Unless otherwise stated, seminars
will take place in Room 7.01 of the
David Hume Tower
at
the University of Edinburgh.

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

Special Seminar Day

Monday,
29 July 2013
at
10am

Wednesday,
22 May 2013

David Hume Tower 11.01

14:30

Francesco Sala
(HW)

In the present talk I will describe a new approach to the study of U(r)-gauge theories on ALE spaces of type A_n. After a brief introduction about instantons and gauge theories on an ALE space X of type A_n, I will describe a conjectural relation between instantons on X and framed sheaves on a "stacky compactification" of X. In the second part of the talk, I will describe how this new approach can give new hints to solve the Alday-Gaiotto-Tachikawa conjecture for (pure) U(1)-gauge theories.

16:00

Alessandro Tanzini
(SISSA and INFN)

We discuss the exact computation of the partition function of a D1-D5 brane system on a resolved A_1 singularity via supersymmetric localisation.
We show how the D1-brane perspective can be used to describe the equivariant Gromov-Witten invariants of the ADHM moduli space in terms of Givental's formalism.
We finally discuss the D5 brane viewpoint and its relation with
higher rank Donaldson-Thomas theory.

Workshop on "Integrability and Hyperbolic Monopoles"

Friday,
10 May 2013
at
TBA

ICMS Newhaven Lecture Theatre

This is a joint Geometry/EMPG seminar.

Thursday,
9 May 2013
at
15:00

Dr Nuno M Romao
(Hausdorff Research Institute for Mathematics, University of Bonn)

I will report on an ongoing project aiming at uncovering fundamental
features of N=(2,2) supersymmetric quantum mechanics on moduli spaces
of vortices on compact Riemann surfaces, in analogy with the
spectrum of quantum dyon-monopole bound states that emerged in
connection with Sen's S-duality conjectures in the 1990s. My focus
in this talk will be on the (topological A-twisted) supersymmetric
Abelian Higgs model coupling to local systems, with both linear
and nonlinear targets; the corresponding ground states can be
investigated by means of the theory of L^2-invariants. I shall
explain why the quanta of such Abelian gauge theories can
nontrivially realize non-Abelian statistics, and motivate a
conjecture regarding the nonlinear superposition of ground states.

Wednesday,
1 May 2013

ICMS Newhaven lecture theatre

14:30

Moustafa Gharamti
(UoE)

We construct a supersymmetic Yang Mills
Higgs theory on H^3, and we show that half of the supersymmetry is
preserved by the supersymmetric hyperbolic monopole configurations. Then,
through studying the low energy dynamics of these solutions we obtain
a multiplet of zero modes that will yield the defining equations
of the geometry of the hyperbolic monopoles via the on shell closure
of its algebra. Finally, knowing the geometry of the moduli space will allow us to tell
something about the dynamics of the hyperbolic monopoles.

16:00

Thomas Quella
(University of Cologne)

We discuss symmetry protected topological phases in one-dimensional
quantum spin chains. Focusing on on-site symmetries only, the
topological classes are shown to be in one-to-one correspondence with
projective representations of the symmetry group.
After having introduced the general setup, we focus on the implications
of spin chains with PSU(N) symmetry. These are shown to admit N
different topological phases. Each of these may be characterized
unambiguously using a non-local string order parameter. Indeed,
analytical and numerical results confirm that this order parameter may
be used to extract a quantized topological invariant. If time permits we
also comment on the possible realization of non-trivial topological
phases in cold atom systems.

Wednesday,
27 March 2013

ICMS Newhaven lecture theatre

14:30

Nelson Merino
(Universidad Catolica de Valparaiso)

It was recently proposed a mechanism by which standard General Relativity in five-dimensional spacetime may indeed emerge at a special critical point of a particular Chern-Simons (CS) action. To achieve this result, both the Lie algebra and the symmetric invariant tensor that define the CS Lagrangian are constructed by means of the Lie algebra S-expansion method with a suitable finite abelian semigroup.
An interesting question that emerge is the following one: are there other Lie algebras that, constructed also by means of the S-expansion method, permits to construct a CS lagrangian that in a certain critical point also lead to standard General Relativity in d=5?
To answer this question the general properties of the expansion method are studied. This permits to perform the S-expansion at the level of the CS Lagrangian (for the AdS algebra) with an arbitrary-unknown semigroup. Then we establish the conditions that the semigroup must satisfy in order to lead the desired connection to standard General Relativity. Finally we implement those conditions by means of computer programs which give us the solution.
We propose this procedure as a useful tool in problems where it is important to find a physical theory or a family of them that, on a certain limit, converge to some particular theory. For example, to study if a similar relation can be generalized to the supersymmetric case.

16:00

Matthew Headrick
(Brandeis U)

Entanglement entropies of spatial regions are useful quantities for characterizing the ground states of quantum field theories. However, their usefulness depends partly on the assumption that they are universal and duality-invariant for a given theory, and that they distinguish between different theories. We will explore whether these two assumptions are correct, focusing on two very simple free two-dimensional CFTs, the Dirac fermion and the compact boson. Explicit calculations of entanglement entropies in the literature suggest that these quantities may fail to agree when calculated in theories that are known to be dual, and may also fail to distinguish between theories that are known not to be dual. While getting at the root of these puzzling discrepancies, we will discover a new kind of duality between these two well-studied theories.

Wednesday,
20 March 2013

ICMS Newhaven lecture theatre

Wednesday,
6 March 2013

ICMS Cramond Room

14:30

Anita Ponsaing
(Université de Genève)

The Brauer loop model is a statistical lattice model with each face
decorated by loops that are allowed to cross. In 2005 de Gier and
Nienhuis noticed a connection between the ground state of the periodic
Brauer loop model and the degrees of some algebraic varieties as
calculated by Knutson in 2003. This connection was explored further by
Di Francesco and Zinn-Justin in 2006, and proved shortly after by
Knutson and Zinn-Justin. In these works a special role was played by the
ground state components in the `permutation sector', that is, the
components that can be viewed as permutations between points 1,..,n
and points n+1,...,2n.
Around the same time Di Francesco calculated the ground state of the
Brauer model with reflecting boundaries, including closed-form
expressions for the sum of all ground state components and the sum of
all components in the permutation sector. In this talk we present a
work-in-progress in collaboration with Paul Zinn-Justin on similar
calculations for the model with non-reflecting boundaries. As in the
earlier works, we use the transfer matrix approach to build a possible
solution, which we then attempt to prove using recursions.

16:00

Simon Gentle
(Durham)

Charged black holes in planar AdS can be unstable to the formation of
charged scalar hair. Through holography, one hopes to use this fact to
uncover general principles governing unconventional superconductors. It
has been shown however that the behaviour of `holographic
superconductors' depends strongly on their embedding into string/M-theory.
In this talk I will discuss two aspects of this issue in which lessons
can be learned. First I will demonstrate how the ground states of these
`top-down' systems may be found by blowing up stars in global AdS, then
I will hunt for the instability of highest temperature in a wider
consistent truncation of supergravity. Both aspects raise concerns that
a new approach to the problem is needed.

Wednesday,
20 February 2013

ICMS Cramond Room

13:00

Sanjaye Ramgoolam
(Queen Mary U.)

Preseminar for Students/Postdocs

14:30

Sanjaye Ramgoolam
(Queen Mary U.)

Quivers are directed graphs which encode information about the gauge groups
and matter content of a large class of gauge theories, many of which
have AdS/CFT duals. The counting of local gauge invariant operators
and the computation of their correlators (in the free field limit)
can be done by simple diagrammatic manipulations of the quiver,
with the help of permutation group theory data. This data includes Young diagrams,
Littlewood-Richardson numbers and branching coefficients of permutation groups.
Riemann surfaces obtained by thickening the quivers are intimately related to these computations.

16:00

Robert de Mello Koch
(University of the Witwatersrand)

In this talk we will discuss how giant gravitons and their open string interactions emerge
from super Yang-Mills Theory. This is accomplished by diagonalizing the one loop
dilatation operator on a class of operators with bare dimension of order N. From the result
of this diagonalization, the Gauss Law governing the allowed open string excitations of
giant gravitons is clearly visible. In addition, we show that this sector of the theory is
integrable.

Wednesday,
13 February 2013

ICMS Cramond Room

13:00

José Figueroa-O'Farrill
(UoE)

Preseminar for Students/Postdocs

14:30

José Figueroa-O'Farrill
(UoE)

We will present a proof of the following result: any background of ten- or eleven-dimensional supergravity which preserves more than half of the supersymmetry is locally homogeneous.

16:00

Maria Johnstone
(UoE)

In this talk we consider families of charged rotating asymptotically
AdS5 Extremal black holes with Vanishing Horizon (EVH black holes)
whose near horizon geometries develop locally AdS3 throats. Using the
AdS3 /CFT2 duality, we propose an EVH/CFT2 correspondence to describe
the near-horizon low energy IR dynamics of near-EVH black holes
involving a speci?c large N limit of the 4d N = 4 SYM. We give a map
between the UV and IR near-EVH excitations, showing that the ?UV ?rst
law? of thermodynamics reduces to the ?IR ?rst law? satis?ed by the
near horizon BTZ black holes in this near-EVH limit. We also discuss
the connection between our EVH/CFT proposal and the Kerr/CFT
correspondence in the cases where the two overlap.

Wednesday,
23 January 2013

ICMS Newhaven lecture theatre

14:30

Christian Saemann
(HW)

I will review my recent work on integrability of M-brane configurations and the description of M-brane models in higher gauge theory. In particular, I will discuss categorified analogues of instantons and present superconformal equations of motion for the non-abelian tensor multiplet in six dimensions.

16:00

Philip Candelas
(Oxford)

Even a cursory inspection of the Hodge plot associated with Calabi-Yau threefolds that are hypersurfaces in toric varieties reveals striking structures. These patterns correspond to webs of elliptic-K3 fibrations whose mirror images are also elliptic-K3 fibrations. Such manifolds arise from reflexive polytopes that can be cut into two parts along slices corresponding to the K3 fibers. Any two half-polytopes over a given slice can be combined into a reflexive polytope. This fact, together with a remarkable relation on the additivity of Hodge numbers, explains much of the structure of the observed patterns.

Wednesday,
28 November 2012

David Hume Tower 7.18

14:30

Anatoly Konechny
(HW)

A lower bound is derived for the boundary entropy s = ln g of a 1+1d
quantum critical system with boundary, under the conditions that the
bulk conformal central charge c is >=1 and the most relevant bulk
scaling dimension is >(c-1)/12. This is the first general restriction on
the possible values of g for bulk critical systems with c >= 1.

16:00

Paul de Medeiros
(Cardiff)

The construction of rigid minimal supersymmetry multiplets in curved spacetime will be reviewed. For conformal supermultiplets, we will show how correction terms in curved spacetime are fixed by the compatibility of conformal and spin structure, leading to rigid supermultiplets on lorentzian manifolds admitting twistor spinors. For a particular class of twistor spinors, we will also show how to incorporate supersymmetric gauge couplings in dimensions not equal to four and describe rigid supersymmetric gauge theories on bosonic supergravity vacua in dimensions six and ten.

Wednesday,
14 November 2012

David Hume Tower 7.01

14:30

Dionysios Mylonas
(HW)

In this talk we will attempt to give an description of the nonassociative geometry probed by closed strings in flat non-geometric R-flux backgrounds. Starting from a suitable Courant sigma-model on an open membrane we will derive a twisted Poisson sigma-model on the boundary of the membrane. The corresponding boundary correlation functions reproduce Kontsevich's deformation quantization formula. For constant R-flux, we will show how to derive closed formulas for the corresponding nonassociative star product and its associator. We will then demonstrate how our approach leads to a consistent quantization of Nambu-Poisson 3-brackets and develop various versions of the Seiberg-Witten map which relate our nonassociative star products to associative ones. Finally, we will show that the Kontsevich formula coincides with the star product obtained by quantizing the dual of a Lie 2-algebra via convolution in an integrating Lie 2-group.

16:00

Athanasios Chatzistavrakidis
(U Hanover)

We discuss the description of flux compactifications in the
context of matrix models for superstrings. These include conventional
compactifications with
geometric fluxes, as well as unconventional non-geometric string
compactifications. The former are related to the study of nilmanifolds,
whose geometry dictates
the conditions which describe a matrix model compactification on them.
Furthermore, we formulate the conditions which describe
compactifications with non-geometric fluxes.
It is argued that the geometric and non-geometric fluxes exchange their
properties when going from position space to momentum space thus
providing a duality among the two.
Moreover, the operations which connect solutions with different fluxes
are described and their relation to T-duality is discussed. Finally, we
discuss flux quantization in this
framework as well as the possibility to describe cases with coexistent
fluxes.

Wednesday,
31 October 2012

David Hume Tower 7.01

14:30

James Lucietti
(UoE)

Recently it has been shown that various extreme black holes
are unstable under linear perturbations at the horizon. I will begin
by describing a result due to Aretakis, which shows that a massless
scalar field at the horizon of an extreme Kerr or Reissner-Nordstrom
black hole is generically unstable. I will then present recent work
which extends this in two ways. Firstly, such a scalar field
instability exists for all known extreme black holes in any dimension.
Secondly, a similar instability occurs for linearized gravitational,
and electromagnetic, perturbations of an extreme Kerr black hole.

16:00

Lou Kauffman
(U of Illinois)

The Jones polynomial invariant in knot theory and the Potts
model in statistical mechanics are closely related through the bracket
state sum model - a partition function defined on knot diagrams that
specializes to the Jones polynomial and can, by different specialization,
represent the dichromatic and Tutte polynomials for plane graphs. Via this
connection, one can use knot and link diagrams to represent the partition
function for the Potts model. The loops in the bracket expansion then
correspond to boundaries of regions of constant spin in the Potts model.
These states (loop collections) in the bracket model are elevated to a
category whose homology is Khovanov homology, an invariant more powerful
than the Jones polynomial. From the point of view of the physics of the
Potts model it is natural to ask for a physical interpretation of this
homology theory based on states delineating regions of constant spin. We
will raise these questions and discuss how Khovanov homology and its
graded Euler characteristic look from the point of view of the Potts
model. We will also point out how this way of thinking leads to a
quantum-information theoretic reformulation of Khovanov homology and the
Jones polynomial.

Wednesday,
17 October 2012

David Hume Tower 7.01

13:00

Nadav Drukker
(King's College)

Preseminar for Students and Postdocs

14:30

Nadav Drukker
(King's College)

The quark-antiquark potential in nonabelian gauge theories is
captured by an infinite rectangular Wilson loop. In this talk I will
concentrate on N=4 supersymmetric YM theory and explain some recent
progress in calculating this potential exactly. To achieve this one first
generalizes the problem to Wilson loops with angles and to Wilson loop with
local operator insertions. It is then possible to reformulate the question
in terms of an open spin chain: The operator insertions are the spins and
the angle is related to the boundary condition on the spin-chain. It is
widely believed that spin chain models arising from N=4 SYM are integrable
and hence can give exact results for all values of the coupling. I will
show how this formalism allows to reproduce the weak coupling expansion and
also mention all-loop results derived from it.

16:00

Sam Palmer
(HW)

The BLG and ABJM theories are conjectured to describe two and arbitrarily many M2-branes,
respectively, the downside to ABJM being a lack of manifest maximal
SUSY. Both can be formulated in terms of 3-algebras. Furthermore
the 3-algebra of functions on a 3-sphere (with Nambu-Poisson bracket)
is thought to describe an infinite number of M2-branes. When these
are stretched between two M5-branes the configuration is similar to a
'magnetic bag', which has an infinite number of D1-branes stretched
between two D3-branes. All these 3-algebras sit in a wider class of
structures known as differential crossed modules. This is also the
language used for non-abelian gerbes, with differential crossed
modules taking the role of Lie algebras for principal bundles.

Wednesday,
10 October 2012

David Hume Tower 7.01

14:30

Arjun Bagchi
(UoE)

Our understanding of the Holographic Principle is mainly restricted to Anti-De Sitter spacetimes and is based essentially on the AdS/CFT correspondence. In this talk, I review recent progress in understanding a dual of flat-spacetimes. My discussion would remain confined to the 3d bulk and the road to the elusive flat holography would be constructed driven by the simple observation that flat-spacetimes can be obtained by a large radius limit of AdS. Symmetry structures would dictate our formalism.

Wednesday,
26 September 2012

David Hume Tower 7.01

13:00

Manu Paranjape
(University of Montreal)

Preseminar for Students/Postdocs

14:30

José Edelstein
(Santiago de Compostela)

Lovelock theory is the natural extension of general relativity to higher dimensions. It can be also thought of as a toy model for ghost-free higher curvature corrections in gravitational theories. It generically admits a family of AdS vacua, most (but not all) of them supporting black hole solutions that display interesting features. This provides an appealing arena to explore different holographic aspects in the context of the AdS/CFT and the fluid/gravity correspondences. I will elaborate on many of these features and will discuss a new type of phase transition possibly arising in the realm of quantum corrected gravitational theories.

16:00

Manu Paranjape
(Université de Montréal)

We consider Euclidean functional integrals involving actions which are not exclusively real. Writing the action in terms of only real fields (which is always possible), such terms appear as explicitly imaginary terms in the Euclidean action. The usual quanization procedure which involves finding the critical points of the action and then quantizing the spectrum of fluctuations about these critical points fails. In the case of complex actions, there do not exist, in general, any critical points of the action on the space of real fields, the critical points are in general complex. The proper definition of the function integral then requires the analytic continuation of the functional integration into the space of complex fields so as to pass through the complex critical points according to the method of steepest descent. We show a simple example where this procedure can be carried out explicitly. The procedure of finding the critical points of the real part of the action and quantizing the
corresponding fluctuations, treating the (exponential of the) complex part of the action as a bounded integrable function is shown to fail in our explicit example, at least perturbatively. Application to tunnelling in spin systems is also studied.

Wednesday,
12 September 2012
at
15:30

David Hume Tower 4.01

Meng-Chwan Tan
(National University of Singapore)

I will explain how a certain quasi-topological N = (0,2) gauged sigma model physically realizes the mathematical theory of “Twisted Chiral Differential Operators” recently formulated by Arakawa et al. In turn, I will give a physical interpretation of the geometric Langlands correspondence for any simply-connected, simple, complex Lie group. I will also explain how worldsheet twisted-instantons can trivialize the chiral algebra of the sigma model completely, whence we would be able to connect a conjecture by Hohn-Stolz on the vanishing of the Witten genus on string manifolds with positive Ricci curvature, to the conditions for the existence of Hecke eigensheaves in the geometric Langlands correspondence at genus zero. If time permits, I will also explain the connections to knot homologies and quantum groups as suggested by the physics of the sigma model.