Three Dimensional Bosonization From Supersymmetry

Three dimensional bosonization is a conjectured duality between non-supersymmetric Chern-Simons theories coupled to matter fields in the fundamental representation of the gauge group. There is a well-established supersymmetric version of this duality, which involves Chern-Simons theories with ${\cal N} = 2$ supersymmetry coupled to fundamental chiral multiplets. Assuming that the supersymmetric duality is valid, we prove that non-supersymmetric bosonization holds for all planar correlators of single-trace operators. The main tool we employ is a double-trace flow from the supersymmetric theory to an IR fixed point, in which the scalars and fermions are effectively decoupled in the planar limit. A generalization of this technique can be used to derive the duality mapping of all renormalizable couplings, in non-supersymmetric theories with both a scalar and a fermion. Our results do not rely on an explicit computation of planar diagrams.Comment: 39 pages, 3 figures. v2: added reference

Recent Efforts in the Computation of String Couplings:

We review recent advances towards the computation of string couplings. Duality symmetry, mirror symmetry, Picard-Fuchs equations, etc. are some of the tools.Comment: Talk hold at the `International Conference on Modern Problems in Quantum Field Theorie, Strings and Quantum Gravity', Kiev, June 1992, 18 page

Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc

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.Comment: This is the version published by Geometry & Topology Monographs on 22 April 200

On Vanishing Two Loop Cosmological Constants in Nonsupersymmetric Strings

It has recently been suggested that in certain special nonsupersymmetric type II string compactifications, at least the first two perturbative contributions to the cosmological constant $\Lambda$ vanish. Support for perturbative vanishing beyond 1-loop (as well as evidence for the absence of some nonperturbative contributions) has come from duality arguments. There was also a direct 2-loop computation which was incomplete; in this note we explain the deficiency of the previous 2-loop calculation and discuss the complete 2-loop computation in two different models. The corrected analysis yields a vanishing 2-loop contribution to $\Lambda$ in these models.Comment: 16 pages, harvmac bi

Gluon-Meson Duality in the Mean Field Approximation

In a gauge-fixed language gluon-meson duality can be described as the Higgs mechanism for ``spontaneous symmetry breaking'' of color. We present a mean field computation which suggests that this phenomenon is plausible in QCD. One obtains realistic masses of the light mesons and baryons.Comment: 12 pages,adaptation of numerical results to hep-ph/000815