Forthcoming events in this series


Wed, 22 Jul 2015
12:00
L5

Einstein Metrics, Harmonic Forms, and Symplectic Manifolds.

Claude LeBrun
(Stonybrook)
Abstract
Given a smooth compact 4-manifold M  which admits Einstein metrics, is its moduli space of Einstein metrics connected?  While the corresponding question in higher dimensions typically has a negative answer, there are interesting 4-manifolds M for which the answer is known to be affirmative. One important class of 4-manifolds for which we do not know the answer, however,  consists of the underlying 4-manifolds of the del Pezzo surfaces. In this lecture, I will explain a  result which provides interesting partial information concerning this case. 
Tue, 16 Jun 2015

12:00 - 13:00
L5

A panoramic view of infrared singularities

Chris White
(Glasgow)
Abstract
The study of infrared singularities, due to the emission of “soft” (low momentum) gauge bosons, remains a highly active research area in a variety of quantum field theories. After motivating both phenomenological and formal reasons as to why we should care about IR singularities, this talk will review their structure in QED, QCD and quantum gravity, examining the similarities and differences between these three contexts. The role of Wilson lines will be examined, which provide a useful unifying language. Finally, I will examine recent work on moving beyond the soft approximation, and why this might be useful.
Tue, 10 Mar 2015

12:00 - 13:30
L5

Tropical Amplitudes

Piotr Tourkine
(University of Cambridge (DAMTP))
Abstract

A systematic understanding of the low energy limit of string theory scattering amplitudes is essential for conceptual and practical reasons. In this talk, I shall report on a work where this limit has been analyzed using tropical geometry. Our result is that the field theory amplitudes arising in the low energy limit of string theory are written in a very compact form as integrals over a single object, the tropical moduli space. This picture provides a general framework where the different aspects of the low energy limit of string theory scattering amplitudes are systematically encompassed; the Feynman graph structure and the ultraviolet regulation mechanism. I shall then give examples of application of the formalism, in particular at genus two, and discuss open issues.

No knowledge of tropical geometry will be assumed and the topic shall be introduced during the talk.

Tue, 24 Feb 2015

12:00 - 13:00
L5

Curved-space supersymmetry and Omega-background for 2d N=(2,2) theories, localization and vortices.

Cyril Closset
(Stonybrook)
Abstract

I will present a systematic approach to two-dimensional N=(2,2) supersymmetric gauge theories in curved space, with a particular focus on the two-dimensional Omega deformation. I will explain how to compute Omega-deformed A-type topological correlation functions in purely field theoretic terms (i.e. without relying on a target-space picture), improving on previous techniques. The resulting general formula simplifies previous results in the Abelian (toric) case, while it leads to new results for non-Abelian GLSMs.

Tue, 10 Feb 2015

12:00 - 13:00
L5

The Geometry of Renormalization on Scalar Field Theories.

Susama Agarwala
(Oxford)
Abstract
In this talk, I develop the Hopf algebra of renormalization, as established by Connes and Kreimer. I then use the correspondence between commutative Hopf algebras and affine groups to show that the energy scale dependence of the renormalized theory can be expressed as a Maurer Cartan connection on the renormalization group.

Tue, 27 Jan 2015

12:00 - 13:00
L5

Tree-Level S-Matrices: from Einstein to Yang-Mills, Born-Infeld, and More

Ellis Yuan
(The Perimeter Institute)
Abstract

In this talk I am going to discuss our recent and on-going work on an integral representation of tree-level S-matrices for massless particles. Starting from the formula for gravity amplitudes, I will introduce three operations acting on the integrand that produce compact and closed formulas for amplitudes in various other theories of massless bosons. In particular these includes Yang-Mills coupled to gravity, (Dirac)-Born-Infeld, U(N) non-linear sigma model, and Galileon theory. The main references are arXiv:1409.8256, arXiv:1412.3479.

Tue, 18 Nov 2014
12:00
L5

On the symmetries of “Yang-Mills squared”

Dr Leron Borsten
(Imperial College London)
Abstract
A recurring theme in attempts to understand the quantum theory of gravity is the idea of "Gravity as the square of Yang-Mills". In recent years this idea has been met with renewed energy, principally driven by a string of discoveries uncovering intriguing and powerful identities relating gravity and gauge scattering amplitudes. In an effort to develop this program further, we explore the relationship between both the global and local symmetries of (super)gravity and those of (super) Yang-Mills theories squared. 



In the context of global symmetries we begin by giving a unified description of D=3 super-Yang-Mills theory with N=1, 2, 4, 8 supersymmeties in terms of the four division algebras: reals, complex, quaternions and octonions. On taking the product of these multiplets we obtain a set of D=3 supergravity theories with global symmetries (U-dualities) belonging to the Freudenthal magic square: “division algebras squared” = “Yang-Mills squared”! By generalising to D=3,4,6,10 we uncover a magic pyramid of Lie algebras.



We then turn our attention to local symmetries. Regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincaré. As a concrete example we focus on the new-minimal (12+12, N=1) off-shell version four-dimensional supergravity obtained by tensoring the off-shell (super) Yang-Mills multiplets (4+4, N =1) and (3+0, N =0).
Tue, 11 Nov 2014

12:00 - 13:00
L5

SYM amplitudes from BRST symmetry

Oliver Schlotterer
(AEI Golm)
Abstract
This talk describes a method to compute supersymmetric tree amplitudes and loop integrands in ten-dimensional super Yang-Mills theory. It relies on the constructive interplay between their cubic graph organization and BRST invariance of the underlying pure spinor superspace description. After a general introduction to this kind of superspace, we discuss a canonical set of multiparticle building blocks which represent tree level subdiagrams and are guided by their BRST transformation. These building blocks are shown to yield a compact solution for tree level amplitudes, and the applicability of the BRST approach to loop integrands is exemplified through recent examples at one-loop.
Mon, 31 Mar 2014
12:00
L5

Perturbative gauge theory and 2+2=4

Barak Kol
(Hebrew University Jerusalem Israel)
Abstract

Abstract: I shall highlight the repeated occurrence of a certain mathematical structure appearing in different manifestations within the field of scattering amplitudes, thereby acting as a leitmotif. In addition, the representations of tree-level color structures under external leg permutations will be characterised.
Tue, 18 Feb 2014
02:45
C6

Cancelled

Jon Toledo
(The Perimeter Institute)
Tue, 28 Jan 2014
12:00
L5

Space and Spaces

Graeme Segal
(Oxford)
Abstract

This is another opportunity to hear the 2013 LMS Presidential Address:

Abstract: The idea of space is central to the way we think.  It is the technology we have evolved for interpreting our experience of the world.  But space is presumably a human creation, and even inside mathematics it plays a variety of different roles, some modelling our intuition very closely and some seeming almost magical.  I shall point out how the homotopy category in particular breaks away from its own roots.  Then I shall describe how quantum theory leads us beyond the well-established notion of a topological space into the realm of noncommutative geometry.  One might think that noncommutative spaces are not very space-like, and yet it is noncommutativity that makes the world look as it does to us, as a collection of point particles.

Tue, 19 Nov 2013
12:00
L5

Ambitwistor strings

Lionel Mason
(Oxford)
Abstract

We show that string theories admit chiral infinite tension analogues in which only the massless parts of the spectrum survive. Geometrically they describe holomorphic maps to spaces of complex null geodesics, known as ambitwistor spaces. They have the standard critical space–time dimensions of string theory (26 in the bosonic case and 10 for the superstring). Quantization leads to the formulae for tree– level scattering amplitudes of massless particles found recently by Cachazo, He and Yuan. These representations localize the vertex operators to solutions of the same equations found by Gross and Mende to govern the behaviour of strings in the limit of high energy, fixed angle scattering. Here, localization to the scattering equations emerges naturally as a consequence of working on ambitwistor space. The worldsheet theory suggests a way to extend these amplitudes to spinor fields and to loop level. We argue that this family of string theories is a natural extension of the existing twistor string theories. 

Fri, 11 Oct 2013
12:00
L5

Large-N QCD as a Topological Field Theory on twistor space

Marco Bochicchio
(University of Rome Sapienza)
Abstract

According to Witten a gauge theory with a mass gap contains a possibly trivial Topological Field Theory  (TFT) in the infrared.  We show that in SU(N) YM it there exists a trivial TFT defined by   twistor Wilson loops whose v.e.v. is 1 in the large-N limit for any shape of the loops supported on certain Lagrangian submanifolds of space-time that lift to Lagrangian submanifolds of twistor space.

We derive a new version of the Makeenko-Migdal loop equation for the topological twistor Wilson loops, the holomorphic loop equation, that involves the change of variables in the YM functional integral from the connection to the anti-selfdual part of the curvature and the choice of a holomorphic gauge.

Employing the holomorphic loop equation and viewing Floer homology the other way around,
we associate to arcs asymptotic in both directions to the cusps of the Lagrangian submanifolds the critical points of an effective action implied by the holomorphic loop equation. The critical points of the effective action, being associated to the homology of the punctured Lagrangian submanifolds, consist of surface operators of the YM theory, supported on the punctures.  The correlators of surface operators in the TFT satisfy for large momentum the constraint that follows by the renormalization group and by the asymptotic freedom and they are saturated by an infinite sum of pure poles of scalar and pseudoscalar glueballs, whose joint spectrum is exactly linear in the mass squared.

For several physical purposes we outline  a related construction of a twistorial Topological String Theory dual to the TFT, that involves the Chern-Simons action on Lagrangian submanifolds of  
twistor space.