218 research outputs found
On membrane interaction in matrix theory
We compute the interaction potential between two parallel transversely
boosted wrapped membranes (with fixed momentum ) in D=11 supergravity with
compact light-like direction. We show that the supergravity result is in exact
agreement with the potential following from the all-order Born-Infeld-type
action conjectured to be the leading planar infra-red part of the quantum super
Yang-Mills effective action. This provides a non-trivial test of consistency of
the arguments relating Matrix theory to a special limit of type II string
theory. We also find the potential between two (2+0) D-brane bound states in
D=10 supergravity (corresponding to the case of boosted membrane configuration
in 11-dimensional theory compactified on a space-like direction). We
demonstrate that the result reduces to the SYM expression for the potential in
the special low-energy (\a'\to 0) limit, in agreement with previous
suggestions. In appendix we derive the action obtained from the D=11 membrane
action by the world-volume duality transformation of the light-like coordinate
into a 3-vector.Comment: 18 pages, latex. v2: Some clarifying remarks and references added.
v3: Further minor corrections and reference
Seiberg-Witten map for noncommutative super Yang-Mills theory
In this letter we derive the Seiberg-Witten map for noncommutative super
Yang-Mills theory in Wess-Zumino gauge. Following (and using results of)
hep-th/0108045 we split the observer Lorentz transformations into a covariant
particle Lorentz transformation and a remainder which gives directly the
Seiberg-Witten differential equations. These differential equations lead to a
theta-expansion of the noncommutative super Yang-Mills action which is
invariant under commutative gauge transformations and commutative observer
Lorentz transformation, but not invariant under commutative supersymmetry
transformations: The theta-expansion of noncommutative supersymmetry leads to a
theta-dependent symmetry transformation. For this reason the Seiberg-Witten map
of super Yang-Mills theory cannot be expressed in terms of superfields.Comment: 9 page
Higher gauge theory -- differential versus integral formulation
The term higher gauge theory refers to the generalization of gauge theory to
a theory of connections at two levels, essentially given by 1- and 2-forms. So
far, there have been two approaches to this subject. The differential picture
uses non-Abelian 1- and 2-forms in order to generalize the connection 1-form of
a conventional gauge theory to the next level. The integral picture makes use
of curves and surfaces labeled with elements of non-Abelian groups and
generalizes the formulation of gauge theory in terms of parallel transports. We
recall how to circumvent the classic no-go theorems in order to define
non-Abelian surface ordered products in the integral picture. We then derive
the differential picture from the integral formulation under the assumption
that the curve and surface labels depend smoothly on the position of the curves
and surfaces. We show that some aspects of the no-go theorems are still present
in the differential (but not in the integral) picture. This implies a
substantial structural difference between non-perturbative and perturbative
approaches to higher gauge theory. We finally demonstrate that higher gauge
theory provides a geometrical explanation for the extended topological symmetry
of BF-theory in both pictures.Comment: 26 pages, LaTeX with XYPic diagrams; v2: typos corrected and
presentation improve
Path Integral for Space-time Noncommutative Field Theory
The path integral for space-time noncommutative theory is formulated by means
of Schwinger's action principle which is based on the equations of motion and a
suitable ansatz of asymptotic conditions. The resulting path integral has
essentially the same physical basis as the Yang-Feldman formulation. It is
first shown that higher derivative theories are neatly dealt with by the path
integral formulation, and the underlying canonical structure is recovered by
the Bjorken-Johnson-Low (BJL) prescription from correlation functions defined
by the path integral. A simple theory which is non-local in time is then
analyzed for an illustration of the complications related to quantization,
unitarity and positive energy conditions. From the view point of BJL
prescription, the naive quantization in the interaction picture is justified
for space-time noncommutative theory but not for the simple theory non-local in
time. We finally show that the perturbative unitarity and the positive energy
condition, in the sense that only the positive energy flows in the positive
time direction for any fixed time-slice in space-time, are not simultaneously
satisfied for space-time noncommutative theory by the known methods of
quantization.Comment: 21 page
Renormalisation of \phi^4-theory on noncommutative R^2 in the matrix base
As a first application of our renormalisation group approach to non-local
matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean
two-dimensional noncommutative \phi^4-theory. It is widely believed that this
model is renormalisable in momentum space arguing that there would be
logarithmic UV/IR-divergences only. Although momentum space Feynman graphs can
indeed be computed to any loop order, the logarithmic UV/IR-divergence appears
in the renormalised two-point function -- a hint that the renormalisation is
not completed. In particular, it is impossible to define the squared mass as
the value of the two-point function at vanishing momentum. In contrast, in our
matrix approach the renormalised N-point functions are bounded everywhere and
nevertheless rely on adjusting the mass only. We achieve this by introducing
into the cut-off model a translation-invariance breaking regulator which is
scaled to zero with the removal of the cut-off. The naive treatment without
regulator would not lead to a renormalised theory.Comment: 26 pages, 44 figures, LaTe
Parallel transport on non-Abelian flux tubes
I propose a way of unambiguously parallel transporting fields on non-Abelian
flux tubes, or strings, by means of two gauge fields. One gauge field
transports along the tube, while the other transports normal to the tube.
Ambiguity is removed by imposing an integrability condition on the pair of
fields. The construction leads to a gauge theory of mathematical objects known
as Lie 2-groups, which are known to result also from the parallel transport of
the flux tubes themselves. The integrability condition is also shown to be
equivalent to the assumption that parallel transport along nearby string
configurations are equal up to arbitrary gauge transformations. Attempts to
implement this condition in a field theory leads to effective actions for
two-form fields.Comment: significant portions of text rewritten, references adde
Probing a D6 + D0 state with D6-branes: SYM - Supergravity correspondence at subleading level
We probe a non-supersymmetric D6 + D0 state with D6-branes and find agreement
at subleading order between the supergravity and super Yang-Mills description
of the long-distance, low-velocity interaction.Comment: LaTeX, 15 pages, no figure
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