Distributed Systems of Intersecting Branes at Arbitrary Angles

A `reduced' action formulation for a general class of the supergravity solutions, corresponding to the `marginally' bound `distributed' systems of various types of branes at arbitrary angles, is developed. It turns out that all the information regarding the classical features of such solutions is encoded in a first order Lagrangian (the `reduced' Lagrangian) corresponding to the desired geometry of branes. The marginal solution for a system of $N$ such distributions (for various distribution functions) span an $N$ dimensional submanifold of the fields' configuration (target) space, parametrised by a set of $N$ independent harmonic functions on the transverse space. This submanifold, which we call it as the `$H$-surface', is a null surface with respect to a metric on the configuration space, which is defined by the reduced Lagrangian. The equations of motion then transform to a set of equations describing the embedding of a null geodesic surface in this space, which is identified as the $H$-surface. Using these facts, we present a very simple derivation of the conventional orthogonal solutions together with their intersection rules. Then a new solution for a (distributed) pair of $p$-branes at SU(2) angles in $D$ dimensions is derived.Comment: Latex file, 58 pages, no figures, 5 tables, This revision contains some minor changes of the original version including those of the title, abstract and referrences. Some comments are adde

Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States

We propose a deformation of ${\cal N}=4$ SYM theoery induced by nonanticommutative star product. The deformation introduces new bosonic terms which we identify with the corresponding Myers terms of a stack of D3-branes in the presence of a five-form RR flux. We take this as an indication that the deformed lagrangian describes D3-branes in such a background. The vacuum states of the theory are also examined. In a specific case where the U(1) part of the gauge field is nonvanishing the (anti)holomorphic transverse coordinates of the brane sit on a fuzzy two sphere. For a supersymmetric vacuum the antiholomorphic coordinates must necessarily commute. However, we also encounter non-supersymmetric vacua for which the antiholomorphic coordinates do not commute.Comment: 14 pages, minor changes, refs. adde

Noncommutative Supersymmetry in Two Dimensions

Based on an argument for the noncommutativity of momenta in noncommutative directions, we arrive at a generalization of the ${\cal N}=1$ super $E^2$ algebra associated to the deformation of translations in a noncommutative Euclidean plane. The algebra is obtained using appropriate representaions of its generators on the space of superfields in a $D=2, {\cal N}=1$ ``noncommutative superspace.'' We find that the (anti)commutators between several (super)translation generators are no longer vanishing, but involve a new set of generators which together with the (super)translation and rotation generators form a consistent closed algebra. We then analyze the spectrum of this algebra in order to obtain its fundamental and adjoint representations.Comment: 30 pages, Latex, no figures, some modifications including change of notations and addition of some comment

One-loop divergences in the two-dimensional non-anticommutative supersymmetric sigma-model

We discuss the structure of the non-anticommutative N=2 non-linear sigma-model in two dimensions, constructing differential operators which implement the deformed supersymmetry generators and using them to reproduce the classical action. We then compute the one-loop quantum corrections and express them in a more compact form using the differential operators.Comment: 20pp, 8 figures, uses LaTeX. Title expanded to clarify conten

Noncommutative Superspace, N=1/2 Supersymmetry, Field Theory and String Theory

We deform the standard four dimensional $\N=1$ superspace by making the odd coordinates $\theta$ not anticommuting, but satisfying a Clifford algebra. Consistency determines the other commutation relations of the coordinates. In particular, the ordinary spacetime coordinates $x$ cannot commute. We study chiral superfields and vector superfields and their interactions. As in ordinary noncommutative field theory, a change of variables allows us to express the gauge interactions in terms of component fields which are subject to standard gauge transformation laws. Unlike ordinary noncommutative field theories, the change of the Lagrangian is a polynomial in the deformation parameter. Despite the deformation, the noncommutative theories still have an antichiral ring with all its usual properties. We show how these theories with precisely this deformation arise in string theory in a graviphoton background.Comment: 19 page

On Instantons and Zero Modes of N=1/2 SYM Theory

We study zero modes of N=1/2 supersymmetric Yang-Mills action in the background of instantons. In this background, because of a quartic antichiral fermionic term in the action, the fermionic solutions of the equations of motion are not in general zero modes of the action. Hence, when there are fermionic solutions, the action is no longer minimized by instantons. By deforming the instanton equation in the presence of fermions, we write down the zero mode equations. The solutions satisfy the equations of motion, and saturate the BPS bound. The deformed instanton equations imply that the finite action solutions have U(1) connections which are not flat anymore.Comment: 9 pages, latex file, added references, minor change

D=2, N=2, Supersymmetric theories on Non(anti)commutative Superspace

The classical action of a two dimensional N=2 supersymmetric theory, characterized by a general K\"{a}hler potential, is written down on a non(anti)commutative superspace. The action has a power series expansion in terms of the determinant of the non(anti)commutativity parameter $C^{\alpha\beta}$. The theory is explicitly shown to preserve half of the N=2 supersymmetry, to all orders in (det C)^n. The results are further generalized to include arbitrary superpotentials as well.Comment: 32 pages, Latex; v2:minor typos corrected and a reference adde

N=1/2 Super Yang-Mills Theory on Euclidean AdS2xS2

We study D-branes in the background of Euclidean AdS2xS2 with a graviphoton field turned on. As the background is not Ricci flat, the graviphoton field must have both self-dual and antiself-dual parts. This, in general, will break all the supersymmetries on the brane. However, we show that there exists a limit for which one can restore half of the supersymmetries. Further, we show that in this limit, the N=1/2 SYM Lagrangian on flat space can be lifted on to the Euclidean AdS2xS2 preserving the same amount of supersymmetries as in the flat case. We observe that without the C-dependent terms present in the action this lift is not possible.Comment: 12 pages, latex file; v2: minor corrections, references adde

Comments on Gluino Condensates in N=1/2 SYM Theory

Using Ward identities of N=1/2 supersymmetric Yang-Mills theory, we show that while the partition function and antichiral gluino condensates remain invariant under the $C$ deformation, chiral gluino correlators can get contributions from all gauge fields with instanton numbers $k\leq 1$. In particular, a Ward identity of the $U(1)_R$ symmetry allows us to determine the explicit dependence of chiral gluino correlators on the deformation parameter.Comment: 11 pages, 4 figures, small changes, added a referenc

Matrix Models, Monopoles and Modified Moduli

Motivated by the Dijkgraaf-Vafa correspondence, we consider the matrix model duals of N=1 supersymmetric SU(Nc) gauge theories with Nf flavors. We demonstrate via the matrix model solutions a relation between vacua of theories with different numbers of colors and flavors. This relation is due to an N=2 nonrenormalization theorem which is inherited by these N=1 theories. Specializing to the case Nf=Nc, the simplest theory containing baryons, we demonstrate that the explicit matrix model predictions for the locations on the Coulomb branch at which monopoles condense are consistent with the quantum modified constraints on the moduli in the theory. The matrix model solutions include the case that baryons obtain vacuum expectation values. In specific cases we check explicitly that these results are also consistent with the factorization of corresponding Seiberg-Witten curves. Certain results are easily understood in terms of M5-brane constructions of these gauge theories.Comment: 27 pages, LaTeX, 2 figure