Q E D 3 theory of underdoped high tem perature superconductors Igor F.H erbut D epartm ent ofPhysics,Sim on Fraser U niversity,B urnaby,B ritish C ol um bia, C anada V 5A 1S6T he l ow -energy theory ofd-w ave quasi parti cl es coupl ed to uctuati ng vortex l oopsthatdescri besthel ossofphase coherence i n a tw o di m ensi onald-w ave superconductor at T = 0 i s deri ved from rst pri nci pl es. T he theory has the form of2+ 1 di m ensi onal quantum el ectrodynam i cs (Q E D 3), and i s proposed asan e ecti ve descri pti on ofthe T = 0 superconductori nsul ator transi ti on and of the pseudogap phase i n underdoped cuprates. T he coupl i ng constant ("charge") i n thi s theory i s proporti onalto the dualorder param eter ofthe X Y m odel ,w hi ch i s assum ed to be descri bi ng uctuati ons ofthe phase ofthe superconducti ng order param eter. Fi ni teness of the charge i s then tantam ount to the appearance ofi n ni tel y l arge vortex l oops, i . e. to the l oss of phase coherence i n the system . T he pri nci palresul t i s thatthe destructi on ofsuperconducti ng phasecoherencei n thed-w avesuperconductors typi cal l y,and i m m edi atel y,l eadsto the appearance ofanti ferrom agneti sm . T hi s transi ti on can be understood i n term s of the spontaneous breaki ng ofan approxi m ate "chi ral " SUc(2) sym m etry, w hi ch m ay be di scerned at l ow enough energi es i n the standard d-w ave superconductor. T he m echani sm of thi s spontaneous sym m etry breaki ng i s form al l y anal ogous to the dynam i cal m ass generati on i n the Q E D 3, w i th the "m ass" here bei ng proporti onal to staggered m agneti zati on. O ther phases w i th broken chi ralsym m etry i ncl ude the transl ati onal l y i nvari ant "d+ i p" and "d+ i s" i nsul ators, and the one-di m ensi onalcharge-densi ty and spi n-densi ty w aves,w hi ch are al li nsul ati ng descendants ofthe d-w ave superconductor. A l lthe i nsul ati ng states have the neutralspi n-1=2 exci tati ons that one can i denti fy i n the superconductor con ned by the l ogari thm i c potenti al . El ectron repul si on i s i n thi s form ali sm represented by a parti cul ar quarti c perturbati on to the Q E D 3 acti on,w hi ch breaks the chi ralsym m etry and sel ects the anti ferrom agnet as the preferred broken sym m etry state. Iform ul ate the m ean-el d theory ofthe anti ferrom agneti c i nstabi l i ty i n presenceofa short-rangerepul si vei nteracti on,and nd the staggered m agneti zati on to be si gni cantl y enhanced deeperi nsi de the i nsul ati ng state. T he theory o ersan expl anati on for the rounded d-w ave-l i ke di spersi on seen i n A R PES experi m ents on the i nsul ati ng C a2C uO 2 C l2 (F.R onni ng et. al .,Sci ence 282,2067 (1998). ) R el ati ons to other theoreti cal approaches to the hi gh-Tc probl em are di scussed.