Confinement dual Meissener effect dual Meissener effect

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あつとしひろもり
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1 BASED ON WORK WITH KENICHI KONISHI (UNIV. OF PISA) [ TO APPEAR IN NPB]

2 Confinement dual Meissener effect dual Meissener effect

3 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

4 SU(N) confinement abelian monopole non abelian monopole Higgsing [ Abelianizacon `80]

5 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

6 4D N=1 pure Yang Mills dual coxeter number theta angle 2 pi

7 confinement Wilson `thoof Loop?

8 [ GODDARD NUYTS OLIVE `77] Nonabelian monopole electric/magnecc duality GNO claim 1 :

10 weight vector weight lajce adjoint weight vector root vector

11 GNO claim 2 : Quanczacon condicon weight vector H root vector H v weight vector Pure Yang Mills adjoint H weight vector

12 electric magnecc adjoint rep. fundamental rep. symmetric tensor rep. anc symmetric tensor rep. non abelian monopole GNO dual

13 Wilson `thoof loop fundamental rep. pure YM Pure SYM gaugino, gluon

14 adjoint R center SU(N) (N ality) N ality

15 Wilson loop N ality N ality

16 Weight vector up to Root vector GNO nonabelian monopole H weight vector magnecc group v

17 Pure YM Wilson thoof Loop

18 Massive vacua [ THOOFT `78 : DONAGI WITTEN `95] skew form mutually local mutually non local

19 1 : (a,b) mutually non local confine 2 : 2 x,y mutually local 3 : massive subgroup

20 N : confining oblique confining Higgs N : N+1 N=6 Mixed

21 electric/magcc charge weight vector theta angle magnecc charge WiRen effect electric charge generate [ KAPUSTIN `05] Simply laced non simply laced Simply laced electric

22 Non Simply laced

23 N N

25 Higgs massive Integrate out product pure SYM confine dual coxeter number

26 Wilson Loop k singlet Area law Higgsing electric screening

27 Wilson Loop GNO weight vector

28 Area law

29 electric screening SU(Ni) N1, N2 singlet Area law electric/magnecc screening Area law Wilson Loop Greatest Common divisor t Confinement Index

30 Area Area Area Area theta angle index Dynkin index of embedding

31 thoof Loop dual group thoof Loop dual group

32 external charge singlet magnecc screening Area law confinement index 2

33 singlet electric screening Area [ AUZZI BOLOGNESI EVSLIN KONISHI MURAYAMA `04] Area law

34 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

35 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

36 [ ASHOK CACHAZO DELL AQUILLA `06] Work in Progress with PI friends

37 Higgs SUSY vacua SUSY breaking vacua SUSY breaking vacua SUSY SUSY breaking vacua index descripcon SW, Konishi Anomaly, Seiberg dual consistency check

38 Perimeter law Area law Perimeter law Area law Perimeter law Area law

39 confinement confinement Wilson thoof Loop QCD subgroup confinement Landscape of field theories superpotencal

40 Wilson thoof Loop confinement index SU(N) with adjoint [ CACHAZO SEIBERG WITTEN`03 ] confinement index open problem ( talk)

41 confinement index 1

SUSY DWs

SUSY DWs @ 2013 1 25 Supersymmetric Domain Walls Eric A. Bergshoeff, Axel Kleinschmidt, and Fabio Riccioni Phys. Rev. D86 (2012) 085043 (arxiv:1206.5697) ( ) Contents 1 2 SUSY Domain Walls Wess-Zumino Embedding