On the classification of fusion rings

The fusion rules and modular matrix of a rational conformal field theory obey a list of properties. We use these properties to classify rational conformal field theories with not more than six primary fields and small values of the fusion coefficients. We give a catalogue of fusion rings which can arise for these field theories. It is shown that all such fusion rules can be realized by current algebras. Our results support the conjecture that all rational conformal field theories are related to current algebras.Comment: 10 pages, CALT-68-196

Singular Monopoles and Gravitational Instantons

We model A_k and D_k asymptotically locally flat gravitational instantons on the moduli spaces of solutions of U(2) Bogomolny equations with prescribed singularities. We study these moduli spaces using Ward correspondence and find their twistor description. This enables us to write down the K\"ahler potential for A_k and D_k gravitational instantons in a relatively explicit form.Comment: 22 pages, LaTe

Tests of Seiberg-like Duality in Three Dimensions

We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI parameters. We find that Seiberg-like duality for N=3 Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level of partition functions and is closely related to level-rank duality in pure Chern-Simons theory. We also clarify the relationship between the Giveon-Kutasov duality and a duality in theories of fractional M2 branes and propose a generalization of the latter. Our analysis also confirms previously known results concerning decoupled free sectors in N=4 gauge theories realized by monopole operators.Comment: 36 pages, 5 figure

On the non-relativistic limit of the quantum sine-Gordon model with integrable boundary condition

We show that the the generalized Calogero-Moser model with boundary potential of the P\"oschl-Teller type describes the non-relativistic limit of the quantum sine-Gordon model on a half-line with Dirichlet boundary condition.Comment: 6 pages, CALT-68-1949, USC-94-01

On the relation between open and closed topological strings

We discuss the relation between open and closed string correlators using topological string theories as a toy model. We propose that one can reconstruct closed string correlators from the open ones by considering the Hochschild cohomology of the category of D-branes. We compute the Hochschild cohomology of the category of D-branes in topological Landau-Ginzburg models and partially verify the conjecture in this case.Comment: 28 pages, corrected the proof of eq. 2

D_k Gravitational Instantons and Nahm Equations

We construct D_k asymptotically locally flat gravitational instantons as moduli spaces of solutions of Nahm equations. This allows us to find their twistor spaces and Kahler potentials.Comment: 20 pages, 4 figures (published version

Nahm Transform For Periodic Monopoles And N=2 Super Yang-Mills Theory

We study Bogomolny equations on $R^2\times S^1$. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperk\"ahler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of $k$ periodic monopoles provides the exact solution of ${\cal N}=2$ super Yang-Mills theory with gauge group $SU(k)$ compactified on a circle of arbitrary radius.Comment: 48 pages, AMS latex. v2: several minor errors corrected, exposition improve

Topological Disorder Operators in Three-Dimensional Conformal Field Theory

Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogues of twist and winding-state operators in free 2d CFTs. We call them monopole operators for reasons explained in the text. The importance of monopole operators is that in the Higgs phase, they create Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in three-dimensional QED using large N_f expansion. In particular, we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N_f. We also show that monopole operators transform non-trivially under the flavor symmetry group, with the precise representation depending on the value of the Chern-Simons coupling.Comment: 24 pages, latex. v2: a reference to prior work has been adde

Nonrenormalization Theorem for Gauge Coupling in 2+1D

We prove that \be-function of the gauge coupling in $2+1D$ gauge theory coupled to any renormalizable system of spinor and scalar fields is zero. This result holds both when the gauge field action is the Chern-Simons action and when it is the topologically massive action.Comment: 8 pages, LaTeX file, CALT-68-191