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1.
Yang-Mills instantons on ALE gravitational instantons were constructed by Kronheimer and Nakajima in terms of matrices satisfying algebraic equations. These were conveniently organized into a quiver. We construct generic Yang-Mills instantons on ALF gravitational instantons. Our data are formulated in terms of matrix-valued functions of a single variable, that are in turn organized into a bow. We introduce the general notion of a bow, its representation, its associated data and moduli space of solutions. For a judiciously chosen bow the Nahm transform maps any bow solution to an instanton on an ALF space. We demonstrate that this map respects all complex structures on the moduli spaces, so it is likely to be an isometry, and use this fact to study the asymptotics of the moduli spaces of instantons on ALF spaces.  相似文献   

2.
 In this paper we explicitly calculate the analogue of the 't Hooft SU(2) Yang–Mills instantons on Gibbons–Hawking multi-centered gravitational instantons, which come in two parallel families: the multi-Eguchi–Hanson, or A k ALE gravitational instantons and the multi-Taub–NUT spaces, or A k ALF gravitational instantons. We calculate their energy and find the reducible ones. Following Kronheimer we also exploit the U(1) invariance of our solutions and study the corresponding explicit singular SU(2) magnetic monopole solutions of the Bogomolny equations on flat ℝ3. Received: 16 September 2002 / Accepted: 22 October 2002 Published online: 21 February 2003 Communicated by A. Connes  相似文献   

3.
The Euclidean vacuum functional of Yang-Mills theory is saturated by infinitely large two-dimensional sheets of calculable universal thickness. The gauge fields inside the sheets are characterised by a distribution of instantons held together by a smooth solution of the field equations. The sheets cannot grow in the transverse directions. Within each sheet the orientation in group space of the average field is correlated to the spatial orientation of the area, while different sheets are totally uncorrelated. We exhibit a class of fluctuations above this background which confine quarks. No assumption about the infra-red behaviour of the Gell-Mann-Low function is used; all quantities are calculable and no free parameters exist beyond the group structure constants.  相似文献   

4.
We find a new gauge in which U(1) noncommutative instantons are explicitly non-singular on noncommutative R 4. We also present a pedagogical introduction into noncommutative gauge theories.  相似文献   

5.
We study the U(1) and U(2) instanton solutions of gauge theory on general nonocmmutative R^4,In all cases considered we obtain explicit results for the projection operators.In some cases we computed numberically the instanton charge and found that it is an integer independent of the noncommutative parametersθ1,2.  相似文献   

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We solve = 2 supersymmetric Yang-Mills theories for an arbitrary classical gauge group, i.e. SU(N), SO(N), Sp(N). In particular, we derive the prepotential of the low-energy effective theory, and the corresponding Seiberg-Witten curves. We manage to do this without resolving singularities of the compactified instanton moduli spaces.To Freeman Dyson, with admirationOn leave of absence from ITEP, Moscow, Russia  相似文献   

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《Nuclear Physics B》1995,433(1):99-122
It is shown that the inhomogeneous saddle points of scale invariant theories make the semiclassical expansion sensitive to the choice of non-renormalizable operators. In particular, the instanton fugacity and the beta function of the two-dimensional non-linear sigmamodel depend on apparently non-renormalizable operators. This represents a non-perturbative breakdown of that concept of universality which is based on low dimensional operators.  相似文献   

11.
We study the U(1) and U(2) instanton solutions of gauge theory on general noncommutative R4. In allcases considered we obtain explicit results for the projection operators. In some cases we computed numerically theinstanton charge and found that it is an integer independent of the noncommutative parameters θ1,2.  相似文献   

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Instanton effects are considered for a sample of supersymmetric theories, namely, quantum mechanics, gluodynamics, Higgs model. The problem is how to reconcile the apparent lack of the boson-fermion symmetry in the effective instanton induced interactions with supersymmetry of the corresponding lagrangians. It is shown that in the case of quantum mechanics and the Higgs model there is actually no conflict between supersymmetry and the instanton calculus since the Ward identities, associated with the supersymmetry transformations, are satisfied. In quantum mechanics this is due to spontaneous symmetry breaking, or pole terms in matrix elements of supercharge, while in the case of the supersymmetric Higgs model the effective fermion interaction just reduces to a total derivative. In the case of supersymmetric gluodynamics, however, the standard instanton calculus explicitly violates naive Ward identities.  相似文献   

14.
We study extrema of the general conformally invariant action:
Sc = ∫1α2CabcdCabcd+γRabcd1Rabcd1+iθRabcd1Rabcd
.We find the first examples in four dimensions of asymptotically euclidean gravitational instantons. These have arbitrary Euler number and Hirzebruch signature. Some of these instantons represent tunneling between zero-curvature vacua that are not related by small gauge transformations. Others represent tunneling between flat space and topologically non-trivial zero-energy initial data. A general formula for the one-loop determinant is derived in terms of the renormalization group invariant masses, the volume of space-time, the Euler number and the Hirzebruch signature.  相似文献   

15.
The multi-instanton solutions of ’t Hooft and of Jackiw, Nohl, and Rebbi are generalized to the case of curvilinear coordinates. The resulting formulas are considerably simplified if the transformation of coordinates is supplemented with a gauge transformation. As a result, the gauge field develops a term that has the same form as in Cartesian coordinates and which describes pseudoparticles and a compensating addition of a geometric origin (it is determined by the coordinate frame used). The singularities of the compensating field are irrelevant to physical quantities, but they can affect gauge-dependent quantities.  相似文献   

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We construct finite-energy instanton connections over ℝ4 which are periodic in two directions via an analogue of the Nahm transform for certain singular solutions of Hitchin's equations defined over a 2-torus. Received: 20 September 1999 / Accepted: 15 April 2000  相似文献   

18.
Any (anti)-instanton yields a set of three contact forms on S7. The basic (anti)-instanton yields a hypercontact structure. Also, we indicate sufficient conditions for the components of an SU (2) connection to be contact forms. Finally, we prove, under a mild hypothesis, that the three contact forms of any hypercontact structure define the same contact structure.  相似文献   

19.
Minimum action solutions for SU(2) Yang-Mills fields in Euclidean 4-space correspond, via the Penrose twistor transform, to algebraic bundles on the complex projective 3-space. These bundles in turn correspond to algebraic curves. The implication of these results for the Yang-Mills fields is described. In particular all solutions are rational and can be constructed from a series of AnsätzeA l forl1.  相似文献   

20.
It is shown that with asymmetric classical vacua the quantum mechanical instanton approach to the energy splitting of degenerate states applies even though the degenerate state in one well is not the quantum mechanical ground state of that well. The instanton approach leads to the correct leading exponential behavior of the energy splitting E, but the prefactor is much more difficult to compute due to the asymmetric nature of the fluctuation potential V(c(t)), which is in turn a direct consequence of the asymmetry of the two classical minima between which the instanton interpolates.  相似文献   

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