3,660 research outputs found
A Note on Higher Dimensional Instantons and Supersymmetric Cycles
We discuss instantons in dimensions higher than four. A generalized self-dual
or anti-self-dual instanton equation in n-dimensions can be defined in terms of
a closed (n-4) form and it was recently employed as a topological
gauge fixing condition in higher dimensional generalizations of cohomological
Yang-Mills theory. When is a calibration which is naturally introduced
on the manifold of special holomony, we argue that higher dimensional instanton
may be locally characterized as a family of four dimensional instantons over a
supersymmetric (n-4) cycle with respect to the calibration .
This is an instanton configuration on the total space of the normal bundle
of the submanifold and regarded as a natural
generalization of point-like instanton in four dimensions that plays a
distinguished role in a compactification of instanton moduli space.Comment: 14 pages, latex, Talk presented at the workshop on Gauge Theory and
Integrable Models (YITP, Kyoto), January 26-29, 1999, the title correcte
Exact Solutions to the Two-dimensional BF and Yang-Mills Theories in the Light-cone Gauge
It is shown that the BRS-formulated two-dimensional BF theory in the
light-cone gauge (coupled with chiral Dirac fields) is solved very easily in
the Heisenberg picture. The structure of the exact solution is very similar to
that of the BRS-formulated two-dimensional quantum gravity in the conformal
gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a
criticism is made on the reasoning of Kato and Ogawa, who derived the critical
dimension D=26 of string theory on the basis of the anomaly of the BRS Noether
charge. By adding the term to the BF-theory Lagrangian
density, the exact solution to the two-dimensional Yang-Mills theory is also
obtained.Comment: 11 pages, LaTe
On reversion phenomena in Cu-Zr-Cr alloys
Reversion phenomena in aged Cu-0.12% Zr-0.28% Cr alloy were investigated by means of resistivity measurement and transmission electron microscopy and compared with those of Cu-0.30% Zr and Cu-0.26% Cr alloys. Specimens in the form of a 0.5 mm sheet were solution-treated at 950 F for 1 hr water-quenched, aged, and finally reversed. The reversion phenomena were confirmed to exist in Cu-Zr and Cu-Zr-Cr alloys as well as Cu-Cr alloys, at aging temperatures of 300 to 500 F. The critical aging temperature for the reversion was not observed in all the alloys. Split aging increased the amount of reversion, particularly in Cu-Zr and Cu-Zr-Cr alloys, compared with that by conventional aging. The amount of reversion in Cu-Zr-Cr alloy was greatly affected by the resolution of Cr precipitate formed by preaging. Structural changes in Cu-Zr-Cr alloy due to the reversion were hardly observed by transmission electron microscopy
Cohomological Yang-Mills Theory in Eight Dimensions
We construct nearly topological Yang-Mills theories on eight dimensional
manifolds with a special holonomy group. These manifolds are the Joyce manifold
with holonomy and the Calabi-Yau manifold with SU(4) holonomy. An
invariant closed four form on the manifold allows us to
define an analogue of the instanton equation, which serves as a topological
gauge fixing condition in BRST formalism. The model on the Joyce manifold is
related to the eight dimensional supersymmetric Yang-Mills theory. Topological
dimensional reduction to four dimensions gives non-abelian Seiberg-Witten
equation.Comment: 9 pages, latex, Talk given at APCTP Winter School on Dualities in
String Theory, (Sokcho, Korea), February 24-28, 199
Special Quantum Field Theories In Eight And Other Dimensions
We build nearly topological quantum field theories in various dimensions. We
give special attention to the case of 8 dimensions for which we first consider
theories depending only on Yang-Mills fields. Two classes of gauge functions
exist which correspond to the choices of two different holonomy groups in
SO(8), namely SU(4) and Spin(7). The choice of SU(4) gives a quantum field
theory for a Calabi-Yau fourfold. The expectation values for the observables
are formally holomorphic Donaldson invariants. The choice of Spin(7) defines
another eight dimensional theory for a Joyce manifold which could be of
relevance in M- and F-theories. Relations to the eight dimensional
supersymmetric Yang-Mills theory are presented. Then, by dimensional reduction,
we obtain other theories, in particular a four dimensional one whose gauge
conditions are identical to the non-abelian Seiberg-Witten equations. The
latter are thus related to pure Yang-Mills self-duality equations in 8
dimensions as well as to the N=1, D=10 super Yang-Mills theory. We also exhibit
a theory that couples 3-form gauge fields to the second Chern class in eight
dimensions, and interesting theories in other dimensions.Comment: 36 pages, latex. References have been added together with a not
Consistency Conditions of the Faddeev-Niemi-Periwal Ansatz for the SU(N) Gauge Field
The consistency condition of the Faddeev-Niemi ansatz for the gauge-fixed
massless SU(2) gauge field is discussed. The generality of the ansatz is
demonstrated by obtaining a sufficient condition for the existence of the
three-component field introduced by Faddeev and Niemi. It is also shown that
the consistency conditions determine this three-component field as a functional
of two arbitrary functions. The consistency conditions corresponding to the
Periwal ansatz for the SU(N) gauge field with N larger than 2 are also
obtained. It is shown that the gauge field obeying the Periwal ansatz must
satisfy extra (N-1)(N-2)/2 conditions.Comment: PTP Tex, 15 pages, Eq.(3.18) inserte
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