1 / 17

N =1 2+1 NCSYM & Supermembrane with Central Charges .

N =1 2+1 NCSYM & Supermembrane with Central Charges. Lyonell Boulton, M.P. Garcia del Moral, Alvaro Restuccia. Hep-th/0609054. TORINO U. & POLITECNICO TORINO & U. ALESSANDRIA. RTN WORKSHOP NAPOLI 2006. OVERVIEW. MOTIVATION D=11 SUPERMEMBRANE ( M2 )

haley-bradshaw
Download Presentation

N =1 2+1 NCSYM & Supermembrane with Central Charges .

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. N=1 2+1 NCSYM & Supermembrane with Central Charges . Lyonell Boulton, M.P. Garcia del Moral, Alvaro Restuccia Hep-th/0609054 TORINO U. & POLITECNICO TORINO & U. ALESSANDRIA RTN WORKSHOP NAPOLI 2006

  2. OVERVIEW • MOTIVATION • D=11 SUPERMEMBRANE (M2) • N=1 SUPERMEMBRANE WITH CENTRAL CHARGES (M2) • N=1 M2 vs 2+1 NCSYM THEORY • DISCRETNESS OF THE BOSONIC SPECTRUM AT EXACT LEVEL • CENTER, CONFINEMENT, TRANSITION PHASE. • INTERPRETATION IN TERMS OF M-THEORY & N=1 SQCD • CONCLUSIONS

  3. MOTIVATION • OPEN PROBLEMS: • NONPERTURBATIVE QUANTIZATION OF STRING THEORY: • QUANTIZATION OF M-THEORY: M2 (SUPERMEMBRANE), M5, • Attempts: QUANTIZATION OF M2 • 2. NONPERTURBATIVE QUANTIZATION OF YANG-MILLS THEORIES TOWARDS A COMPLETE DESCRIPTION OF QCD. • Attempts: SPIN CHAINS, TWISTORS, GAUGE-GRAVITY, • LARGE N MATRIX MODELS.. THE CANONICAL QUANTIZATION OF THE SUPERMEMBRANE CENTRALCHARGES CANONICAL QUANTIZATION 2+1 NCSYM THEORY

  4. RESULTS • At exact level, the first results of the spectral properties of • N=1 2+1 NCYM that can live in 4D: • - purely discrete with eingenvalues of finite multiplicity • - mass gap. • At exat level, the first results of the spectral properties of • the N=1 supermembrane with central charges, 4D: • - purely discrete with eigenvalues of finite multiplicity • - mass gap • It represents a nonperturbative quantization of a sector of • M-theory

  5. RESULTS • We have identified the center of the group as a • mechanism for confinement in both theories, • at exact and regularized level. • Interpretation in terms of SQCD: • - The N=1 NCSYM or the Supermembrane with central • charges are the IR phase of the theory. • - Through a breaking of the center due a • topological transition the theory enters in a • - UV phase that corresponds to the compactified • N=4 Supermembrane as a many body object interpreted • in terms of a quark-gluon plasma

  6. MATRIX MODELS ORIGINAL POINT OF VIEW: Halpern, Hoppe, De Wit, Hoppe, Nicolai , de wit, Peeters, Plefka etc.. COMPACT. M2 H H H EXACT EXACT EXACT ? ? ? SYMMETRIES COMPACT H H REGULARIZED REGULARIZED M2 NCSYM H =H EXACT RECENT RESULT OUR RESULTS FOLLOW ORIGINAL POINT OF VIEW: M2 H REGULARIZED BFSS/IKKT CONJECTURE: D0 OR D-1 ACTION IS TAKEN AS THE FUNDAMENTAL SYMMETRIES: EX. BMN MODEL ETC..

  7. H= M, N=1,..,9 CLASSICALLY: STRING-LIKE SPIKES: QUANTUM: BOSONIC FERMIONIC PURELY DISCRETE CONTINUUM!! 2º QUANTIZED THEORY!!!: MANY BODY OBJECT OF D0´S OLD PROBLEMS OF M2 QUANTIZATION (L.C.G)De Wit+Hoppe+Nicolai; De wit+Marquard+ Nicolai, De wit+Luscher+Nicolai, D.wit+Peeters+Plefka, MPGM+Navarro+Perez+Restuccia

  8. THE SUPERMEMBRANE WITH CENTRAL CHARGES Martin,Ovalle,Restuccia;MPGM,Restuccia(1); Boulton,MPGM.,Restuccia(3), Boulton,MPGM.,Martin, Restuccia,Boulton(2),MPGM+R, Bellorin,Restuccia,97-06 SU(N) Spectrum: CLASSICALLY: NOTSTRING-LIKE SPIKES (1) QUANTUM: BOSONIC PURELY DISCRETE SPECTRUM (2) FERMIONIC PURELY DISCRETE SPECTRUM (3) TOPOLOGICAL CONDITION CENTRAL CHARGE CONDITION: &

  9. With the decomposition allowed by fixed central charges: A N=1 2+1 symplectic NCSYM coupled to scalars proceeding from NCSYM 10D reduccion=N=1 Supermembrane with Z The only degrees of freedom to quantize are (X, A).

  10. SU(N) REGULARIZATION OF THE M2 GAUGE FIXING CONDITION: CONSTRAINS:

  11. SPECTRAL PROPERTIES: SU(N) LEVEL CLASSICALLY: NO-STRING-LIKE SPIKES MPGM+ A. Restuccia QUANTUM LEVEL: BOSONIC SECTOR Boulton+MPGM+Martin+Restuccia QUANTUM LEVEL FERMIONIC SECTOR Boulton+MPGM+Martin+Restuccia Eigenvalues of V(X)

  12. Large N for semiclassical aproximation Semiclassical quantization of M2 brane Duff, Inami, Pope, Sezgin,Stelle Semiclassical description of the regularized M2 brane Matrix regularization Gaussian measure on l2 Dg Well-defined

  13. Spectrum of the exact bosonic hamiltonian I Su(N) proof: Exact proof: Compact Phase Space Infinite dimensional Phase Space Configuration Space (X,A) Banach space Potential Defining

  14. Spectrum of the exact Bosonic Hamiltonian II WITH NON-COMPACT INFINITE DIMENSIONAL LAPLACIAN

  15. The center as a mechanism of confinement Symmetries at exact level: NON-COMMUTATIVE THEORY FIXING THE HARMONIC SECTOR Symmetries at SU(N) level: CENTER OF MASS TERMS Mass terms

  16. SQCD & M-Theory Interpretation IR UV Topological transition Many-body object Dirac monopoles, Mass terms m(Z) Z(2) string , glueballs CONFINEMENT QUARK-GLUON PLASMA N=4 Compactified Supermembrane (N=1) Supermembrane with Z= (N=1) NCYM

  17. MATRIX MODELS D=11 SUPERMEMBRANES 10D SYM MATRIX REGULARIZATION DIMEN. REDUCCION 0+1 SU(N) H= LARGE N LIMIT ? PROBLEM OF CLOSED HARMONIC FORMS MATRIX REGULARIZATION IN COMPACTIFIED SPACES? TOPOLOGICAL INFORMATION? De Wit+Peeters+Plefka

More Related