The Classification of Non-Local Chiral CFT with <Emphasis Type="Italic">c</Emphasis> < 1

All non-local but relatively local irreducible extensions of Virasoro chiral CFTs with c < 1 are classified. The classification, which is a prerequisite for the classification of local c < 1 boundary CFTs on a two-dimensional half-space, turns out to be 1 to 1 with certain pairs of A-D-E graphs with distinguished vertices. Dedicated to Hans-Jürgen Borchers on the occasion of his 80th birthday Supported in part by JSPS. Supported in part by EU network “Quantum Spaces - Noncommutative Geometry” HPRN-CT-2002-00280. Supported in part by GNAMPA and MIUR.     

On the Jones Index Values for Conformal Subnets

We consider the smallest values taken by the Jones index for an inclusion of local conformal nets of von Neumann algebras on S ¹ and show that these values are quite more restricted than for an arbitrary inclusion of factors. Below 4, the only non-integer admissible value is 4 cos² π/10, which is known to be attained by a certain coset model. Then no index value is possible in the interval between 4 and ${3 +\sqrt{3}}$ . The proof of this result is based on α-induction arguments. In the case of values below 4 we also give a second proof of the result. In the course of the latter proof we classify all possible unitary braiding symmetries on the ADE tensor categories, namely the ones associated with the even vertices of the A _n , D _2n , E ₆, E ₈ Dynkin diagrams.     

Conformal transformations of <Emphasis Type="Italic">S</Emphasis>-matrix in scalar field theory

In this paper, three methods for describing the conformal transformations of the S-matrix in quantum field theory are proposed. They are illustrated by applying the algebraic renormalization procedure to the quantum scalar field theory, defined by the LSZ reduction mechanism in the BPHZ renormalization scheme. Central results are shown to be independent of scheme choices and derived to all orders in loop expansions. Firstly, the local Callan-Symanzik equation is constructed, in which the insertion of the trace of the energy-momentum tensor is related to the beta function and the anomalous dimension. With this result, the Ward identities for the conformal transformations of the Green functions are derived. Then the conformal transformations of the S-matrix defined by the LSZ reduction procedure are calculated. Secondly, the conformal transformations of the S-matrix in the functional formalism are related to charge constructions. The commutators between the charges and the S-matrix operator are written in a compact way to represent the conformal transformations of the S-matrix. Lastly, the massive scalar field theory with local coupling is introduced in order to control breaking of the conformal invariance further. The conformal transformations of the S-matrix with local coupling are calculatedReceived: 3 June 2003, Revised: 24 July 2003, Published online: 2 October 2003Yong Zhang: Supported by Graduiertenkolleg Quantenfeldtheorie: Mathematische Struktur und physikalische Anwendungen, University Leipzig.     

Unitary equivalence between a spin 1/2 charged particle in a two-dimensional magnetic field and a spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electric field

We prove the unitary equivalence between the Dirac HamiltonianH _D for a relativistic spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electrostatic fieldE = (E ₁,E ₂) and the direct sum of the Dirac-Weyl operatorsD(±A) for a spin 1/2 charged particle in two-dimensional magnetic fields ±dA with the vector potentialA =E ₂ dx ¹ -E ₁ dx ², (x ¹,x ²) ². As applications, we investigate the ground state and the spectra ofH _D.     

<Emphasis Type="Italic">W</Emphasis><Subscript>4</Subscript> toda example as hidden Liouville CFT

We construct correlators in the W ₄ Toda 2d conformal field theory for a particular class of representations and demonstrate a relation to a W ₂ (Virasoro) theory with different central charge. The relevance of the classical limits of the constructed 3-point functions and braiding matrices to problems in 4d conformal theories is discussed.     

On the Unitarity of <Emphasis Type="Italic">D</Emphasis> = 9, 10, 11 Conformal Supersymmetry

We consider the unitarity of D = 9, 10, 11 conformal supersymmetry using the recently established classification of the UIRs of the superalgebras osp(12n, ).     

Mirror Extensions of Local Nets

In this paper we prove a general theorem on the extensions of local nets which was inspired by recent examples of exotic extensions for Virasoro nets with central charge less than one and earlier work on cosets and conformal inclusions. When applying the theorem to conformal inclusions and diagonal inclusions, we obtain infinite series of new examples of completely rational nets. Supported in part by NSF.     

Mirror Symmetry on Kummer Type <Emphasis Type="Italic">K</Emphasis>3 Surfaces

We investigate both geometric and conformal field theoretic aspects of mirror symmetry on N=(4,4) superconformal field theories with central charge c=6. Our approach enables us to determine the action of mirror symmetry on (non-stable) singular fibers in elliptic fibrations of _N orbifold limits of K3. The resulting map gives an automorphism of order 4,8, or 12, respectively, on the smooth universal covering space of the moduli space. We explicitly derive the geometric counterparts of the twist fields in our orbifold conformal field theories. The classical McKay correspondence allows for a natural interpretation of our results.     

On the Representation Theory of Virasoro Nets

We discuss various aspects of the representation theory of the local nets of von Neumann algebras on the circle associated with positive energy representations of the Virasoro algebra (Virasoro nets). In particular we classify the local extensions of the c=1 Virasoro net for which the restriction of the vacuum representation to the Virasoro subnet is a direct sum of irreducible subrepresentations with finite statistical dimension (local extensions of compact type). Moreover we prove that if the central charge c is in a certain subset of (1, ), including [2, ), and h(c–1)/24, the irreducible representation with lowest weight h of the corresponding Virasoro net has infinite statistical dimension. As a consequence we show that if the central charge c is in the above set and satisfies c25 then the corresponding Virasoro net has no proper local extensions of compact type.Supported in part by the Italian MIUR and GNAMPA-INDAM.     

Axiomatic Conformal Theory in Dimensions &gt;2 and AdS/CT Correspondence

We formulate axioms of conformal theory (CT) in dimensions >2 modifying Segal’s axioms for two-dimensional CFT. (In the definition of higher-dimensional CFT, one includes also a condition of existence of energy-momentum tensor.) We use these axioms to derive the AdS/CT correspondence for local theories on AdS. We introduce a notion of weakly local quantum field theory and construct a bijective correspondence between conformal theories on the sphere S^d and weakly local quantum field theories on \({H^{d+1}}\) that are invariant with respect to isometries. (Here \({H^{d+1}}\) denotes hyperbolic space = Euclidean AdS space.) We give an expression of AdS correlation functions in terms of CT correlation functions. The conformal theory has conserved energy-momentum tensor iff the AdS theory has graviton in its spectrum.     

A 3-quasiparticle isomer in neutron-rich <Superscript>183</Superscript>Ta

Excited states in neutron-rich ¹⁸³Ta have been studied using a two-neutron transfer reaction of ¹⁸¹Ta(¹⁸O,¹⁶O) . In-beam -rays were measured in coincidence with scattered ions detected by a high-resolution E -E Si telescope for reaction channel selection. Previously known 1-quasiparticle bands are extended to higher spins, and several levels including a T _1/2 = 0.9(3) μs 3-quasiparticle isomer are identified.     

The algebra of the energy-momentum tensor and the Noether currents in classical non-linear sigma models

The recently derived current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is extended to include the energy-momentum tensor. It is found that in two dimensions the energy-momentum tensor , the Noether currentj associated with the global symmetry of the theory and the composite fieldj appearing as the coefficient of the Schwinger term in the current algebra, together with the derivatives ofj andj, generate a closed algebra. The subalgebra generated by the light-cone components of the energy-momentum tensor consists of two commuting copies of the Virasoro algebra, with central chargec=0, reflecting the classical conformal invariance of the theory, but the current algebra part and the semidirect product structure are quite different from the usual Kac-Moody/Sugawara type construction.Supported by the Deutsche Forschungsgemeinschaft, Contract No. Ro 864/2-1Supported by the Studienstiftung des Deutschen Volkes     

D<Subscript>s0</Subscript><Superscript>+</Superscript>(2317) as an iso-triplet four-quark meson

Although assigning D _s0 ⁺(2317) to the I ₃ = 0 component of iso-triplet four-quark mesons is favored by experiments, its neutral and doubly charged partners have not yet been observed. It is discussed why they were not observed in inclusive e ⁺ e ^-→cˉ experiment and that they can be observed in B decays.     

Electron paramagnetic resonance of Cr<Superscript>3+</Superscript>-Li<Superscript>+</Superscript> centers in (Cr,Li): Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> synthetic forsterite

Synthetic single crystals of chromium-and lithium-doped forsterite, namely, (Cr,Li): Mg₂SiO₄, are studied using electron paramagnetic resonance spectroscopy. It is revealed that, apart from the known centers Cr³⁺(M1) and Cr³⁺(M2) (with local symmetries C_i and C_s, respectively), these crystals involve two new types of centers with C₁ symmetry, namely, Cr³⁺(M1)′ and Cr³⁺(M2)′ centers. The standard parameters D and E in a zero magnetic field [zero-field splitting (ZFS) parameters expressed in GHz] and principal components of the g tensor are determined as follows: D=31.35, E=8.28, and g=(1.9797, 1.9801, 1.9759) for Cr³⁺(M1)′ centers and D=15.171, E=2.283, and g=(1.9747, 1.9769, 1.9710) for Cr³⁺(M2)′ centers. It is found that the lowsymmetric effect of misalignment of the principal axes of the ZFS and g tensors most clearly manifests itself (i.e., its magnitude reaches 19°) in the case of Cr³⁺(M2)′ centers. The structural models Cr³⁺(M1)-Li⁺(M2) and Cr³⁺(M2)-Li⁺(M1) are proposed for the Cr³⁺(M1)′ and Cr³⁺(M2)′ centers, respectively. The concentrations of both centers are determined. It is demonstrated that, upon the formation of Cr³⁺-Li⁺ ion pairs, the M1 position for chromium appears to be two times more preferable than the M2 position. Reasoning from the results obtained, the R₁ line (the ²E → ⁴A₂ transition) observed in the luminescence spectra of (Cr,Li): Mg₂SiO₄ crystals in the vicinity of 699.6 nm is assigned to the Cr³⁺(M1)′ center.     

From free fields to AdS: The case of particles with spin

It is shown that one-loop diagrams with three external lines in the usual conformal field theory in D dimensions are equal to a finite sum of tree diagrams with one vertex in theory with the AdS _{D + 1} metric. Some terms of the dual Lagrangian that are responsible for interaction are calculated. Spin-0, spin-1/2, and spin-1 particles are considered.     

Bethe Algebra of Homogeneous <Emphasis Type="Italic">XXX</Emphasis> Heisenberg Model has Simple Spectrum

We show that the algebra of commuting Hamiltonians of the homogeneous XXX Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional -modules. As a byproduct we show that there exist exactly two-dimensional vector subspaces with a basis such that deg f = l, deg g = n − l + 1 and f (u)g(u − 1) − f (u − 1)g(u) = (u + 1) ⁿ . Supported in part by NSF grant DMS-0601005. Supported in part by RFFI grant 08-01-00638. Supported in part by NSF grant DMS-0555327.     

The Ising Model on a Quenched Ensemble of c=−5 Gravity Graphs

We study with Monte Carlo methods an ensemble of c=–5 gravity graphs, generated by coupling a conformal field theory with central charge c=–5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent _s and the intrinsic fractal dimension d _H. We find _s=–1.5(1) and d _H=3.36(4), in reasonable agreement with theoretical predictions. In addition, we study the critical behavior of an Ising model on a quenched ensemble of the c=–5 graphs and show that it agrees, within numerical accuracy, with theoretical predictions for the critical behavior of an Ising model coupled dynamically to two-dimensional quantum gravity, with a total central charge of the matter sector c=–5.     

Investigations into the alpha-decay of <Superscript>195</Superscript>At

The low-energy nuclear structure and decay properties of the neutron-deficient isotopes ¹⁹⁵At and ¹⁹¹Bi have been studied. ¹⁹⁵At was produced in the reaction ¹⁴²Nd(⁵⁶Fe,p2n)¹⁹⁵At and ¹⁹¹Bi as the daughter activity of ¹⁹⁵At. The activities were implanted in a position-sensitive silicon detector after being separated from the primary beam by a gas-filled recoil separator. The 1/2⁺ intruder state was determined to be the ground state in ¹⁹⁵At with an alpha-decay energy of E _α = 6953(3) keV and a half-life T _1/2 = 328(20) ms. Another state with an alpha-decay energy E _α = 7075(4) keV and a half-life T _1/2 = 147(5) ms was found to decay to a 148.7(5) keV excited state in ¹⁹¹Bi for which a spin and parity of 7/2^- were deduced. Consequently, the same 7/2^- character was assigned to the initial state at 32(7) keV in ¹⁹⁵At on the basis of unhindered alpha-decay. The 9/2^- state, being the ground state in heavier odd-mass astatine isotopes, was not observed. Received: 16 September 2002 / Accepted: 19 December 2002 / Published online: 25 March 2003 RID="a" ID="a"e-mail: heikki.kettunen@phys.jyu.fi RID="b" ID="b"Present address: Laboratory of Radiochemistry, P.O. Box 55, FIN-00014, University of Helsinki, Finland. RID="c" ID="c"Present address: Radiation and Nuclear Safety Authority, P.O. Box 14, FIN-00881 Helsinki, Finland. Communicated by W. Henning     

On classification ofN=2 supersymmetric theories

We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetricN=2 conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A-D-E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.