Past Relativity Seminar

28 January 2014
12:00
Graeme Segal
Abstract
<p>This is another opportunity to hear the 2013 LMS Presidential Address:</p> <p>Abstract: The idea of space is central to the way we think.&nbsp; It is the technology we have evolved for interpreting our experience of the world.&nbsp; 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.&nbsp; I shall point out how the homotopy category in particular breaks away from its own roots.&nbsp; Then I shall describe how quantum theory leads us beyond the well-established notion of a topological space into the realm of noncommutative geometry.&nbsp; 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.</p>
19 November 2013
12:00
Lionel Mason
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. 

11 October 2013
12:00
Marco Bochicchio
Abstract
<p>According to Witten a gauge theory with a mass gap contains a possibly trivial&nbsp;Topological Field Theory &nbsp;(TFT) in the infrared. &nbsp;We show that in SU(N) YM it there exists a trivial TFT defined by &nbsp;&nbsp;twistor Wilson loops&nbsp;whose v.e.v. is 1 in the large-N limit for any shape of the loops supported on certain&nbsp;Lagrangian submanifolds of space-time that lift to Lagrangian&nbsp;submanifolds of twistor space.<br /> <!--break--> <br />We derive a new version of the Makeenko-Migdal loop equation for the topological twistor Wilson loops,&nbsp;the holomorphic loop equation, that&nbsp;involves the change of variables in the YM functional integral from the connection to the anti-selfdual part of the curvature&nbsp;and the choice of a holomorphic gauge.<br /><br />Employing the holomorphic loop equation and viewing Floer homology the other way around,<br />we associate to arcs asymptotic in both directions to the cusps of&nbsp;the Lagrangian submanifolds the critical points of an effective action&nbsp;implied by the holomorphic loop equation.&nbsp;The critical points of the effective action, being associated to the&nbsp;homology of the punctured Lagrangian submanifolds,&nbsp;consist of surface operators of the YM theory, supported on the punctures. &nbsp;The correlators of surface operators in the TFT satisfy for large&nbsp;momentum the constraint that follows by the renormalization group&nbsp;and by the asymptotic freedom and they are saturated by an infinite sum of pure poles of scalar and pseudoscalar glueballs,&nbsp;whose joint spectrum is exactly linear in the mass squared.<br /><br />For several physical purposes we outline &nbsp;a related construction of a&nbsp;twistorial Topological String Theory dual to the TFT,&nbsp;that involves the Chern-Simons action on Lagrangian submanifolds of&nbsp;&nbsp;<br />twistor space.</p>

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