698 research outputs found
Ten-dimensional super-Yang-Mills with nine off-shell supersymmetries
After adding 7 auxiliary scalars to the d=10 super-Yang-Mills action, 9 of
the 16 supersymmetries close off-shell. In this paper, these 9 supersymmetry
generators are related by dimensional reduction to scalar and vector
topological symmetry in =2 d=8 twisted super-Yang-Mills. Furthermore, a
gauge-invariant superspace action is constructed for d=10 super-Yang-Mills
where the superfields depend on 9 anticommuting theta variables.Comment: 15 page
Reconstruction of N=1 supersymmetry from topological symmetry
The scalar and vector topological Yang-Mills symmetries on Calabi-Yau
manifolds geometrically define consistent sectors of Yang-Mills D=4,6 N=1
supersymmetry, which fully determine the supersymmetric actions up to twist.
For a CY_2 manifold, both N=1,D=4 Wess and Zumino and superYang-Mills theory
can be reconstructed in this way. A superpotential can be introduced for the
matter sector, as well as the Fayet-Iliopoulos mechanism. For a CY_3 manifold,
the N=1, D=6 Yang-Mills theory is also obtained, in a twisted form. Putting
these results together with those already known for the D=4,8 N=2 cases, we
conclude that all Yang--Mills supersymmetries with 4, 8 and 16 generators are
determined from topological symmetry on special manifolds.Comment: 13 page
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
Superconformal invariance from N=2 supersymmetry Ward identities
We algebraically prove the cancellation of the β function at all order of perturbation theory of Script N = 2 supersymmetric gauge theories with a vanishing one-loop β function. The proof generalises that recently given for the Script N = 4 case. It uses the consistent Slavnov-Taylor identities of the shadow dependent formulation. We also demonstrate the cancellation at all orders of the anomalous dimensions of vector and hypermultiplet ½BPS operators
Symmetries of topological field theories in the BV-framework
Topological field theories of Schwarz-type generally admit symmetries whose
algebra does not close off-shell, e.g. the basic symmetries of BF models or
vector supersymmetry of the gauge-fixed action for Chern-Simons theory (this
symmetry being at the origin of the perturbative finiteness of the theory). We
present a detailed discussion of all these symmetries within the algebraic
approach to the Batalin-Vilkovisky formalism. Moreover, we discuss the general
algebraic construction of topological models of both Schwarz- and Witten-type.Comment: 30 page
A note on the UV behaviour of maximally supersymmetric Yang-Mills theories
The question of whether BPS invariants are protected in maximally
supersymmetric Yang-Mills theories is investigated from the point of view of
algebraic renormalisation theory. The protected invariants are those whose
cohomology type differs from that of the action. It is confirmed that one-half
BPS invariants () are indeed protected while the double-trace one-quarter
BPS invariant () is not protected at two loops in D=7, but is protected
at three loops in D=6 in agreement with recent calculations. Non-BPS
invariants, i.e. full superspace integrals, are also shown to be unprotected.Comment: 12 pages. Minor changes to text. References adde
BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization)
We consider the massless scalar field on the four-dimensional sphere .
Its classical action is degenerate
under the global invariance . We then quantize
the massless scalar field as a gauge theory by constructing a BRST-invariant
quantum action. The corresponding gauge-breaking term is a non-local one of the
form where
is a gauge parameter and is the volume of . It allows us to
correctly treat the zero mode problem. The quantum theory is invariant under
SO(5), the symmetry group of , and the associated two-point functions have
no infrared divergence. The well-known infrared divergence which appears by
taking the massless limit of the massive scalar field propagator is therefore a
gauge artifact. By contrast, the massless scalar field theory on de Sitter
space - the lorentzian version of - is not invariant under the
symmetry group of that spacetime SO(1,4). Here, the infrared divergence is
real. Therefore, the massless scalar quantum field theories on and
cannot be linked by analytic continuation. In this case, because of zero modes,
the euclidean approach to quantum field theory does not work. Similar
considerations also apply to massive scalar field theories for exceptional
values of the mass parameter (corresponding to the discrete series of the de
Sitter group).Comment: This paper has been published under the title "Zero modes,
euclideanization and quantization" [Phys. Rev. D46, 2553 (1992)
Finiteness Properties of the N=4 Super-Yang--Mills Theory in Supersymmetric Gauge
With the introduction of shadow fields, we demonstrate the renormalizability of the N=4 super-Yang--Mills theory in component formalism, independently of the choice of UV regularization. Remarkably, by using twisted representations, one finds that the structure of the theory and its renormalization is determined by a subalgebra of supersymmetry that closes off-shell. Starting from this subalgebra of symmetry, we prove some features of the superconformal invariance of the theory. We give a new algebraic proof of the cancellation of the function and we show the ultraviolet finiteness of the 1/2 BPS operators at all orders in perturbation theory. In fact, using the shadow field as a Maurer--Cartan form, the invariant polynomials in the scalar fields in traceless symmetric representations of the internal R-symmetry group are simply related to characteristic classes. Their UV finiteness is a consequence of the Chern--Simons formula
Fracture functions from cut vertices
Using a generalized cut vertex expansion we introduce the concept of an
extended fracture function for the description of semi-inclusive deep inelastic
processes in the target fragmentation region. Extended fracture functions are
shown to obey a standard homogeneous DGLAP-type equation which, upon
integration over t, becomes the usual inhomogeneous evolution equation for
ordinary fracture functions.Comment: latex, 15 pages including 7 postscript figure
Split dimensional regularization for the Coulomb gauge at two loops
We evaluate the coefficients of the leading poles of the complete two-loop
quark self-energy \Sigma(p) in the Coulomb gauge. Working in the framework of
split dimensional regularization, with complex regulating parameters \sigma and
n/2-\sigma for the energy and space components of the loop momentum,
respectively, we find that split dimensional regularization leads to
well-defined two-loop integrals, and that the overall coefficient of the
leading pole term for \Sigma(p) is strictly local. Extensive tables showing the
pole parts of one- and two-loop Coulomb integrals are given. We also comment on
some general implications of split dimensional regularization, discussing in
particular the limit \sigma \to 1/2 and the subleading terms in the
epsilon-expansion of noncovariant integrals.Comment: 32 pages Latex; figures replaced, text unchange
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