5,151 research outputs found
Noncommutative open strings from Dirac quantization
We study Dirac commutators of canonical variables on D-branes with a constant
Neveu-Schwarz 2-form field by using the Dirac constraint quantization method,
and point out some subtleties appearing in previous works in analyzing
constraint structure of the brane system. Overcoming some ad hoc procedures, we
obtain desirable noncommutative coordinates exactly compatible with the result
of the conformal field theory in recent literatures. Furthermore, we find
interesting commutator relations of other canonical variables.Comment: 13 pages, revtex, Expressions are change
Einstein Manifolds As Yang-Mills Instantons
It is well-known that Einstein gravity can be formulated as a gauge theory of
Lorentz group where spin connections play a role of gauge fields and Riemann
curvature tensors correspond to their field strengths. One can then pose an
interesting question: What is the Einstein equations from the gauge theory
point of view? Or equivalently, what is the gauge theory object corresponding
to Einstein manifolds? We show that the Einstein equations in four dimensions
are precisely self-duality equations in Yang-Mills gauge theory and so Einstein
manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R
gauge theory. Specifically, we prove that any Einstein manifold with or without
a cosmological constant always arises as the sum of SU(2)_L instantons and
SU(2)_R anti-instantons. This result explains why an Einstein manifold must be
stable because two kinds of instantons belong to different gauge groups,
instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay
into a vacuum. We further illuminate the stability of Einstein manifolds by
showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.
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