wodimensionalgaugetheoriesandquantumintegrablesys：兩維規(guī)范理論量子可積系統(tǒng)-資料下載頁
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【正文】 Y Symmetries QUIVER GAUGE THEORY Symmetries QUIVER GAUGE THEORY Charged matter Adjoint chiral multiplet Fundamental chiral multiplet Antifundamental chiral multiplet Bifundamental chiral multiplet QUIVER GAUGE THEORY Matter fields: adjoints QUIVER GAUGE THEORY Matter fields: fundamentals+antifundamentals QUIVER GAUGE THEORY Matter fields: bifundamentals QUIVER GAUGE THEORY Quiver gauge theory: full content QUIVER GAUGE THEORY: MASSES Adjoints i QUIVER GAUGE THEORY: MASSES Fundamentals Antifundamentals i a = 1, …. , Li QUIVER GAUGE THEORY: MASSES Bifundamentals i j QUIVER GAUGE THEORY What is so special about these masses? QUIVER GAUGE THEORY From the gauge theory point of view nothing special….. QUIVER GAUGE THEORY The mass puzzle! The mass puzzle The Bethe ansatz like equations Can be written for an arbitrary matrix The mass puzzle However the Yangian symmetry Y(H) would get replaced by some ugly infinitedimensional 171。 free 187。 algreba without nice representations The mass puzzle Therefore we conclude that our choice of masses is dictated by the hidden symmetry that of the dual spin chain The Standard Model has many free parameters Among them are the fermion masses Is there a (hidden) symmetry principle behind them? The Standard Model has many free parameters In the supersymmetric models we considered the mass tuning can be 171。 explained 187。 using a duality to some quantum integrable system Further generalizations: Superpotential from prepotential Tree level part Induced by twist Flux superpotential (Losev,NN, Shatashvili’97) The N=2* theory on R2 X S2 Superpotential from prepotential Magic flux Electric flux In the limit of vanishing S2 the magic flux should vanish Instanton corrected BA equations Q u i ck T i me ? a n d aT I F F (U n co m p re s se d ) d e co m p re ss o ra re n e e d e d t o se e t h i s p i ct u re .Effective Smatrix contains 2body, 3body, … interactions Instanton corrected BA equations Q u ickT ime ? a n d aT I F F (U n co m p re s se d ) d e co m p re sso ra re n e e d e d t o se e t h is p i ct u re .Instanton corrected BA equations The prepotential of the lowenergy effective theory Is governed by a classical (holomorphic) integrable system DonagiWitten’95 Liouville tori = Jacobians of SeibergWitten curves Classical integrable system vs Quantum integrable system That system is quantized when the gauge theory is subject to the Omegabackground NN’02 NN,Okounkov’03 Braverman’03 Our quantum system is different! Blowing up the twosphere Wallcrossing phenomena (new states, new solutions) Something for the future Naturalness of our quivers Somewhat unusual matter content Branes at orbifolds typically lead to smth like Naturalness of our quivers This picture would arise in the sa(i) ? 0 limit BA for QCD FaddeevKorchemsky’94 Naturalness of our quivers Other quivers? Naturalness of our quivers Possibly with the help of ’s construction CONCLUSIONS 1. We found the Bethe Ansatz equations are the equations describing the vacuum configurations of certain quiver gauge theories in two dimensions 2. The duality to the spin chain requires certain relations between the masses of the matter fields to be obeyed. This could have phenomenological consequences. CONCLUSIONS 3. The algebraic Bethe ansatz seems to provide a realization of the brane creation operators something of major importance both for topological and physical string theories 4. Obviously this is a beginning of a beautiful story….
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