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M. Shifman

Publications and source records attributed to M. Shifman.

At least 163 records · Page 9Linked to original sources

Families as Neighbors in Extra Dimension

We propose a new mechanism for explanation of the fermion hierarchy without introducing any family symmetries. Instead, we postulate that different generations live on different branes embedded in a relatively large extra dimension, where the gauge fields can propagate. The electroweak symmetry is broken on a separate brane, which is a source of exponentially decaying Higgs profile in the bulk. The resulting fermion masses and mixings are determined by an exponentially suppressed overlap of the fermion and Higgs wave functions and are automatically hierarchical even if all copies are identical and there is no hierarchy of distances. In this framework the well known pattern of the "nearest neighbor mixing" is predicted due to the fact that the families are literally neighbors in the extra space. This picture may also provide a new way of a hierarchically weak supersymmetry breaking, provided that the combination of three family branes is a non-BPS configuration, although each of them, individually taken, is. This results in exponentially weak supersymmetry breaking. We also discuss the issue of embedding identical branes in the compact spaces and localization of the fermionic zero modes.

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More on the Tensorial Central Charges in N=1 Supersymmetric Gauge Theories (BPS Wall Junctions and Strings)

We study the central extensions of the N=1 superalgebras relevant to the soliton solutions with the axial geometry - strings, wall junctions, etc. A general expression valid in any four-dimensional gauge theory is obtained. We prove that the only gauge theory admitting BPS strings at weak coupling is supersymmetric electrodynamics with the Fayet-Iliopoulos term. The problem of ambiguity of the (1/2,1/2) central charge in the generalized Wess-Zumino models and gauge theories with matter is addressed and solved. A possibility of existence of the BPS strings at strong coupling in N=2 theories is discussed. A representation of different strings within the brane picture is presented.

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Calculating the tension of domain wall junctions and vortices in generalized Wess-Zumino models

We study BPS saturated objects with axial geometry (wall junctions, vortices) in generalized Wess-Zumino models. It is observed that the tension of such objects is negative in general (although ``exceptional'' models are possible). We show how an ambiguity in the definition of central charges does not affect physical quantities, and we comment on the stability of the junctions and vortices. We illustrate these issues in two classes of models with Z_N symmetry. On the basis of analytical large N calculations and numerical calculations at finite N, we argue that the domain wall junctions in these models are indeed BPS saturated, and we calculate the junction tensions explicitly.

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BPS Saturated Solitons in N=2 Two-Dimensional Theories on RxS (Domain Walls in Theories with Compactified Dimensions)

We discuss topologically stable solitons in two-dimensional theories with the extended supersymmetry assuming that the spatial coordinate is compact. This problem arises in the consideration of the domain walls in the popular theories with compactified extra dimensions. Contrary to naive expectations, it is shown that the solitons on the cylinder can be BPS saturated. In the case of one chiral superfield, a complete theory of the BPS saturated solitons is worked out. We describe the classical solutions of the BPS equations. Depending on the choice of the Kahler metric, the number of such solutions can be arbitrarily large. Although the property of the BPS saturation is preserved order by order in perturbation theory, nonperturbative effects eliminate the majority of the classical BPS states upon passing to the quantum level. The number of the quantum BPS states is found. It is shown that the N=2 field theory includes an auxiliary N=1 quantum mechanics, Witten's index of which counts the number of the BPS particles.

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D-Walls and Junctions in Supersymmetric Gluodynamics in the Large N Limit Suggest the Existence of Heavy Hadrons

A number of arguments exists that the "minimal" BPS wall width in large N supersymmetric gluodynamics vanishes as 1/N. There is a certain tension between this assertion and the fact that the mesons coupled to the gluino condensate have masses which do not scale with N. To reconcile these facts we argue that there should exist additional soliton-like states with masses scaling as N. The BPS walls must be "made" predominantly of these heavy states which are coupled to the gluino condensate stronger than the conventional mesons. The tension of the BPS wall junction scales as N^2, which serves as an additional argument in favor of the 1/N scaling of the wall width. The heavy states can be thought of as solitons of the corresponding closed string theory. They are related to certain fivebranes in the M-theory construction. We study the issue of the wall width in toy models which capture some features of supersymmetric gluodynamics. We speculate that special hadrons with mass scaling as N should also exist in the large N limit of non-supersymmetric gluodynamics.

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Introduction to the Yuri Golfand Memorial Volume "Many Faces of Superworld"

The Yuri Golfand Memorial Volume commemorates Thirty Years of Supersymmetry. It will be published soon by World Scientific. The participants of the project are: D. Brace, L. Brink, S. Deser, G. Dvali, B. Feng, D. Freedman, G.-L. Gervais, G. Gabadadze, M. Grisaru, A. Hanany, Y.-H. He, S. Hellerman, E. D'Hoker, P. Fayet, V. Kac, I. Klebanov, N. Koretz-Golfand, D. Kutasov, E. Likhtman, A. Losev, M. Marinov, S. Mathur, A. Matusis, B. Morariu, N. Nekrasov, J. Polchinski, E. Rabinovici, L. Rastelli, P. Ramond, J. Schwarz, N. Seiberg, A. Semikhatov, G. Senjanovic, S. Shatashvili, M. Shifman, A. Smilga, M. Strassler, A. Tseytlin, M. Vasiliev, J. Wess, P. West, E. Witten, B. Zumino.

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Exact Results in Gauge Theories: Putting Supersymmetry to Work. The 1999 Sakurai Prize Lecture

Powerful methods based on supersymmetry allow one to find exact solutions to certain problems in strong coupling gauge theories. The inception of some of these methods (holomorphy in the gauge coupling and other chiral parameters, in conjunction with instanton calculations) dates back to the 1980's. I describe the early exact results -- the calculation of the beta function and the gluino condensate -- and their impact on the subsequent developments. A brief discussion of the recent breakthrough discoveries where these results play a role is given.

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Tilting the Brane, or Some Cosmological Consequences of the Brane Universe

We discuss theories in which the standard-model particles are localized on a brane embedded in space-time with large compact extra dimensions, whereas gravity propagates in the bulk. In addition to the ground state corresponding to a straight infinite brane, such theories admit a (one parameter) family of stable configurations corresponding to branes wrapping with certain periodicity around the extra dimension(s) when one moves along a noncompact coordinate (tilted walls). In the effective four-dimensional field-theory picture, such walls are interpreted as one of the (stable) solutions with the constant gradient energy, discussed earlier. In the cosmological context their energy "redshifts" by the Hubble expansion and dissipates slower then the one in matter or radiation. The tilted wall eventually starts to dominate the Universe. The upper bound on the energy density coincides with the present critical energy density. Thus, this mechanism can become significant any time in the future. The solutions we discuss are characterized by a tiny spontaneous breaking of both the Lorentz and rotational invariances. Small calculable Lorentz noninvariant terms in the standard-model Lagrangian are induced. Thus, the tilted walls provide a framework for the spontaneous breaking of the Lorentz invariance.

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Surviving on the Slope: Supersymmetric Vacuum in the Theories Where It Is Not Supposed to Be

In supersymmetric models with the run-away vacua or with the stable but non-supersymmetric ground state there exist stable field configurations (vacua) which restore one half of supersymmetry and are characterized by constant positive energy density. The formal foundation for such vacua is provided by the central extension of the N =1 superalgebra with the infinite central charge.

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A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure

Starting from a one-particle quasi-exactly solvable system, which is characterized by an intrinsic sl(2) algebraic structure and the energy-reflection symmetry, we construct a daughter N-body Hamiltonian presenting a deformation of the Calogero model. The features of this Hamiltonian are (i) it reduces to a quadratic combination of the generators of sl(N+1); (ii) the interaction potential contains two-body terms and interaction with the force center at the origin; (iii) for quantized values of a certain cohomology parameter n it is quasi-exactly solvable, the multiplicity of states in the algebraic sector is (N+n)!/(N!n!); (iv) the energy-reflection symmetry of the parent system is preserved.

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Energy Reflection Symmetry of Lie-Algebraic Problems: Where the Quasiclassical and Weak Coupling Expansions Meet

We construct a class of one-dimensional Lie-algebraic problems based on sl(2) where the spectrum in the algebraic sector has a dynamical symmetry E -> - E. All 2j+1 eigenfunctions in the algebraic sector are paired, and inside each pair are related to each other by simple analytic continuation x -> ix, except the zero mode appearing if j is integer. At j-> infinity the energy of the highest level in the algebraic sector can be calculated by virtue of the quasiclassical expansion, while the energy of the ground state can be calculated as a weak coupling expansion. The both series coincide identically.

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Domain Walls and Decay Rate of the Excited Vacua in the Large N Yang-Mills Theory

In the (non-supersymmetric) Yang-Mills theory in the large N limit there exists an infinite set of non-degenerate vacua. The distinct vacua are separated by domain walls whose tension determines the decay rate of the false vacua. I discuss the phenomenon from a field-theoretic point of view, starting from supersymmetric gluodynamics and then breaking supersymmetry, by introducing a gluino mass. By combining previously known results, the decay rate of the excited vacua is estimated, Γ\sim \exp (-const \times N^4). The fourth power of N in the exponent is a consequence of the fact that the wall tension is proportional to N.

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BPS-Saturated Walls in Supersymmetric Theories

Domain-wall solutions in four-dimensional supersymmetric field theories with distinct discrete vacuum states lead to the spontaneous breaking of supersymmetry, either completely or partially. We consider in detail the case when the domain walls are the BPS-saturated states, and 1/2 of supersymmetry is preserved. Several useful criteria that relate the preservation of 1/2 of supersymmetry on the domain walls to the central extension appearing in the N=1 superalgebras are established. We explain how the central extension can appear in N=1 supersymmetry and explicitly obtain the central charge in various models: the generalized Wess-Zumino models, and supersymmetric Yang-Mills theories with or without matter. The BPS-saturated domain walls satisfy the first-order differential equations which we call the creek equations, since they formally coincide with the (complexified) equations of motion of an analog high-viscosity fluid on a profile which is given by the superpotential of the original problem. Some possible applications are considered.

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Heavy flavor decays, OPE and duality in two-Dimensional 't Hooft model

The 't Hooft model (two-dimensional QCD in the limit of large number of colors) is used as a laboratory for exploring various aspects of the heavy quark expansions in the nonleptonic and semileptonic decays of heavy flavors. We perform a complete operator analysis and construct the operator product expansion (OPE) up to terms O(1/m_Q^4), inclusively. The OPE-based predictions for the inclusive widths are then confronted with the "phenomenological" results, obtained by summation of all open exclusive decay channels, one by one. The summation is carried out analytically, by virtue of the 't Hooft equation. The two alternative expressions for the total widths match. We comment on the recent claim in the literature of a 1/m_Q correction to the total width which would be in clear conflict with the OPE result. The issue of duality violations both in the simplified setting of the 't Hooft model and in actual QCD is discussed. The amplitude of oscillating terms is estimated.

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Supersymmetric Domain Walls (New Exact Results in Supersymmetric Gluodynamics)

Supersymmetric domain walls are reviewed. The main emphasis is made on saturated walls in strongly coupled gauge theories. The central charge of the N=1 superalgebra appears in supersymmetric gluodynamics as a quantum anomaly. I also consider some rather unusual general features of supersymmetric domain walls.

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Snapshots of Hadrons, or the Story of How the Vacuum Medium Determines the Properties of the Classical Mesons Which Are Produced, Live and Die in the QCD Vacuum

1. QCD Sum Rules: 20 Years After; 2. QCD Vacuum and Basics of the SVZ Method: 2.1 General ideas; 2.2. Getting started/Playing with toy models; 3. Vacuum Condensates; 4. Rho Meson in QCD; 5. Basic Theoretical Instrument -- Wilson's OPE; 6. Practical Version of OPE; 7. Low Energy Theorems; 8. Are All Hadrons Alike? 9. Ecological Niche; 10. New Developments: 10.1 Light-cone sum rules; 10.2 Heavy flavor sum rules; 11. Sum Rules and Lattices; 12. Vacuum Fluctuations are Subtle Creatures; 13. Instead of Conclusions.

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Domain Walls in Supersymmetric Yang-Mills Theories

We present a detailed analysis of the domain walls in supersymmetric gluodynamics and SQCD. We use the (corrected) Veneziano-Yankielowicz effective Lagrangians to explicitely obtain the wall profiles and check recent results of Dvali and Shifman (Phys. Lett. B396, (1997) 64: (i) the BPS-saturated nature of the walls; (ii) the exact expressions for the wall energy density which depend only on global features of dynamics (the existence of a non-trivial central extension of N=1 superalgebra in the theories which admit wall-like solutions). If supersymmetry is softly broken by the gluino mass, the degeneracy of the distinct vacua is gone, and one can consider the decay rate of the "false" vacuum into the genuine one. We do this calculation in the limit of the small gluino mass. Finally, we comment on the controversy regarding the existence of $N$ distinct chirally asymmetric vacua in SU(N) SUSY gluodynamics.

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Non-Perturbative Dynamics in Supersymmetric Gauge Theories

I give an introductory review of recent, fascinating developments in supersymmetric gauge theories. I explain pedagogically the miraculous properties of supersymmetric gauge dynamics allowing one to obtain exact solutions in many instances. Various dynamical regimes emerging in supersymmetric Quantum Chromodynamics and its generalizations are discussed. I emphasize those features that have a chance of survival in QCD and those which are drastically different in supersymmetric and non-supersymmetric gauge theories. Unlike most of the recent reviews focusing almost entirely on the progress in extended supersymmetries (the Seiberg-Witten solution of N=2 models), these lectures are mainly devoted to N=1 theories. The primary task is extracting lessons for non-supersymmetric theories.

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