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

11 October 2013
Marco Bochicchio
<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>