Showing papers in "Advances in Theoretical and Mathematical Physics in 2001"
TL;DR: In this paper, a class of correlation functions of half-BPS composite operators are computed exactly (at finite N ) in the zero coupling limit of N = 4 SYM theory.
Abstract: A class of correlation functions of half-BPS composite operators are computed exactly ( at finite N ) in the zero coupling limit of N = 4 SYM theory. These have a simple dependence on the four-dimensional spacetime coordinates and are related to correlators in a one-dimensional Matrix Model with complex Matrices obtained by dimensional reduction of N = 4 SYM on a three-sphere. A key technical tool is Frobenius-Schur duality between symmetric and Unitary groups and the results are expressed simply in terms of U(N) group integrals or equivalently in terms of Littlewood-Richardson coefficients. These correlation functions are used to understand the existence/properties of giant gravitons and related solutions in the string theory dual on AdS5 × S 5 . Some of their properties hint at integrability in N = 4 SYM.
631 citations
344 citations
TL;DR: In this article, the Lagrangian boundary invariants of stable maps with Lagrangians were studied. But their main application is to a situation where their proposed theory leads to a well-defined algebro-geometric computation very similar to well-known localization techniques in Gromov-Witten theory.
Abstract: In this paper, we present foundational material towards the development of a rigorous enumerative theory of stable maps with Lagrangian boundary conditions, ie stable maps from bordered Riemann surfaces to a symplectic manifold, such that the boundary maps to a Lagrangian submanifold. Our main application is to a situation where our proposed theory leads to a well-defined algebro-geometric computation very similar to well-known localization techniques in Gromov–Witten theory. In particular, our computation of the invariants for multiple covers of a generic disc bounding a special Lagrangian submanifold in a Calabi–Yau threefold agrees completely with the original predictions of Ooguri and Vafa based on string duality. Our proposed invariants depend more generally on a discrete parameter which came to light in the work of Aganagic, Klemm, and Vafa which was also based on duality, and our more general calculations agree with theirs up to sign.
236 citations
TL;DR: In this article, the existence of lump solutions of arbitrary codimension in cubic open string field theory has been shown and the ratio of tensions of these Green's functions of different dimensions has been calculated.
Abstract: Assuming that around the tachyon vacuum the kinetic term of cubic open string field theory is made purely of ghost operators we are led to gauge invariant actions which manifestly implement the absence of open string dynamics around this vacuum. We test this proposal by showing the existence of lump solutions of arbitrary codimension in this string field theory. The key ingredients in this analysis are certain assumptions about the analyticity properties of tachyon Green’s functions. With the help of some further assumptions about the properties of these Green’s functions, we also calculate the ratios of tensions of lump solutions of different dimensions. The result is in perfect agreement with the known answers for the ratios of tensions of D-branes of different dimensions.
224 citations
TL;DR: In this paper, the authors search for classical solutions describing D-branes of different dimensions using the ansatz that the solutions factorize into the direct product of a matter state and a universal ghost state.
Abstract: In a previous paper [hep-th/0012251] we proposed a simple class of actions for string field theory around the tachyon vacuum In this paper we search for classical solutions describing D-branes of different dimensions using the ansatz that the solutions factorize into the direct product of a matter state and a universal ghost state We find closed form expressions for the matter state describing D-branes of all dimensions For the space filling D25-brane the state is the matter part of the zero angle wedge state, the ``sliver'', built in [hep-th/0006240] For the other D-brane solutions the matter states are constructed using a solution generating technique outlined in [hep-th/0008252] The ratios of tensions of various D-branes, requiring evaluation of determinants of infinite dimensional matrices, are calculated numerically and are in very good agreement with the known results
147 citations
TL;DR: In this article, a family of genus one fibered Calabi-Yau threefolds with fundamental group Z/2 is described and a positive dimensional family of Mumford stable bundles whose symmetry group is the Standard Model group SU(3) × SU(2) × U(1) and which have c3 = 6.
Abstract: We describe a family of genus one fibered Calabi-Yau threefolds with fundamental group Z/2. On each Calabi-Yau Z in the family we exhibit a positive dimensional family of Mumford stable bundles whose symmetry group is the Standard Model group SU(3) × SU(2) × U(1) and which have c3 = 6. We also show that for each bundle V in our family, c2(Z) − c2(V ) is the class of an effective curve on Z. These conditions ensure that Z and V can be used for a phenomenologically relevant compactification of Heterotic M-theory. MSC 2000: 14D21, 14J32
140 citations
TL;DR: In this paper, a class of N = 1 supersymmetric models of particle physics, derived directly from heterotic M-theory, were presented, which contain three families of chiral quarks and leptons coupled to the gauge group SU(3)C×SU(2)L×U(1)Y. The requirement of three families coupled to fundamental conditions of anomaly freedom and supersymmetry, constrains these models to contain additional five-branes wrapped around holomorphic curves in the Calabi-Yau threefold.
Abstract: We present a class of N = 1 supersymmetric models of particle physics, derived directly from heterotic M-theory, that contain three families of chiral quarks and leptons coupled to the gauge group SU(3)C×SU(2)L×U(1)Y. These models are a fundamental form of “brane-world” theories, with an observable and hidden sector each confined, after compactification on a Calabi–Yau threefold, to a BPS three-brane separated by a five dimensional bulk space with size of the order of the intermediate scale. The requirement of three families, coupled to the fundamental conditions of anomaly freedom and supersymmetry, constrains these models to contain additional five-branes wrapped around holomorphic curves in the Calabi–Yau threefold. These five-branes “live” in the bulk space and represent new, non-perturbative aspects of these particle physics vacua. We discuss, in detail, the relevant mathematical structure of a class of torusfibered Calabi–Yau threefolds with non-trivial first homotopy groups and construct holomorphic vector bundles over such threefolds, which, by including Wilson lines, break the gauge symmetry to the standard model gauge group. Rules for constructing phenomenological particle physics models in this context are presented and we give a number of explicit examples. CERN-TH/99-407, UPR-853T December 1999 ∗current address
138 citations
TL;DR: In this paper, the supersymmetric index Tr (-1)^F for Yang-Mills theory with any simple gauge group G is discussed. And the results of the analysis are confirmed via microscopic calculations.
Abstract: This paper is devoted to a systematic discussion of the supersymmetric index Tr (-1)^F for the minimal supersymmetric Yang-Mills theory -- with any simple gauge group G -- primarily in four spacetime dimensions. The index has refinements that probe confinement and oblique confinement and the possible spontaneous breaking of chiral symmetry and of global symmetries, such as charge conjugation, that are derived from outer automorphisms of the gauge group. Predictions for the index and its refinements are obtained on the basis of standard hypotheses about the infrared behavior of gauge theories. The predictions are confirmed via microscopic calculations which involve a Born-Oppenheimer computation of the spectrum as well as mathematical formulas involving triples of commuting elements of G and the Chern-Simons invariants of flat bundles on the three-torus.
134 citations
TL;DR: In this article, the exact N = 1 superpotential of a class of 4D string compactications is computed by the closed topological string compactied to two dimensions, which is used to define a special geometry for n = 1 mirror symmetry.
Abstract: We show that the exact N = 1 superpotential of a class of 4d string compactications is computed by the closed topological string compactied to two dimensions. A relation to the open topological string is used to dene a special geometry for N = 1 mirror symmetry. Flat coordinates, an N = 1 mirror map for chiral multiplets and the exact instanton corrected superpotential are obtained from the periods of a system of dierential equations. The result points to a new class of open/closed string dualities which map individual string world-sheets with boundary to ones without. It predicts an mathematically unexpected coincidence of the closed string Gromov{Witten invariants of one Calabi{Yau geometry with the open string invariants of the dual Calabi{Yau .
122 citations
TL;DR: In this article, the authors obtained optimal lower tail estimates for the probability distribution of the properly scaled length of the longest up/right path of the last passage site percolation model considered by Johansson in [12].
Abstract: In this paper, we obtain optimal uniform lower tail estimates for the probability distribution of the properly scaled length of the longest up/right path of the last passage site percolation model considered by Johansson in [12]. The estimates are used to prove a lower tail moderate deviation result for the model. The estimates also imply the convergence of moments, and also provide a verification of the universal scaling law relating the longitudinal and the transversal fluctuations of the model.
113 citations
TL;DR: In this article, the authors describe a family of rational elliptic surfaces admitting an involution with isolated fixed points, and calculate the action of a spectral version of the involution on global line bundles and on spectral data.
Abstract: In this paper we describe a four dimensional family of special rational elliptic surfaces admitting an involution with isolated fixed points. For each surface in this family we calculate explicitly the action of a spectral version of the involution (namely of its Fourier-Mukai conjugate) on global line bundles and on spectral data. The calculation is carried out both on the level of cohomology and in the derived category. We find that the spectral involution behaves like a fairly simple affine transformation away from the union of those fiber components which do not intersect the zero section. These results are the key ingredient in the construction of Standard-Model bundles in [DOPWa]. MSC 2000: 14D20, 14D21, 14J60
TL;DR: In this paper, the authors give a Hamiltonian definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof.
Abstract: We give a Hamiltonian definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We show that our definition provides a geometric invariant for a spacelike hypersurface embedded in a space-time.
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TL;DR: In this article, a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces was established, and the electric/magnetic pairing of branes was determined by the condition that the union of the corresponding spheres represent the anticanonical class of the del pezzo.
Abstract: We establish a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces. M-theory on T k corresponds to P 2 blown up at k generic points; Type IIB corresponds to P 1 × P 1 . The moduli of compactifications of M-theory on rectangular tori are mapped to Kahler moduli of del Pezzo surfaces. The U-duality group of M-theory corresponds to a group of classical symmetries of the del Pezzo represented by global diffeomorphisms. The 1 -BPS brane charges of M-theory corre- spond to spheres in the del Pezzo, and their tension to the exponentiated volume of the corresponding spheres. The electric/magnetic pairing of branes is determined by the condition that the union of the corresponding spheres represent the anticanonical class of the del Pezzo. The condition that a pair of 1 -BPS states form a bound state is mapped to a condition on the intersection of the corresponding spheres. We present some speculations about the meaning of this duality.
TL;DR: In this paper, it was shown that the relation between hyperbolic geometry and Arakelov geometry at arithmetic infinity involves exactly the same geometric data as the Euclidean AdS_3 holography of black holes.
Abstract: According to the holography principle (due to G. ‘t Hooft, L. Susskind, J. Maldacena, et al.), quantum gravity and string theory on certain manifolds with boundary can be studied in terms of a conformal field theory on the boundary. Only a few mathematically exact results corroborating this exciting program are known. In this paper we interpret from this perspective several constructions which arose initially in the arithmetic geometry of algebraic curves. We show that the relation
between hyperbolic geometry and Arakelov geometry at arithmetic infinity involves exactly the same geometric data as the Euclidean AdS_3 holography of black holes. Moreover, in the case of Euclidean AdS_2 holography, we present some results on bulk/boundary correspondence where the boundary is a non–commutative space.
TL;DR: In this paper, a new construction of the minimal unitary representation of the exceptional group E8(8) on a Hilbert space of complex functions in 29 variables is presented, which is well suited for applications in supergravity and superstring theory.
Abstract: We give a new construction of the minimal unitary representation of the exceptional group E8(8) on a Hilbert space of complex functions in 29 variables. Due to their manifest covariance with respect to the E7(7) subgroup of E8(8) our formulas are simpler than previous realizations, and thus well suited for applications in supergravity and superstring theory. One possible application arises in the context of the conformal quantum mechanics description of extremal black holes in maximally extended supergravity.
TL;DR: In this paper, the authors show how topological open string theory amplitudes can be computed by using relative stable morphisms in the algebraic category, by explicitly working through an example which has been previously considered by Ooguri and Vafa from the point of view of physics.
Abstract: We show how topological open string theory amplitudes can be computed by using relative stable morphisms in the algebraic category. We achieve our goal by explicitly working through an example which has been previously considered by Ooguri and Vafa from the point of view of physics. By using the method of virtual localization, we successfully reproduce their results for multiple covers of a holomorphic disc, whose boundary lies in a Lagrangian submanifold of a Calabi‐Yau 3‐fold, by Riemann surfaces with arbitrary genera and number of boundary components. In particular we show that in the case we consider there are no open string instantons with more than one boundary component ending on the Lagrangian submanifold. 14N35; 14D21 Reproduced by kind permission of International Press from: Advances in Theoretical and Mathematical Physics, Volume 5 (2002) pages 69‐91
TL;DR: In this paper, the brane functional was used to generalize some of the works that Schoen and I [4] did many years ago, and the key idea is that if a three dimensional manifold M has a boundary with strongly positive mean curvature, the effect of this mean curvatures can influence the internal geometry of M.
Abstract: In this paper, we observe that the brane functional studied in hep-th/9910245 can be used to generalize some of the works that Schoen and I [4] did many years ago. The key idea is that if a three dimensional manifold M has a boundary with strongly positive mean curvature, the effect of this mean curvature can influence the internal geometry of M. For example, if the scalar curvature of M is greater than certain constant related to this boundary effect, no incompressible surface of higher genus can exist.
TL;DR: In this article, the authors describe how to construct immersed Lagrangian submanifolds in C 2 that are asymptotic at large distance from the origin to a given braid in the 3-sphere.
Abstract: This article explains how to construct immersed Lagrangian submanifolds in C 2 that are asymptotic at large distance from the origin to a given braid in the 3‐sphere. The self-intersections of the Lagrangians are related to the crossings of the braid. These Lagrangians are then used to construct immersed Lagrangians in the vector bundle O. 1/ O. 1/ over the Riemann sphere which are asymptotic at large distance from the zero section to braids. 53D45; 53D12, 57M27 Reproduced by kind permission of International Press from: Advances in Theoretical and Mathematical Physics, Volume 5 (2002) pages 139‐163
TL;DR: In this paper, an electron, spin 1/2, minimally coupled to the quantized radiation field in the nonrelativistic approximation, a situation defined by the Pauli-Fierz Hamiltonian, was considered.
Abstract: We consider an electron, spin 1/2, minimally coupled to the quantized radiation field in the nonrelativistic approximation, a situation defined by the Pauli-Fierz Hamiltonian $H$. There is no external potential and $H$ fibers according to the total momentum $p$. We prove that the ground state subspace of $H$ with a total momentum $p$ is two-fold degenerate provided the charge $e$ and the total momentum $p$ are sufficiently small. We also establish that the total angular momentum of the ground state subspace is $\pm1/2$ and study the case of a confining external potential.
TL;DR: A spin foam model for Riemannian general relativity is introduced by systematically implementing constraints as restrictions on paths in the state-sum of the BF theory by treating classical Plebanski's action as a BF action supplemented by constraints.
Abstract: The goal of this work is two-fold. In the first part of this paper we regard classical Plebanski's action as a BF action supplemented by constraints. We introduce a spin foam model for Riemannian general relativity by systematically implementing these constraints as restrictions on paths in the state-sum of the BF theory. The spin foam model obtained is precisely the Barrett-Crane model. This provides a clear-cut connection of the model with a simplicial action. In the second part of the paper we study the quantization of the effective action corresponding to the degenerate sectors of Plebanski's theory and obtain a very simple spin foam model. This model turns out to be precisely the one introduced by De Pietri et al. as an alternative to the one proposed by Barrett and Crane.
TL;DR: In this article, the authors study D-branes on non-simply-connected Calabi-Yau 3-folds, with particular interest in the Dbranes whose charges are torsion elements of the K-theory.
Abstract: In a geometrical background, D-brane charge is classified by topological K-theory. The corresponding classification of D-brane charge in an arbitrary, nongeometrical, compactification is still a mystery. We study D-branes on non-simply-connected Calabi-Yau 3-folds, with particular interest in the D-branes whose charges are torsion elements of the K-theory. We argue that we can follow the D-brane charge through the nongeometrical regions of the Kahler moduli space and, as evidence, explicitly construct torsion D-branes at the Gepner point in some examples. In one of our examples, the Gepner theory is a nonabelian orbifold of a tensor product of minimal models, and this somewhat exotic situation seems to be essential to the physics. Work supported in part DOE Grant DE-FG02-96ER40959. Work supported in part by NSF Grant PHY0071512 and the Robert A. Welch Foundation.
TL;DR: In this paper, the locations of G orbifold conformal field theories, G=Z_M, M=2,3,4,6, G =\hat D_n, n=4,5, or G the binary tetrahedral group \hat T, within the moduli space M^{K3} of N=(4,4) superconformal field theory associated to K3, were explicitly determined.
Abstract: We explicitly determine the locations of G orbifold conformal field theories, G=Z_M, M=2,3,4,6, G=\hat D_n, n=4,5, or G the binary tetrahedral group \hat T, within the moduli space M^{K3} of N=(4,4) superconformal field theories associated to K3. This is achieved purely from the known description of the moduli space [AM94] and the requirement of a consistent embedding of orbifold conformal field theories within M^{K3}. We calculate the Kummer type lattices for all these orbifold limits. Our method allows an elementary derivation of the B-field values in direction of the exceptional divisors that arise from the orbifold procedure [Asp95,Dou97,BI97], without recourse to D-geometry. We show that our consistency requirement fixes these values uniquely and determine them explicitly. The relation of our results to the classical McKay correspondence is discussed.
TL;DR: In this article, the spectrum above the kink ground states of the spin J ferromagnetic XXZ chain with Ising anisotropy was investigated using perturbation theory, numerical, and asymptotic analysis.
Abstract: We investigate the spectrum above the kink ground states of the spin J ferromagnetic XXZ chain with Ising anisotropy �. Our main theorem is that there is a non-vanishing gap above all ground states of this model for all values of J. Using a variety of methods, we obtain additional information about the magnitude of this gap, about its be- havior for large �, about its overall behavior as a function ofand its dependence on the ground state, about the scaling of the gap and the structure of the low-lying spectrum for large J, and about the existence of isolated eigenvalues in the excitation spectrum. By combining in- formation obtained by perturbation theory, numerical, and asymptotic analysis we arrive at a number of interesting conjectures. The proof of the main theorem, as well as some of the numerical results, rely on a comparison result with a Solid-on-Solid (SOS) approximation. This SOS model itself raises interesting questions in combinatorics, and we believe it will prove useful in the study of interfaces in the XXZ model in higher dimensions.
TL;DR: In this paper, the authors studied the entire solution of the difference Schrodinger equation with trigonometric polynomial coefficients and showed that the monodromy matrices corresponding to the minimal entire solutions are trigonometric polynomials of the same order as $M.
Abstract: In this paper, we study entire solutions of the difference equation $\psi(z+h)=M(z)\psi(z)$, $z\in{\mathbb C}$, $\psi(z)\in {\mathbb C}^2$. In this equation, $h$ is a fixed positive parameter and $M: {\mathbb C}\to SL(2,{\mathbb C})$ is a given matrix function. We assume that $M(z)$ is a $2\pi$-periodic trigonometric polynomial. We construct the minimal entire solutions, i.e. entire solutions with the minimal possible growth simultaneously as for im$z\to+\infty$ so for im$z\to-\infty$. We show that the monodromy matrices corresponding to the minimal entire solutions are trigonometric polynomials of the same order as $M$. This property relates the spectral analysis of difference Schr\"odinger equations with trigonometric polynomial coefficients to an analysis of finite dimensional dynamical systems.
TL;DR: In this paper, the stability of D-branes in the compactification of Calabi-Yau manifolds has been studied in the context of the K-theory model.
Abstract: We study D-branes on Calabi-Yau manifolds, carrying charges which are torsion elements of the K-theory. Interesting physics ensues when we follow these branes into nongeometrical phases of the compactification. On the level of K-theory, we determine the monodromies of the group of charges as we circle singular loci in the closed string moduli space. Going beyond K-theory, we discuss the stability of torsion D-branes as a function of the K\"ahler moduli. When the fundamental group of the Calabi-Yau is nonabelian, we find evidence for new threshold bound states of BPS branes. In a two-parameter example, we compare our results with computations in the Gepner model. Our study of the torsion D-branes in the compactification of [FHSV] sheds light on the physics of that model. In particular, we develop a proposal for the group of allowed D-brane charges in the presence of discrete RR fluxes.
TL;DR: In this article, the photoelectric effect on the example of a simplifi ed model of an atom with a single bound state coupled to the quantized electromagnetic field was studied and shown to be qualitatively and quantitatively correct to leading order in the coupling parameter.
Abstract: We study the photoelectric effect on the example of a simplifi ed model of an atom with a single bound state, coupled to the quantized electromagnetic field. For this model, we show that Einstein’s prediction for the ph otoelectric effect is qualitatively and quantitatively correct to leading order in the coupling parameter. More specifically, considering the ionization of the atom by an in cident photon cloud consisting of N photons, we prove that the total ionized charge is additive i n the N involved photons. Furthermore, if the photon cloud is approaching the atom from a large distance, the kinetic energy of the ejected electron is shown to be given by the difference of the photon energy of each single photon in the photon cloud and the ionization energy.
TL;DR: In this paper, the Hopfield model with pure p-spin interactions with even p ≥ 4, and a number of patterns, was studied and the existence of a critical temperature βp characterized as the first time quenched and annealed free energy differ.
Abstract: We study the Hopfield model with pure p-spin interactions with even p ≥ 4, and a number of patterns, M(N) growing with the system size, N, as M(N) = αN p−1 . We prove the existence of a critical temperature βp characterized as the first time quenched and annealed free energy differ. We prove that as p ↑ ∞, βp → √ α2ln2. Moreover, we show that for any α > 0 and for all inverse temperatures β, the free energy converges to that of the REM at inverse temperature β/ √ α. Moreover, above the critical temperature the distribution of the replica overlap is concentrated at zero. We show that for large enough α, there exists a non-empty interval of in the low temperature regime where the distribution has mass both near zero and near ±1. As was first shown by M. Talagrand in the case of the p-spin SK model, this implies the the Gibbs measure at low temperatures is concentrated, asymptotically for large N, on a countable union of disjoint sets, no finite subset of which has full mass. Finally, we show that there is αp ∼ 1/p! such that for α > αp the set carrying almost all mass does not contain the original patterns. In this sense we describe a genuine spin glass transition. Our approach follows that of Talagrand's analysis of the p-spin SK-model. The more complex structure of the random interactions necessitates, however, considerable technical modifications. In particular, various results that follow easily in the Gaussian case from
TL;DR: In this article, the authors derived determinant representations and nonlinear differential equations for the scaled 2-point functions of the 2D Ising model on the cylinder, which generalize well-known results for the infinite lattice.
Abstract: We derive determinant representations and nonlinear differential equations for the scaled 2-point functions of the 2D Ising model on the cylinder. These equations generalize well-known results for the infinite lattice (Painleve III equation and the equation for the τ -function of Painleve V). e-print archive: http://xxx.lanl.gov/hep-th/0108015
TL;DR: In this article, the moduli space of a super Chern-Simons theory on a manifold with the topology R × Σ, where Σ is a compact surface, is studied.
Abstract: We study the moduli space of a super Chern-Simons theory on a manifold with the topology R × Σ, where Σ is a compact surface. The moduli space is that of flat super connections modulo gauge transformations on Σ, and we study in detail the case when Σ is atorus and the supergroup is OSp(m|2n). The bosonic moduli space is determined by the flat connections for the maximal bosonic subgroup O(m)×Sp(2n), while the fermionic moduli appear only for special parts of the bosonic moduli space, which are determined by a vanishing determinant of a matrix associated to the bosonic part of the holonomy. If the CS supergroup is the exponential of a super Lie algebra, the fermionic moduli appear only for the bosonic holonomies whose generators have zero determinant in the fermion-fermion block of the super-adjoint representation. A natural symplectic structure on the moduli space is induced by the super Chern-Simons theory and it is determined by the Poisson bracket algebra of the holonomies. We show that the symplectic structure of homogenous connections is useful for understanding the properties of the moduli space and the holonomy algebra, and we illustrate this on the example of the OSp(1|2) supergroup. E-mail address: amikovic@math.ist.utl.pt. On leave of absence from Institute of Physics, P.O.Box 57, 11001 Belgrade, Yugoslavia E-mail address: rpicken@math.ist.utl.pt
TL;DR: In this article, the Seiberg-Witten analysis of the low-energy effective action of d = 4 N = 2 SYM theories reveals the relation between the Donaldson and Seberg-witten (SW) monopole invariants.
Abstract: The Seiberg-Witten analysis of the low-energy effective action of d=4 N=2 SYM theories reveals the relation between the Donaldson and Seiberg-Witten (SW) monopole invariants. Here we apply analogous reasoning to d=3 N=4 theories and propose a general relationship between Rozansky-Witten (RW) and 3-dimensional Abelian monopole invariants. In particular, we deduce the equality of the SU(2) Casson invariant and the 3-dimensional SW invariant (this includes a special case of the Meng-Taubes theorem relating the SW invariant to Milnor torsion). Since there are only a finite number of basic RW invariants of a given degree, many different topological field theories can be used to represent essentially the same topological invariant. This leads us to advocate using higher rank Abelian gauge theories to shed light on the higher (non-Abelian) RW invariants and we write down candidate higher rank SW equations.