generalised orbifold procedure. This talk is based on joint work with Daniel Murfet and Ingo Runkel.

Wednesday,
16 May 2012

Room 11.18

14:30

Francesco Sala
(HW)

After a brief introduction on the theory of framed sheaves and their
moduli spaces, I will give a description of a modified Atiyah class of
a family of framed sheaves, which allows to define a framed version of
the Kodaira-Spencer map. Moreover, I will construct closed two-forms
on the moduli spaces of framed sheaves on surfaces. As an application,
we define a symplectic structure on the moduli spaces of framed
sheaves on some birationally ruled surfaces.

16:00

Elizabeth Gasparim
(Unicamp (Brazil)/UoE)

This is a report of joint work with T. Koeppe, P. Majumdar and K. Ray. We define new partition functions for theories with targets on toric singularities via products of old partition functions on crepant resolutions.

Wednesday,
25 April 2012

Room 12.18

13:00

Martin Wolf
(Surrey)

Subject of this talk is the twistor geometry discussion of a five-dimensional generalisation of the instanton equation known as the contact instanton equation. This equation was recently introduced in the context of (twisted) supersymmetric Yang-Mills theory on the five-dimensional sphere. If time permits, certain extensions to higher dimensions and supersymmetric generalisations will also be presented.

14:30

Chong-Sun Chu
(Durham)

I will talk about a recent construction for an action for
non-abelian 2-form in 6-dimensions. The action consists of a non-abelian
generalization of the abelian action of Perry and Schwarz for a single
M5-brane. It admits a self-duality equation on the field strength as the
equation of motion. It has a modified 6d Lorentz symmetry. On dimensional
reduction on a circle, our action gives the 5d Yang-Mills action.
Based on these properties, we propose that our theory describes the gauge
sector of multiple M5-branes in flat space.

16:00

Raphael Benichou
(Vrije Universiteit Brussel/Solvay Insitutes)

I will discuss quantum integrability in a family of 2D sigma-models on superspaces. In particular I will show how to derive perturbatively the Hirota equation that encodes the exact spectrum of these models. As a particular case we obtain a first-principles proof of the Y-system that has been proposed as a solution to the spectrum problem in N=4 SYM.

Wednesday,
18 April 2012
at
16:00

Room 7.18

Niclas Wyllard

I will describe relations of "AGT-type" between 2d CFTs and 4d gauge theories. I will give an overview of older results and also discuss some more recent developments.

Wednesday,
11 April 2012

Room 7.18

14:30

Luigi Cantini
(Université de Cergy-Pontoise)

In 2001 Razumov and Stroganov conjectured that the (properly normalized)
components of the ground state of the dense O(1) loop model on a
semi-infinite cylinder enumerate fully-packed loop (FPL) configurations
on the square, with alternating boundary conditions, refined according
to the link pattern for the boundary points. This conjecture has arisen
a lot of interest both in the physics and in the mathematics community.
In this talk, after reviewing the main background, I shall discuss a
stronger (but easier to prove!) version of the correspondence: on the
`dense O(1) side', the ground state of Hamiltonian H of the loop model
is replaced by the one of the Scattering Matrix S(t); on the `FPL side',
one considers the refinement according to the position of the unique
straight tile on the last row.

16:00

Christian Hagendorf
(University of Geneva)

In this talk I consider spin chains and vertex models with dynamical supersymmetry. The corresponding supercharges act non-locally and change the number of sites. The simplest example is the spin-1/2 XXZ chain/six-vertex model with periodic boundary conditions at the combinatorial point, which possesses an N=(2,2) supersymmetry on the lattice. I will explain the construction of the representations of this algebra for arbitrary spin, leading to fused vertex models. Furthermore I will discuss elliptic models (which do not enjoy spin/particle number conservation) with supersymmetry, in particular the spin-1/2 XYZ chain along a special line of couplings, and the elliptic extension of the Fateev-Zamolodchikov spin chain with special emphasis on the properties of the ground states (supersymmetry singlets), which display a variety of connections to combinatorics and classically integrable equations.

Wednesday,
28 March 2012

Room 7.18

14:30

Pau Figueras
(Cambridge)

In this talk I will discuss the construction of braneworld black holes in the context of the Randall-Sundrum infinite braneworld scenario (RS2). As I shall explain, the existence of large braneworld black holes can be understood as perturbations of the a solution in AdS corresponding to the gravitational dual of N=4 super-Yang-Mills on the background of the 4d Schwarzschild solution.

16:00

Alexander Schenkel
(University of Wuppertal)

A noncommutative (NC) gauge theory is typically described in terms of connections on finite projective modules over NC algebras. While the notion of curvature is standard in this setting, there is not yet a general theory of parallel transports. In my talk I will propose a definition of parallel transport on modules over NC algebras. Instead of transporting a vector along a curve, which is the usual LOCAL concept of parallel transport in commutative geometry, we transport an element of the module (a "section" of a NC vector bundle) along a one-parameter group of algebra automorphisms, which is a GLOBAL concept as required by NC geometry. I study in detail parallel transports on finite projective modules over fuzzy spaces and show that they naturally give rise to a set of gauge invariant observables. For modules equipped with a hermitian structure I prove that any hermitian connection can be reconstructed up to gauge equivalence from this set of observables. This is not possible using
observables based on the curvature, indicating the importance of module parallel transports in the formulation of (quantum) gauge theories on NC spaces.

Wednesday,
14 March 2012

Room 7.18

13:00

Simone Zonetti
(UC Louvain)

A subclass of (1+1)-dimensional dilaton-Maxwell gravity is studied in the Dirac approach to constrained dynamics. By exploiting a newly found duality with Liouville Field theory, it is shown that the requirement of a quantum realization of the conformal algebra for physical quantum states of the fields naturally constrains the cosmological constant to take values in a well determined and mostly discrete spectrum. Furthermore the contribution of the quantum fluctuations of the single dynamical degree of freedom in the gravitational sector, namely the conformal mode, to the cosmological constant is negative, in contrast to the positive contributions of the quantum fluctuations of the matter fields, possibly opening an avenue towards addressing the cosmological constant problem in a more general context.

14:30

Neil Copland
(Sogang University)

I will show how the equations of motion of double field theory can
also be derived as the one-loop background field equations of a
doubled sigma model, both being the vanishing of the so called
'generalised Ricci tensor'. This raises the possibility of deriving
higher order corrections to double field theory from a sigma model
approach.

Wednesday,
1 February 2012

Room 7.18

14:30

Noel Hustler
(UE)

The bosonic field equations of type IIB supergravity are reduced on a
locally (Cartan) symmetric space and through the complete classification
of symmetric spaces, we identify all symmetric backgrounds up to local
isometry.

16:00

Bernd Schroers
(HW)

This talk is based on joint work with Michael Atiyah and Nick Manton,
described in arXiv:1108.5151. The paper contains a proposal to describe
particles in terms of Riemannian 4-manifolds. This description is
radically different from established models of particle physics. I will
review the proposal, and illustrate it with geometric models for the
electron and the proton. I will end by sketching some recent ideas for
describing the neutron and beta decay geometrically.

Wednesday,
18 January 2012

Room 7.18

14:30

Alexander Quintero Velez
(Glasgow)

In this talk, we discuss the boundary coupling of a Poisson
sigma model associated to a Lie algebroid E over a smooth manifold X.
The discussion is done within the context of the Batalin–Vilkovisky
formalism in the AKSZ geometrical formulation. The main result is that a
boundary condition corresponding to a Lie subalgebroid F of E over a
submanifold Y of X can be coupled to a representation up to homotopy of
F in a way that is consistent with the BRST symmetry. If time permits, I
will explain how these considerations lead to a conjectural description
of topological D-branes on generalized complex manifolds, which includes
A-branes and B-branes as special cases.

16:00

Brian Dolan
(Maynooth/Dublin Institute for Advanced Studies)

Interpreting the cosmological constant as a pressure, black-hole
thermodynamic potentials can be used to define a black-hole volume
as the thermodynamically conjugate variable to the pressure.
The properties of the thermodynamic volume are analysed and
its physical consequences explored. The Euclidean free energy is
identified as the Gibbs free energy, beloved of chemists, and the
resulting PdV term in the first law modifies the amount of emergy that can
be extracted in a Penrose process --- the maximum efficiency of a
charged rotating black-hole is shown to be 75% when the PdV term is
included, as opposed to the currently accepted value of 50%.
The limit of zero angular-momentum is rather subtle
and must be trated with care.

This is an IoP Mathematical and Theoretical Physics Group workshop.

Thursday,
8 December 2011
at
13:30

Beginning of

Thursday,
8 December 2011

Room 7.18

14:30

Parthasarathi Majumdar
(Saha Institute for Theoretical Physics (India) and Oxford)

I shall start with an idea (somewhat heuristic) I call `Thermal Holography' and use that to probe the thermal behaviour of quantum horizons, i.e., without using any classical geometry, but using ordinary statistical mechanics with Gaussian fluctuations. This approach leads to a criterion for thermal stability for thermally active horizons with an Isolated horizon as an equilibrium configuration, whose (microcanonical) entropy has been computed using Loop Quantum Gravity (I shall outline this computation). As fiducial checks, we briefly look at some very well-known classical black hole metrics for their thermal stability and recover known results. Finally, I shall speculate about a possible link between our stability criterion and the Chandrasekhar upper bound for the mass of stable neutron stars.

Wednesday,
30 November 2011

Room 7.18

14:30

Anne Taormina
(Durham)

A novel map between two even self-dual lattices of signature
(3,19) and (24,0) will be presented. This map is important in
identifying a symmetry group larger than the largest finite symplectic
automorphisms group of K3 surfaces by orders of magnitude. The
significance of this overarching symmetry will be stressed in the
context of Mathieu 24 Moonshine.

16:00

Derek Harland
(Durham)

Instanton equations in dimensions 5 and higher were introduced nearly 30 years ago. They appear naturally in Yang-Mills theory and supergravity, and also in recent attempts to generalise the Donaldson invariants. I will discuss some new examples of Yang-Mills instantons on spheres and Euclidean planes, and more generally, on manifolds with real Killing spinors and their cones.

This talk is an EMPG-Topology seminar.

Friday,
25 November 2011
at
15:00

James Clerk Maxwell Building Room 6311

Christian Blohmann
(MPIM Bonn)

Traditionally, prequantization constructs a representation of the Lie algebra of functions on a symplectic manifold by operators on the space of sections of a line bundle. First, I will explain how this can be generalized by associating a Lie algebroid to the symplectic manifold, integrating it to a Lie groupoid, and constructing the groupoid convolution algebra. Then I give an example of a symplectic manifold with a singularity that becomes removable when described in terms of the Lie algebroid. As a consequence, its prequantization via groupoids leads to an algebra that is different from the one obtained by the traditional method. I will construct this algebra explicitly and interpret it as noncommutative geometry generated by the singularity. From the viewpoint of physics, the procedure can be seen as quantization of a 2D-magnetic monopole by a local version of the Peierls transformation.

Wednesday,
16 November 2011

Room 7.18

14:30

Nikos Karaiskos
(University of Patras)

We present a large family of junction-type representations of the
Temperley-Lieb algebra. After introducing the representation, we discuss its
associated symmetries. Apart from certain manifest ones, we are able to
extract some non-trivial quantum symmetries of the representation. We
present the extension to the boundary Temperley-Lieb algebra and we
briefly discuss the corresponding spin chain.

16:00

Harry Braden
(UoE)

The modern approach to integrability proceeds via a Riemann surface, the spectral
curve. In many applications this curve is specified by transcendental constraints in terms of
periods. In some cases, including the construction of magnetic monopoles, physical symmetries
are inherited by the spectral curve and there may be consequent simplifications of the
transcendental constraints. We shall look at this interplay of ideas.

Wednesday,
2 November 2011

Room 7.18

14:30

Rinat Kedem
(University of Illinois)

I will give a short tour of discrete integrable systems related to quantum
spin chains, and their relation to cluster algebras. I will show how to use
integrability to solve these systems and use this to prove positivity
conjectures in cluster algebras algebras. The connection to cluster algebras
allows us to prove the completeness of Bethe ansatz states of the spin chain.
I will also explain how this point of view can be generalized to
non-commutative integrable systems.Cluster algebras are a rather general construction in algebraic combinatorics
introduced by Fomin and Zelevinsky about a decade ago. Originally inspired by
positivity questions in canonical basis theory of quantum groups, they have
found applications in Donaldson-Thomas invariant theory, the proof of the
periodicity conjectures of Zamolodchikov in TBA, representation theory, etc. I
will describe these algebras without assuming any previous familiarity with
the subject.

16:00

Robert Weston
(HW)

We consider the 6-vertex model on a 2D geometry with an integrable
fracture running from the origin to spatial infinity.
In the language of the associated XXZ quantum spin chain, the picture is
that of a spin chain separated into two separate domains at time t≤0
that are joined together for t>0. Such a scenario is called a local
quantum quench. This model is very natural to consider in the language
of Baxter's corner transfer matrix. Exploiting this fact, we use the
machinery of the vertex operator approach to integrable systems in order
to compute exact expressions for correlation functions. Specialising to
the case of the magnetization in the vicinity of the tip of the
fracture, we obtain a simple exact formula that is analogous to
Baxter's formula for the spontaneous magnetisation of the usual XXZ chain.

Wednesday,
19 October 2011

Room 7.18

14:30

Richard Davison
(Oxford)

I will discuss the bosonic excitations present in certain
strongly-interacting holographic field theory states with a large
density of matter. Particular attention will be paid to the properties
of the sound modes of these theories and how they compare with the
properties of the sound mode of a Landau-Fermi liquid.

16:00

Jock McOrist
(DAMTP, Cambridge)

Compactifications of the heterotic string on a Calabi-Yau manifold are
a relatively unexplored area of string theory despite their promise in
cultivating novel mathematics as well as promising phenomenology. In
this talk I will summarise recent developments in understanding the
worldsheet descriptions of heterotic vacua, its implications for
computing physical observables (e.g. Yukawa couplings) and mathematics
(e.g. mirror symmetry).

Wednesday,
12 October 2011

Appleton Tower Room 2.14

14:30

Nicolas Behr
(MPI Potsdam)

The main topic of this talk is the correspondence between D-branes in a certain type of rational conformal field theories, namely the Grassmannian Kazama-Suzuki models SU(3)_k/U(2), and matrix factorizations of the associated Landau-Ginzburg theories. Such a correspondence has been found on the level of bulk theories already around 1989, followed by considerable progress in the case of A-type boundary conditions, for which a correspondence between D-branes and solitons of the LG theories with perturbed superpotentials could be established. A correspondence for B-type boundary conditions, which are described by means of matrix factorizations in the LG theory, remained elusive except for certain explicit examples of RCFTs including the minimal models of CFT. The results obtained in collaboration with S. Fredenhagen suggest that this has a beautiful mathematical reason: it appears that the structure of matrix factorizations alone is not enough to find the "dictionary" between D-branes and matrix
factorzations. As I will present, at least in the sufficiently generic case of the SU(3)_k/U(2) KS models, a successful strategy involves incorporating defects into the picture, or rather defect functors, a concept that seems to be new and thus will be defined in the seminar. In effect, the symmetry structure of the superpotential is sufficient to construct a defect functor semi-ring that generates all MFs corresponding to Cardy branes in the RCFT from a small set of simple solutions. In addition, these defect functors are the exact analogues of the CFT defects. Finally, an outlook to potential applications of these findings both in mathematics and in physics will be given.

16:00

José Miguel Figueroa-O'Farrill
(UoE)

I will summarise the search for candidate dual geometries to 3-dimensional N-extended superconformal field theories, with N>4. This includes a classification of eleven-dimensional homogeneous lorentzian manifolds with a transitive isometric action of SO(3,2) x SO(N). We find no (new) backgrounds with N>5, but several new backgrounds with N=5, at least one of which is supersymmetric.

Wednesday,
5 October 2011

Room 7.18

14:30

Raymond Vozzo
(University of Adelaide)

In physics T-duality is a phenomenon which relates certain types of string theories to one another. From a topological point of view, one can view T-duality as a duality between line bundles carrying a degree three cohomology class (the H-flux). Bundle gerbes provide a geometric realisation of the degree three cohomology of a manifold. In this talk we will use bundle gerbes to give a geometric realisation of the H-flux and explain how to construct the T-dual of a line bundle together with its T-dual bundle gerbe.

Wednesday,
21 September 2011

Appleton Tower Room 2.14

14:30

Cornelius Schmidt-Colinet
(IPMU Tokyo)

We consider bounds on the entropy of certain infrared-stable conformal field theories at the self-dual temperature which are imposed by modular invariance.

16:00

Anatoly Konechny
(HW)

In a non-unitary two-dimensional conformal quantum field theory there
may be
conserved currents which do not split into a holomorphic and an
antiholomorphic components.
We construct such models via a current-current perturbation of WZW
models on supergroups.
Such models emerge in string theory and condensed matter physics.
We present some perturbative and non-perturbative results that probe
the structure of the
current OPE algebra in such models as well as the correlation functions
and equal time commutators.