18 research outputs found
1/4-BPS states on noncommutative tori
We give an explicit expression for classical 1/4-BPS fields in supersymmetric
Yang-Mills theory on noncommutative tori. We use it to study quantum 1/4-BPS
states. In particular we calculate the degeneracy of 1/4-BPS energy levels.Comment: 15 pages, Latex; v.2 typos correcte
Moduli spaces of maximally supersymmetric solutions on noncommutative tori and noncommutative orbifolds
A maximally supersymmetric configuration of super Yang-Mills living on a
noncommutative torus corresponds to a constant curvature connection. On a
noncommutative toroidal orbifold there is an additional constraint that the
connection be equivariant. We study moduli spaces of (equivariant) constant
curvature connections on noncommutative even-dimensional tori and on toroidal
orbifolds. As an illustration we work out the cases of Z_{2} and Z_{4}
orbifolds in detail. The results we obtain agree with a commutative picture
describing systems of branes wrapped on cycles of the torus and branes stuck at
exceptional orbifold points.Comment: 21 pages, Late
Supergeometry and Arithmetic Geometry
We define a superspace over a ring as a functor on a subcategory of the
category of supercommutative -algebras. As an application the notion of a
-adic superspace is introduced and used to give a transparent construction
of the Frobenius map on -adic cohomology of a smooth projective variety over
the ring of -adic integers.Comment: 14 pages, expanded introduction, more detail
Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Theory
We shall try to exhibit a relation between black hole entropy and topological
entropy using the famous Baum-Connes conjecture for foliated manifolds which
are particular examples of noncommutative spaces. Our argument is qualitative
and it is based on the microscopic origin of the Beckenstein-Hawking
area-entropy formula for black holes, provided by superstring theory, in the
more general noncommutative geometric context of M-Theory following the Connes-
Douglas-Schwarz article.Comment: 17 pages, Latex, contains an important paragraph in section 2 which
gives a better understandin
On maximally supersymmetric Yang-Mills theories
We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM
theory) and its dimensional reductions, in particular, BFSS and IKKT models. We
formulate these theories using algebraic techniques based on application of
differential graded Lie algebras and associative algebras as well as of more
general objects, L_{\infty}- and A_{\infty}- algebras.
We show that using pure spinor formulation of 10D SUSY YM theory equations of
motion and isotwistor formalism one can interpret these equations as
Maurer-Cartan equations for some differential Lie algebra. This statement can
be used to write BV action functional of 10D SUSY YM theory in Chern-Simons
form. The differential Lie algebra we constructed is closely related to
differential associative algebra Omega of (0, k)-forms on some supermanifold;
the Lie algebra is tensor product of Omega and matrix algebra .
We construct several other algebras that are quasiisomorphic to Omega and,
therefore, also can be used to give BV formulation of 10D SUSY YM theory and
its reductions. In particular, Omega is quasiisomorphic to the algebra B
constructed by Berkovits. The algebras Omega_0 and B_0 obtained from Omega and
B by means of reduction to a point can be used to give a BV-formulation of IKKT
model.
We introduce associative algebra SYM as algebra where relations are defined
as equations of motion of IKKT model and show that Koszul dual to the algebra
B_0 is quasiisomorphic to SYM.Comment: 43 pages. Details are added in the construction of trace in section
4. Added references. Formula for vector filed E on p.5,11 correcte
On Continuous Moyal Product Structure in String Field Theory
We consider a diagonalization of Witten's star product for a ghost system of
arbitrary background charge and Grassmann parity. To this end we use a
bosonized formulation of such systems and a spectral analysis of Neumann
matrices. We further identify a continuous Moyal product structure for a
combined ghosts+matter system. The normalization of multiplication kernel is
discussed.Comment: 18+7 pages, 1 figure, typos correction
NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion
Using the algebraic geometric approach of Berenstein et {\it al}
(hep-th/005087 and hep-th/009209) and methods of toric geometry, we study non
commutative (NC) orbifolds of Calabi-Yau hypersurfaces in toric varieties with
discrete torsion. We first develop a new way of getting complex mirror
Calabi-Yau hypersurfaces in toric manifolds with a action and analyze the general group of the
discrete isometries of . Then we build a general class of
complex dimension NC mirror Calabi-Yau orbifolds where the non
commutativity parameters are solved in terms of discrete
torsion and toric geometry data of in which the original
Calabi-Yau hypersurfaces is embedded. Next we work out a generalization of the
NC algebra for generic dimensions NC Calabi-Yau manifolds and give various
representations depending on different choices of the Calabi-Yau toric geometry
data. We also study fractional D-branes at orbifold points. We refine and
extend the result for NC to higher dimensional torii orbifolds
in terms of Clifford algebra.Comment: 38 pages, Late