The Dirac field in Taub-NUT background

We investigate the SO(4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza-Klein monopole, pointing out that the quantum modes can be recovered from a Klein-Gordon equation analogous to the Schr\" odinger equation in the Taub-NUT background. Moreover, we show that there is a large collection of observables that can be directly derived from those of the scalar theory. These offer many possibilities of choosing complete sets of commuting operators which determine the quantum modes. In addition there are some spin- like and Dirac-type operators involving the covariantly constant Killing-Yano tensors of the hyper-K\" ahler Taub-NUT space. The energy eigenspinors of the central modes in spherical coordinates are completely evaluated in explicit, closed form.Comment: 20 pages, latex, no figure

Quantum Metamorphosis of Conformal Transformation in D3-Brane Yang-Mills Theory

We show how the linear special conformal transformation in four-dimensional N=4 super Yang-Mills theory is metamorphosed into the nonlinear and field-dependent transformation for the collective coordinates of Dirichlet 3-branes, which agrees with the transformation law for the space-time coordinates in the anti-de Sitter (AdS) space-time. Our result provides a new and strong support for the conjectured relation between AdS supergravity and super conformal Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence.Comment: 8 pages, no figure

A Superstring Theory in Four Curved Space-Time Dimensions

Neveu-Schwarz-Ramond type heterotic and type-II superstrings in four dimensional curved space-time are constructed as exact $N=1$ superconformal theories. The tachyon is eliminated with a GSO projection. The theory is based on the N=1 superconformal gauged WZW model for the anti-de Sitter coset $SO(3,2)/SO(3,1)$ with integer central extension $k=5$. The model has dynamical duality properties in its space-time metric that are similar to the large-small ($R\rightarrow 1/R$) duality of tori. To first order in a $1/k$ expansion we give expressions for the metric, the dilaton, the Ricci tensor and their dual generalizations. The curvature scalar has several singularities at various locations in the 4-dimensional manifold. This provides a new singular solution to Einstein's equations in the presence of matter in four dimensions. A non-trivial path integral measure which we conjectured in previous work for gauged WZW models is verified.Comment: 12 page

SL(2,R)xSU(2)/R2SL(2,R)xSU(2)/R^2 string model in curved spacetime and exact conformal results

Pursuing further the recent methods in the algebraic Hamiltonian approach to gauged WZW models, we apply them to the bosonic SL(2,R) X SU(2)/R^2 model recently investigated by Nappi and Witten. We find the global space and compute the conformally exact metric and dilaton fields to all orders in the $1/k$ expansion. The semiclassical limit $k',k\to \infty$ of our exact results agree with the lowest order perturbation computation which was done in the Lagrangian formalism. We also discuss the supersymmetric type-II and heterotic versions of this model and verify the non-renormalization of $e^\Phi\sqrt{-G}$.Comment: USC-92/HEP-B3, 13 pages and 1 figur

Effective action of magnetic monopole in three-dimensional electrodynamics with massless matter and gauge theories of superconductivity

We compute one-loop effective action of magnetic monopole in three-dimensional electrodynamics of massless bosons and fermions and find that it contains an infrared logarithm. So, when the number of massless matter species is sufficiently large, monopoles are suppressed and in the weak coupling limit charged particles are unconfined. This result provides some support to gauge theories of high-temperature superconductors. It also provides a mechanism by which interlayer tunneling of excitations with one unit of the ordinary electric charge can be suppressed while that of a doubly charged object is allowed.Comment: 8 pages, LATEX, UCLA/93/TEP/41 (the last sentence of the paragraph concerning applications at the end of the paper has been deleted; mailing problems have been corrected

Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level

We introduce the infinite-dimensional Lie superalgebra ${\mathcal A}$ and construct a family of mappings from certain category of ${\mathcal A}$-modules to the category of A_1^(1)-modules of critical level. Using this approach, we prove the irreducibility of a family of A_1^(1)-modules at the critical level. As a consequence, we present a new proof of irreducibility of certain Wakimoto modules. We also give a natural realizations of irreducible quotients of relaxed Verma modules and calculate characters of these representations.Comment: 21 pages, Late

No N=4 Strings on Wolf Spaces

We generalize the standard $N=2$ supersymmetric Kazama-Suzuki coset construction to the $N=4$ case by requiring the {\it non-linear} (Goddard-Schwimmer) $N=4~$ quasi-superconformal algebra to be realized on cosets. The constraints that we find allow very simple geometrical interpretation and have the Wolf spaces as their natural solutions. Our results obtained by using components-level superconformal field theory methods are fully consistent with standard results about $N=4$ supersymmetric two-dimensional non-linear sigma-models and $N=4$ WZNW models on Wolf spaces. We construct the actions for the latter and express the quaternionic structure, appearing in the $N=4$ coset solution, in terms of the symplectic structure associated with the underlying Freudenthal triple system. Next, we gauge the $N=4~$ QSCA and build a quantum BRST charge for the $N=4$ string propagating on a Wolf space. Surprisingly, the BRST charge nilpotency conditions rule out the non-trivial Wolf spaces as consistent string backgrounds.Comment: 31 pages, LaTeX, special macros are include

Wave functions and correlation functions for GKP strings from integrability

We develop a general method of computing the contribution of the vertex operators to the semi-classical correlation functions of heavy string states, based on the state-operator correspondence and the integrable structure of the system. Our method requires only the knowledge of the local behavior of the saddle point configuration around each vertex insertion point and can be applied to cases where the precise forms of the vertex operators are not known. As an important application, we compute the contributions of the vertex operators to the three-point functions of the large spin limit of the Gubser-Klebanov-Polyakov (GKP) strings in $AdS_3$ spacetime, left unevaluated in our previous work [arXiv:1110.3949] which initiated such a study. Combining with the finite part of the action already computed previously and with the newly evaluated divergent part of the action, we obtain finite three-point functions with the expected dependence of the target space boundary coordinates on the dilatation charge and the spin.Comment: 80 pages, 7 figures, v2: typos and minor errors corrected, a reference added, v3: typos and a reference corrected, published versio

Current-Current Deformations of Conformal Field Theories, and WZW Models

Moduli spaces of conformal field theories corresponding to current-current deformations are discussed. For WZW models, CFT and sigma model considerations are compared. It is shown that current-current deformed WZW models have WZW-like sigma model descriptions with non-bi-invariant metrics, additional B-fields and a non-trivial dilaton.Comment: 30 pages, latex, v2: remarks and references adde