75 research outputs found
Basic and Equivariant Cohomology in Balanced Topological Field Theory
We present a detailed algebraic study of the N=2 cohomological set--up
describing the balanced topological field theory of Dijkgraaf and Moore. We
emphasize the role of N=2 topological supersymmetry and internal
symmetry by a systematic use of superfield techniques and of an
covariant formalism. We provide a definition of N=2 basic and equivariant
cohomology, generalizing Dijkgraaf's and Moore's, and of N=2 connection. For a
general manifold with a group action, we show that: ) the N=2 basic
cohomology is isomorphic to the tensor product of the ordinary N=1 basic
cohomology and a universal group theoretic factor: ) the affine
spaces of N=2 and N=1 connections are isomorphic.Comment: 50 pages, Plain TeX, no figures, requires AMS font files amssym.def
and amssym.tex; historical part of the introduction revise
N=4 Yang--Mills theory as a complexification of the N=2 theory
A complexification of the twisted theory allows one to determine the
N=4 Yang--Mills theory in its third twist formulation. The imaginary part of
the gauge symmetry is used to eliminate two scalars fields and create gauge
covariant longitudinal components for the imaginary part of the gauge field.
The latter becomes the vector field of the thirdly twisted theory.
Eventually, one gets a one to one correspondence between the fields of both
theories. Analogous complexifications can be done for topological 2d-gravity
and topological sigma models
A Suggestion for Modification of Vafa-Witten Theory
Using the Mathai-Quillen formalism we reexamine the twisted N=4
supersymmetric model of Vafa-Witten theory. Smooth out the relation between the
supersymmetric action and the path integral representation of the Thom class.Comment: Latex, 23kb, 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
Topological twisting of conformal supercharges
Putting a twisted version of N=4 super Yang-Mills on a curved
four-dimensional manifold generically breaks all conformal supersymmetries. In
the special case where the four-manifold is a cone, we show that exactly two
conformal supercharges remain unbroken. We construct an off-shell formulation
of the theory such that the two unbroken conformal supercharges combine into a
family of topological charges parameterized by CP^1. The resulting theory is
topological in the sense that it is independent of the metric on the
three-dimensional base of the cone.Comment: 1+33 pages; references added, an address change
Observables in Topological Yang-Mills Theories With Extended Shift Supersymmetry
We present a complete classification, at the classical level, of the
observables of topological Yang-Mills theories with an extended shift
supersymmetry of N generators, in any space-time dimension. The observables are
defined as the Yang-Mills BRST cohomology classes of shift supersymmetry
invariants. These cohomology classes turn out to be solutions of an N-extension
of Witten's equivariant cohomology. This work generalizes results known in the
case of shift supersymmetry with a single generator.Comment: 27 pages, Late
Africans winning the World Cup? What 'decolonisation by integration' could teach us about black French identity
Following claims that Africa actually won the 2018 FIFA World Cup, students Arbie Baguios (MSc International Development and Humanitarian Emergencies), Ynis Isimbi (Msc Development Studies) and David Yamron (MSc Development Management) explore French identity and its colonial past
Mass Perturbations in Twisted N=4 Supersymmetric Gauge Theories
Mass perturbations of the twisted N=4 supersymmetric gauge theory considered
by Vafa and Witten to test S-duality are studied for the case of Kahler
four-manifolds. It is shown that the resulting mass-perturbed theory can be
regarded as an equivariant extension associated to a U(1) symmetry of the
twisted theory, which is only present for Kahler manifolds. In addition, it is
shown that the partition function, the only topological invariant of the
theory, remains invariant under the perturbation.Comment: 36 pages, phyzzx, a footnote and two references adde
Africans winning the World Cup? What 'decolonisation by integration' could teach us about black French identity
Following claims that Africa actually won the 2018 FIFA World Cup, students Arbie Baguios (MSc International Development and Humanitarian Emergencies), Ynis Isimbi (Msc Development Studies) and David Yamron (MSc Development Management) explore French identity and its colonial past
Euclidean SYM Theories by Time Reduction and Special Holonomy Manifolds
Euclidean supersymmetric theories are obtained from Minkowskian theories by
performing a reduction in the time direction. This procedure elucidates certain
mysterious features of Zumino's N=2 model in four dimensions, provides
manifestly hermitian Euclidean counterparts of all non-mimimal SYM theories,
and is also applicable to supergravity theories. We reanalyse the twists of the
4d N=2 and N=4 models from this point of view. Other applications include SYM
theories on special holonomy manifolds. In particular, we construct a twisted
SYM theory on Kaehler 3-folds and clarify the structure of SYM theory on
hyper-Kaehler 4-folds.Comment: 21 pages, LaTeX fil
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