Hamiltonian formulation of nonAbelian noncommutative gauge theories

We implement the Hamiltonian treatment of a nonAbelian noncommutative gauge theory, considering with some detail the algebraic structure of the noncommutative symmetry group. The first class constraints and Hamiltonian are obtained and their algebra derived, as well as the form of the gauge invariance they impose on the first order action.Comment: enlarged version, 7 pages, RevTe

Diffeomorphism, kappa transformations and the theory of non-linear realisations

We will show how the theory of non-linear realisations can be used to naturally incorporate world line diffeomorphisms and kappa transformations for the point particle and superpoint particle respectively. Similar results also hold for a general p-brane and super p-brane, however, we must in these cases include an additional Lorentz transformation.Comment: 19pages, no figure. References are added and typos are correcte

BIons in topological string theory

When many fundamental strings are stacked together, they puff up into D-branes. BIons and giant gravitons are the examples of such D-brane configurations that arise from coincident strings. We propose and demonstrate analogous transitions in topological string theory. Such transitions can also be understood in terms of the Fourier transform of D-brane amplitudes.Comment: 21 pages; v.2 references added; v.3 reference added; v.4 minor corrections; v.5 substantial rewritin

A Note on Unitarity of Non-Relativistic Non-Commutative Theories

We analyze the unitarity of a non-relativistic non-commutative scalar field theory. We show that electric backgrounds spoil unitarity while magnetic ones do not. Furthermore, unlike its relativistic counterparts, unitarity can not be restored (at least at the level of one-to-one scattering amplitude) by adding new states to the theory. This is a signal that the model cannot be embedded in a natural way in string theory.Comment: 6 pages, 2 figures. References adde

A prediction for bubbling geometries

We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.Comment: 21 pages, latex; v.2 reference added; v.3 minor correction

D-branes as a Bubbling Calabi-Yau

We prove that the open topological string partition function on a D-brane configuration in a Calabi-Yau manifold X takes the form of a closed topological string partition function on a different Calabi-Yau manifold X_b. This identification shows that the physics of D-branes in an arbitrary background X of topological string theory can be described either by open+closed string theory in X or by closed string theory in X_b. The physical interpretation of the ''bubbling'' Calabi-Yau X_b is as the space obtained by letting the D-branes in X undergo a geometric transition. This implies, in particular, that the partition function of closed topological string theory on certain bubbling Calabi-Yau manifolds are invariants of knots in the three-sphere.Comment: 32 pages; v.2 reference adde

Holographic Gauge Theories in Background Fields and Surface Operators

We construct a new class of supersymmetric surface operators in N=4 SYM and find the corresponding dual supergravity solutions. We show that the insertion of the surface operator - which is given by a WZW model supported on the surface - appears by integrating out the localized degrees of freedom along the surface which arise microscopically from a D3/D7 brane intersection. Consistency requires constructing N=4 SYM in the D7 supergravity background and not in flat space. This enlarges the class of holographic gauge theories dual to string theory backgrounds to gauge theories in non-trivial supergravity backgrounds. The dual Type IIB supergravity solutions we find reveal - among other features - that the holographic dual gauge theory does indeed live in the D7-brane background.Comment: 42 pages, harvmac, corrected typo

Wilson Loops, Geometric Transitions and Bubbling Calabi-Yau's

Motivated by recent developments in the AdS/CFT correspondence, we provide several alternative bulk descriptions of an arbitrary Wilson loop operator in Chern-Simons theory. Wilson loop operators in Chern-Simons theory can be given a description in terms of a configuration of branes or alternatively anti-branes in the resolved conifold geometry. The representation of the Wilson loop is encoded in the holonomy of the gauge field living on the dual brane configuration. By letting the branes undergo a new type of geometric transition, we argue that each Wilson loop operator can also be described by a bubbling Calabi-Yau geometry, whose topology encodes the representation of the Wilson loop. These Calabi-Yau manifolds provide a novel representation of knot invariants. For the unknot we confirm these identifications to all orders in the genus expansion.Comment: 26 pages; v.2 typos corrected, explanations clarified; v.3 typos corrected, reference adde