BASED ON WORK WITH KENICHI KONISHI (UNIV. OF PISA) [0909.3781 TO APPEAR IN NPB]
Confinement dual Meissener effect dual Meissener effect
1) Perturbed SU(N) Seiberg WiRen theory : 2) SU(N) with Flavors at Higgs Branch root: 3) Pouliot Type duality [ SEIBERG WITTEN `94, DOUGLAS SHENKER `96] [ CARLINO KONISHI KUMAR MURAYAMA `01] [ STRASSLER `98] Q: QCD A: confinement SUSY SUSY
SU(N) confinement abelian monopole non abelian monopole Higgsing [ Abelianizacon `80]
1) N=1 Pure Yang Mills Theories Review of SUSY vacua GNO duality Wilson `thoof loop `thoof classificacon WiRen effect 2) N=1 SYM with a Higgs field set up electric/magnecc screening Confinement index 3) Conclusion
4D N=1 pure Yang Mills dual coxeter number theta angle 2 pi
confinement Wilson `thoof Loop?
[ GODDARD NUYTS OLIVE `77] Nonabelian monopole electric/magnecc duality GNO claim 1 :
weight vector weight lajce adjoint weight vector root vector
GNO claim 2 : Quanczacon condicon weight vector H root vector H v weight vector Pure Yang Mills adjoint H weight vector
electric magnecc adjoint rep. fundamental rep. symmetric tensor rep. anc symmetric tensor rep. non abelian monopole GNO dual
Wilson `thoof loop fundamental rep. pure YM Pure SYM gaugino, gluon
adjoint R center SU(N) (N ality) N ality
Wilson loop N ality N ality
Weight vector up to Root vector GNO nonabelian monopole H weight vector magnecc group v
Pure YM Wilson thoof Loop
Massive vacua [ THOOFT `78 : DONAGI WITTEN `95] skew form mutually local mutually non local
1 : (a,b) mutually non local confine 2 : 2 x,y mutually local 3 : massive subgroup
N : confining oblique confining Higgs N : N+1 N=6 Mixed
electric/magcc charge weight vector theta angle magnecc charge WiRen effect electric charge generate [ KAPUSTIN `05] Simply laced non simply laced Simply laced electric
Non Simply laced
N N
Higgs massive Integrate out product pure SYM confine dual coxeter number
Wilson Loop k singlet Area law Higgsing electric screening
Wilson Loop GNO weight vector
Area law
electric screening SU(Ni) N1, N2 singlet Area law electric/magnecc screening Area law Wilson Loop Greatest Common divisor t Confinement Index
Area Area Area Area theta angle index Dynkin index of embedding
thoof Loop dual group thoof Loop dual group
external charge singlet magnecc screening Area law confinement index 2
singlet electric screening Area [ AUZZI BOLOGNESI EVSLIN KONISHI MURAYAMA `04] Area law
SU(N) N singlet confinement index Area law Nontrivial r theta angle U(N) USp Dynkin index of embedding U(N) theta angle confinement index
N=1 Wilson `thoof Loop confinement index t order t subgroup confinement index t G theta angle SW Wilson `t Hoof loop? Wilson t Hoof loop
[ ASHOK CACHAZO DELL AQUILLA `06] Work in Progress with PI friends
Higgs SUSY vacua SUSY breaking vacua SUSY breaking vacua SUSY SUSY breaking vacua index descripcon SW, Konishi Anomaly, Seiberg dual consistency check
Perimeter law Area law Perimeter law Area law Perimeter law Area law
confinement confinement Wilson thoof Loop QCD subgroup confinement Landscape of field theories superpotencal
Wilson thoof Loop confinement index SU(N) with adjoint [ CACHAZO SEIBERG WITTEN`03 ] confinement index open problem ( talk)
confinement index 1