7,168 research outputs found
Symmetries and Observables for BF-theories in Superspace
The supersymmetric version of a topological quantum field theory describing
flat connections, the super BF-theory, is studied in the superspace formalism.
A set of observables related to topological invariants is derived from the
curvature of the superspace. Analogously to the non-supersymmetric versions,
the theory exhibits a vector-like supersymmetry. The role of the vector
supersymmetry and an additional new symmetry of the action in the construction
of observables is explained.Comment: 11 pages, LaTe
An analytic Approach to Turaev's Shadow Invariant
In the present paper we extend the "torus gauge fixing approach" by Blau and
Thompson (Nucl. Phys. B408(1):345--390, 1993) for Chern-Simons models with base
manifolds M of the form M= \Sigma x S^1 in a suitable way. We arrive at a
heuristic path integral formula for the Wilson loop observables associated to
general links in M. We then show that the right-hand side of this formula can
be evaluated explicitly in a non-perturbative way and that this evaluation
naturally leads to the face models in terms of which Turaev's shadow invariant
is defined.Comment: 44 pages, 2 figures. Changes have been made in Sec. 2.3, Sec 2.4,
Sec. 3.4, and Sec. 3.5. Appendix C is ne
Vector Supersymmetry of 2D Yang-Mills Theory
The vector supersymmetry of the 2D topological BF model is extended to 2D
Yang-Mills. The consequences of the corresponding Ward identity on the
ultraviolet behavior of the theory are analyzed.Comment: Some references adde
Topological Aspects of Gauge Fixing Yang-Mills Theory on S4
For an space-time manifold global aspects of gauge-fixing are
investigated using the relation to Topological Quantum Field Theory on the
gauge group. The partition function of this TQFT is shown to compute the
regularized Euler character of a suitably defined space of gauge
transformations. Topological properties of the space of solutions to a
covariant gauge conditon on the orbit of a particular instanton are found using
the isometry group of the base manifold. We obtain that the Euler
character of this space differs from that of an orbit in the topologically
trivial sector. This result implies that an orbit with Pontryagin number
\k=\pm1 in covariant gauges on contributes to physical correlation
functions with a different multiplicity factor due to the Gribov copies, than
an orbit in the trivial \k=0 sector. Similar topological arguments show that
there is no contribution from the topologically trivial sector to physical
correlation functions in gauges defined by a nondegenerate background
connection. We discuss possible physical implications of the global gauge
dependence of Yang-Mills theory.Comment: 13 pages, uuencoded and compressed LaTeX file, no figure
New Results on N=4 SuperYang-Mills Theory
The N=4 SuperYang--Mills theory is covariantly determined by a U(1) \times
SU(2) \subset SL(2,R) \times SU(2) internal symmetry and two scalar and one
vector BRST topological symmetry operators. This determines an off-shell closed
sector of N=4 SuperYang-Mills, with 6 generators, which is big enough to fully
determine the theory, in a Lorentz covariant way. This reduced algebra derives
from horizontality conditions in four dimensions. The horizontality conditions
only depend on the geometry of the Yang-Mills fields. They also descend from a
genuine horizontality condition in eight dimensions. In fact, the SL(2,R)
symmetry is induced by a dimensional reduction from eight to seven dimensions,
which establishes a ghost-antighost symmetry, while the SU(2) symmetry occurs
by dimensional reduction from seven to four dimensions. When the four
dimensional manifold is hyperKahler, one can perform a twist operation that
defines the N=4 supersymmetry and its SL(2,H)\sim SU(4) R-symmetry in flat
space. (For defining a TQFT on a more general four manifold, one can use the
internal SU(2)-symmetry and redefine a Lorentz SO(4) invariance). These results
extend in a covariant way the light cone property that the N=4 SuperYang-Mills
theory is actually determined by only 8 independent generators, instead of the
16 generators that occur in the physical representation of the superPoincare
algebra. The topological construction disentangles the off-shell closed sector
of the (twisted) maximally supersymmetric theory from the (irrelevant) sector
that closes only modulo equations of motion. It allows one to escape the
question of auxiliary fields in N=4 SuperYang-Mills theory.Comment: 14 page
Cubic String Field Theory in pp-wave Background and Background Independent Moyal Structure
We study Witten open string field theory in the pp-wave background in the
tensionless limit, and construct the N-string vertex in the basis which
diagonalizes the string perturbative spectrum. We found that the Witten
*-product can be viewed as infinite copies of the Moyal product with the same
noncommutativity parameter . Moreover, we show that this Moyal
structure is universal in the sense that, written in the string bit basis,
Witten's *-product for any background can always be given in terms of the
above-mentioned Moyal structure. We identify some projective operators in this
algebra that we argue to correspond to D-branes of the theory.Comment: Latex, 23 pages, reference adde
Light-like Big Bang singularities in string and matrix theories
Important open questions in cosmology require a better understanding of the
Big Bang singularity. In string and matrix theories, light-like analogues of
cosmological singularities (singular plane wave backgrounds) turn out to be
particularly tractable. We give a status report on the current understanding of
such light-like Big Bang models, presenting both solved and open problems.Comment: 20 pages, invited review for Class. Quant. Grav; v3: section 2.3
shortened, discussion on DLCQ added in section 3.1, published versio
G_2 invariant 7D Euclidean super Yang-Mills theory as a higher-dimensional analogue of the 3D super-BF theory
A formulation of the N_T=1, D=8 Euclidean super Yang-Mills theory with
generalized self-duality and reduced Spin(7)-invariance is given which avoids
the peculiar extra constraints of Nishino and Rajpoot, hep-th/0210132. Its
reduction to 7 dimensions leads to the G_2-invariant N_T=2, D=7 super
Yang-Mills theory which may be regarded as a higher-dimensional analogue of the
N=2, D=3 super-BF theory. When reducing further that G_2-invariant theory to 3
dimensions one gets the N_T=2 super-BF theory coupled to a spinorial
hypermultiplet.Comment: 9 pages, Late
Swimming in curved space or The Baron and the cat
We study the swimming of non-relativistic deformable bodies in (empty) static
curved spaces. We focus on the case where the ambient geometry allows for rigid
body motions. In this case the swimming equations turn out to be geometric. For
a small swimmer, the swimming distance in one stroke is determined by the
Riemann curvature times certain moments of the swimmer.Comment: 19 pages 6 figure
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