11 October 2013

12:00

Marco Bochicchio

Abstract

<p>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.<br />
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<br />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.<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 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.<br /><br />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 <br />twistor space.</p>