4,871 research outputs found
Brane Dynamics and 3D Seiberg Duality on the Domain Walls of 4D N=1 SYM
We study a three-dimensional U(k) Yang-Mills Chern-Simons theory with adjoint
matter preserving two supersymmetries. According to Acharya and Vafa, this
theory describes the low-energy worldvolume dynamics of BPS domain walls in
four-dimensional N=1 SYM theory. We demonstrate how to obtain the same theory
in a brane configuration of type IIB string theory that contains threebranes
and fivebranes. A combination of string and field theory techniques allows us
to re-formulate some of the well-known properties of N=1 SYM domain walls in a
geometric language and to postulate a Seiberg-like duality for the Acharya-Vafa
theory. In the process, we obtain new information about the dynamics of branes
in setups that preserve two supersymmetries. Using similar methods we also
study other N=1 CS theories with extra matter in the adjoint and fundamental
representations of the gauge group.Comment: 25 pages, 5 figure
Geometry of N=1 Dualities in Four Dimensions
We discuss how N=1 dualities in four dimensions are geometrically realized by
wrapping D-branes about 3-cycles of Calabi-Yau threefolds. In this setup the
N=1 dualities for SU, SO and USp gauge groups with fundamental fields get
mapped to statements about the monodromy and relations among 3-cycles of
Calabi-Yau threefolds. The connection between the theory and its dual requires
passing through configurations which are T-dual to the well-known phenomenon of
decay of BPS states in N=2 field theories in four dimensions. We compare our
approach to recent works based on configurations of D-branes in the presence of
NS 5-branes and give simple classical geometric derivations of various exotic
dynamics involving D-branes ending on NS-branes.Comment: 16 pages, harvma
Discrete Poincaré Lemma
This paper proves a discrete analogue of the Poincar´e lemma in the context of a discrete exterior calculus based on simplicial cochains. The proof requires the construction of a generalized cone operator, p : Ck(K) -> Ck+1(K), as the geometric cone of a simplex cannot, in general, be interpreted as a chain in the simplicial complex. The corresponding cocone operator H : Ck(K) -> Ck−1(K) can be shown to be a homotopy operator, and this yields the discrete Poincar´e lemma.
The generalized cone operator is a combinatorial operator that can be constructed for any simplicial complex that can be grown by a process of local augmentation. In particular, regular triangulations and tetrahedralizations of R2 and R3 are presented, for which the discrete Poincar´e lemma is globally valid
Mixed Mimetic Spectral Element Method for Stokes Flow: A Pointwise Divergence-Free Solution
In this paper we apply the recently developed mimetic discretization method
to the mixed formulation of the Stokes problem in terms of vorticity, velocity
and pressure. The mimetic discretization presented in this paper and in [50] is
a higher-order method for curvilinear quadrilaterals and hexahedrals.
Fundamental is the underlying structure of oriented geometric objects, the
relation between these objects through the boundary operator and how this
defines the exterior derivative, representing the grad, curl and div, through
the generalized Stokes theorem. The mimetic method presented here uses the
language of differential -forms with -cochains as their discrete
counterpart, and the relations between them in terms of the mimetic operators:
reduction, reconstruction and projection. The reconstruction consists of the
recently developed mimetic spectral interpolation functions. The most important
result of the mimetic framework is the commutation between differentiation at
the continuous level with that on the finite dimensional and discrete level. As
a result operators like gradient, curl and divergence are discretized exactly.
For Stokes flow, this implies a pointwise divergence-free solution. This is
confirmed using a set of test cases on both Cartesian and curvilinear meshes.
It will be shown that the method converges optimally for all admissible
boundary conditions
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