Past Relativity Seminar

24 February 2015
12:00
Cyril Closset
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.

10 February 2015
12:00
Susama Agarwala
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.
27 January 2015
12:00
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.

18 November 2014
12:00
Dr Leron Borsten
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).
11 November 2014
12:00
Oliver Schlotterer
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.

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