Continuous Symmetries of Lattice Conformal Field Theories and their Z2Z_2-Orbifolds

Following on from a general observation in an earlier paper, we consider the continuous symmetries of a certain class of conformal field theories constructed from lattices and their reflection-twisted orbifolds. It is shown that the naive expectation that the only such (inner) symmetries are generated by the modes of the vertex operators corresponding to the states of unit conformal weight obtains, and a criterion for this expectation to hold in general is proposed.Comment: 15 page

Intertwiners in Orbifold Conformal Field Theories

Following on from earlier work relating modules of meromorphic bosonic conformal field theories to states representing solutions of certain simple equations inside the theories, we show, in the context of orbifold theories, that the intertwiners between twisted sectors are unique and described explicitly in terms of the states corresponding to the relevant modules. No explicit knowledge of the structure of the twisted sectors is required. Further, we propose a general set of sufficiency conditions, illustrated in the context of a third order no-fixed-point twist of a lattice theory, for verifying consistency of arbitrary orbifold models in terms of the states representing the twisted sectors.Comment: 18 pages LaTeX. To appear in Nuclear Physics

Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.Comment: 34 pages, v2 contains minor corrections to the published versio

On the Uniqueness of the Twisted Representation in the Z_2 Orbifold Construction of a Conformal Field Theory from a Lattice

Following on from recent work describing the representation content of a meromorphic bosonic conformal field theory in terms of a certain state inside the theory corresponding to a fixed state in the representation, and using work of Zhu on a correspondence between the representations of the conformal field theory and representations of a particular associative algebra constructed from it, we construct a general solution for the state defining the representation and identify the further restrictions on it necessary for it to correspond to a ground state in the representation space. We then use this general theory to analyze the representations of the Heisenberg algebra and its $Z_2$-projection. The conjectured uniqueness of the twisted representation is shown explicitly, and we extend our considerations to the reflection-twisted FKS construction of a conformal field theory from a lattice.Comment: 27 pages LaTeX. Typos corrected -- no major change

On Four-Point Functions of Half-BPS Operators in General Dimensions

We study four-point correlation functions of half-BPS operators of arbitrary weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for these correlators and present them in a universal form. We then solve these identities, employing Jack polynomial expansions. We show that the general solution is parameterized by a set of arbitrary two-variable functions, with the exception of the case d=4, where in addition functions of a single variable appear. We also discuss the operator product expansion using recent results on conformal partial wave amplitudes in arbitrary dimension.Comment: The discussion of the case d=6 expanded; references added/correcte

Some Systematics of the Coupling Constant Dependence of N=4 Yang-Mills

The operator, O_\tau, that generates infinitesimal changes of the coupling constant in N=4 Yang-Mills sits in the same supermultiplet as the superconformal currents. We show how superconformal current Ward identities determine a class of terms in the operator product expansion of O_\tau with any other operator. In certain cases, this leads to constraints on the coupling dependence of correlation functions in N=4 Yang-Mills. As an application, we demonstrate the exact non-renormalization of two and certain three-point correlation functions of BPS operators.Comment: 56 pages, LaTeX; amended and expanded arguments, added reference

Vortex states in superconducting rings

The superconducting state of a thin superconducting disk with a hole is studied within the non-linear Ginzburg-Landau theory in which the demagnetization effect is accurately taken into account. We find that the flux through the hole is not quantized, the superconducting state is stabilized with increasing size of the hole for fixed radius of the disk, and a transition to a multi-vortex state is found if the disk is sufficiently large. Breaking the circular summetry through a non central location of the hole in the disk enhances the multi-vortex state.Comment: 11 pages, 23 figures (postscript). To appear in Physical Review B, Vol. 61 (2000

Superparticle and superstring in AdS_3 x S^3 Ramond-Ramond background in light-cone gauge

We discuss superparticle and superstring dynamics in AdS_3 x S^3 supported by R-R 3-form background using light-cone gauge approach. Starting with the superalgebra psu(1,1|2) + psu(1,1|2) representing the basic symmetry of this background we find the light-cone superparticle Hamiltonian. We determine the harmonic decomposition of light-cone superfield describing fluctuations of type IIB supergravity fields expanded near AdS_3 x S^3 background and compute the corresponding Kaluza-Klein spectrum. We fix the fermionic and bosonic light-cone gauges in the covariant Green-Schwarz AdS_3 x S^3 superstring action and find the light-cone string Hamiltonian. We also obtain a realization of the generators of psu(1,1|2) + psu(1,1|2) in terms of the superstring 2-d fields in the light-cone gauge.Comment: 32 pages, late

Superextendons with a modified measure

For superstrings, the consequences of replacing the measure of integration $\sqrt{-\gamma}d^2 x$ in the Polyakov's action by $\Phi d^2 x$ where $\Phi$ is a density built out of degrees of freedom independent of the metric $\gamma_{ab}$ defined in the string are studied. As in Siegel reformulation of the Green Schwarz formalism the Wess-Zumino term is the square of supersymmetric currents. As opposed to the Siegel case, the compensating fields needed for this do not enter into the action just as in a total derivative. They instead play a crucial role to make up a consistent dynamics. The string tension appears as an integration constant of the equations of motion. The generalization to higher dimensional extended objects is also studied using in this case the Bergshoeff and Sezgin formalism with the associated additional fields, which again are dynamically relevant unlike the standard formulation. Also unlike the standard formulation, there is no need of a cosmological term on the world brane.Comment: typos corrected, references adde

Superconformal operators in N=4 super-Yang-Mills theory

We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building blocks into multi-particle quasipartonic operators. The latter are determined by the condition that their twist equals the number of elementary constituent fields from which they are built. A unique feature of the N=4 SYM is that all quasipartonic operators with different SU(4) quantum numbers fall into a single supermultiplet. Among them there is a subsector of the operators of maximal helicity, which has been known to be integrable in the multi-color limit in QCD, independent of the presence of supersymmetry. In the N=4 SYM theory, this symmetry is extended to the whole supermultiplet of quasipartonic operators and the one-loop dilatation operator coincides with a Hamiltonian of integrable SL(2|4) Heisenberg spin chain.Comment: 45 pages, Latex, 4 figure