109 research outputs found

    BPS and non-BPS Domain Walls in Supersymmetric QCD with SU(3) Gauge Group

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    We study the spectrum of the domain walls interpolating between different chirally asymmetric vacua in supersymmetric QCD with the SU(3) gauge group and including 2 pairs of chiral matter multiplets in fundamental and anti-fundamental representations. For small enough masses m < m* = .286... (in the units of \Lambda), there are two different domain wall solutions which are BPS-saturated and two types of ``wallsome sphalerons''. At m = m*, two BPS branches join together and, in the interval m* < m < m** = 3.704..., BPS equations have no solutions but there are solutions to the equations of motion describing a non-BPS domain wall and a sphaleron. For m > m**, there are no solutions whatsoever.Comment: 10 pages LaTeX, 5 postscript figure

    Born--Oppenheimer corrections to the effective zero-mode Hamiltonian in SYM theory

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    We calculate the subleading terms in the Born--Oppenheimer expansion for the effective zero-mode Hamiltonian of N = 1, d=4 supersymmetric Yang--Mills theory with any gauge group. The Hamiltonian depends on 3r abelian gauge potentials A_i, lying in the Cartan subalgebra, and their superpartners (r being the rank of the group). The Hamiltonian belongs to the class of N = 2 supersymmetric QM Hamiltonia constructed earlier by Ivanov and I. Its bosonic part describes the motion over the 3r--dimensional manifold with a special metric. The corrections explode when the root forms \alpha_j(A_i) vanish and the Born--Oppenheimer approximation breaks down.Comment: typos correcte

    Effective Lagrangians for (0+1) and (1+1) dimensionally reduced versions of D=4 N=2 SYM theory

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    We consider dimensionally reduced versions of N=2 four- dimensional supersymmetric Yang-Mills theory and determine the one-loop effective Lagrangians associated with the motion over the corresponding moduli spaces. In the (0+1) case, the effective Lagrangian describes an N=4 supersymmetric quantum mechanics of the Diaconescu--Entin type. In (1+1) dimensions, the effective Lagrangian represents a twisted N=4 supesymmetric sigma model due to Gates, Hull, and Rocek. We discuss the genetic relationship between these two models and present the explicit results for all gauge groups.Comment: 16 pages, no figures, minor correction

    Chiral anomalies in higher-derivative supersymmetric 6D gauge theories

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    We show that the recently constructed higher-derivative 6D SYM theory involves an internal chiral anomaly breaking gauge invariance. The anomaly is cancelled when adding to the theory an adjoint matter hypermultiplet.Comment: A missed contribution added. The article is rather essentially reshuffle

    Normalized Vacuum States in N = 4 Supersymmetric Yang--Mills Quantum Mechanics with Any Gauge Group

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    We study the question of existence and the number of normalized vacuum states in N = 4 super-Yang-Mills quantum mechanics for any gauge group. The mass deformation method is the simplest and clearest one. It allowed us to calculate the number of normalized vacuum states for all gauge groups. For all unitary groups, #(vac) = 1, but for the symplectic groups [starting from Sp(6) ], for the orthogonal groups [starting from SO(8)] and for all the exceptional groups, it is greater than one. We also discuss at length the functional integral method. We calculate the ``deficit term'' for some non-unitary groups and predict the value of the integral giving the ``principal contribution''. The issues like the Born-Oppenheimer procedure to derive the effective theory and the manifestation of the localized vacua for the asymptotic effective wave functions are also discussed.Comment: 41 pages, 5 Postscript figures. Minor corrections. References and some further illustrative examples adde

    Fractons in Twisted Multiflavor Schwinger Model

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    We consider two-dimensional QED with several fermion flavors on a finite spatial circle. A modified version of the model with {\em flavor-dependent} boundary conditions ψp(L)=e2πip/Nψp(0)\psi_p(L) = e^{2\pi ip/ N} \psi_p(0), p=1,,Np = 1, \ldots , N is discussed (NN is the number of flavors). In this case a non-contactable contour in the space of the gauge fields is {\em not} determined by large gauge transformations. The Euclidean path integral acquires the contribution from the gauge field configurations with fractional topological charge. The configuration with ν=1/N\nu = 1/N is responsible for the formation of the fermion condensate ψˉpψp0\langle\bar{\psi}_p \psi_p\rangle_0. The condensate dies out as a power of L1L^{-1} when the length LL of the spatial box is sent to infinity. Implications of this result for non-abelian gauge field theories are discussed in brief.Comment: 29 pages, 3 figures available upon request, Report TPI-MINN-94-24-T Plain LATE

    Ghost-free higher-derivative theory

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    We present an example of the quantum system with higher derivatives in the Lagrangian, which is ghost-free: the spectrum of the Hamiltonian is bounded from below and unitarity is preserved.Comment: 13 pages, 1 figur

    Comments on the Dynamics of the Pais-Uhlenbeck Oscillator

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    We discuss the quantum dynamics of the PU oscillator, i.e. the system with the Lagrangian L = ½ [ ¨q² - (Ω₁² + Ω₂²) ·q² + Ω₁²Ω₂²q ] (+ nonlinear terms). When Ω₁ ≠ Ω₂, the free PU oscillator has a pure point spectrum that is dense everywhere. When Ω₁ = Ω₂, the spectrum is continuous, E ∊ {–∞, ∞}. The spectrum is not bounded from below, but that is not disastrous as the Hamiltonian is Hermitian and the evolution operator is unitary. Generically, the inclusion of interaction terms breaks unitarity, but in some special cases unitarity is preserved. We discuss also the nonstandard realization of the PU oscillator suggested by Bender and Mannheim, where the spectrum of the free Hamiltonian is positive definite, but wave functions grow exponentially for large real values of canonical coordinates. The free nonstandard PU oscillator is unitary at Ω₁ ≠ Ω₂, but unitarity is broken in the equal frequencies limit

    Comments on thermodynamics of supersymmetric matrix models

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    We present arguments that the structure of the spectrum of the supersymmetric matrix model with 16 real supercharges in the large N limit is rather nontrivial, involving besides the natural energy scale ~\lambda^{1/3} = (g^2 N)^{1/3} also a lower scale ~\lambda^{1/3}N^{-5/9}. This allows one to understand a nontrivial behaviour of the mean internal energy of the system, E proportional to T^{14/5}, predicted by AdS duality arguments.Comment: 16 pages, LaTe

    Conformal properties of hypermultiplet actions in six dimensions

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    We consider scale-invariant interactions of 6D N=1 hypermultiplets with the gauge multiplet. If the canonical dimension of the matter scalar field is assumed to be 1, scale-invariant lagrangians involve higher derivatives in the action. Though scale-invariant, all such lagrangians are not invariant with respect to special conformal transformations and their superpartners. If the scalar canonical dimension is assumed to be 2, conformal invariance holds at the classical, but not at the quantum level.Comment: 14 pages, 1 figur