Einstein–Maxwell gravity with additional corrections

Motivated by the E ₈×E ₈ heterotic string theory, we obtain topological black hole solutions of Einstein–Maxwell gravity with additional corrections. We consider the Gauss–Bonnet (GB) and (F _μν F ^μν )² terms as an effective quartic order Lagrangian of gauge–gravity coupling and investigate geometric and thermodynamic properties of the black hole solutions. We also analyze the effects of the GB term as well as the correction of Maxwell field on the properties of the solutions.     

Small E8 instantons and tensionless non-critical strings

T-duality is used to extract information on an instanton of zero size in the E₈ × E₈ heterotic string. We discuss the possibility of the appearance of a tensionless anti-self-dual non-critical string through an implementation of the mechanism suggested by Strominger of two coincident 5-branes. It is argued that when an instanton shrinks to zero size a tensionless non-critical string appears at the core of the instanton. It is further conjectured that the appearance of tensionless strings in the spectrum leads to new phase transitions in six dimensions in much the same way as massless particles do in four dimensions.     

Orbifold models and modular transformation

The orbifold models of the heterotic string are constructed on the quotient spaces of generalized tori by translational and rotational discrete symmetries. In order to obtain the consistent orbifold models, the conditions of the modular invariance are derived from a one-loop vacuum amplitude. Z₃ orbifold models satisfying such conditions are searched systematically. It is shown that there are infinite possible models with N = 2 supersymmetry. Among these models, two examples having E₆ and E₇ gauge groups are discussed. The orbifold models with N = 1 supersymmetry are also discussed in detail. It is shown that there are only five consistent models in the class of these models based on E₈ ⊗ E′₈ heterotic string in which the extra six-dimensional torus and the E₈ ⊗ E′₈ maximal torus are modded out by the rotational and the translational Z₃ symmetries respectively.     

E 6,7,8 magnetized extra-dimensional models

We study 10D super Yang–Mills theory with the gauge groups E ₆, E ₇ and E ₈. We consider the torus/orbifold compactification with magnetic fluxes and Wilson lines. They lead to 4D interesting models with three families of quarks and leptons, whose profiles in extra dimensions are quasi-localized because of magnetic fluxes.     

High-spin states in48Ti

The⁴⁵Sc(α, p γ) reaction has been investigated atE ^α=11, 12 and 13MeV. Theγ-decay of 198 levels in⁴⁸Ti up to 8,323 keV excitation energy has been observed. High-spin states were investigated by proton-γ ray angular correlation measurements atE=11 and 13MeV and by DSAM lifetime measurements atE=11 MeV. From the combined evidence spin (-parity) assignments were obtained for the levels atE _x =8,323 keV (J= 10,8,6), 8,091(12, 10, 8, 6), 7,668(10, 8), 7,427(9, 7), 7,374(11, 9, 7), 6,906(10, 8, 6), 6,172(8⁺,6⁺), 6,102(10⁺,8⁺), 6,039(6), 6,034(9⁺, 7⁺), 5,630(7), 5,197(8⁺), 5,169(7⁺), 5,155(5), 4,404(5), 4,398(6⁺) and 4,046keV (5). Most of the ambiguous spin assignments become unique if the 8,091 keV level hasJ=12, an assumption which is favoured by its excitation function. The level spectrum thus obtained is well reproduced by shell model calculations in the pure (f _7/2)⁸ configuration space. Discrepancies exist in the reproduction ofγ-decay modes. The reason is found in low-lying high-spin intruder states which include the 7,427 and 8,323 keV levels. The spectrum of negative-parity states is understood qualitatively by a comparison with⁴⁶Ti and⁴²Ca.     

New aspects of the rotational model in25Mg

Spin assignments have been made to the²⁵Mg levels in theE _x=5–6 MeV region fromγ-ray angular distributions measured in the²²Ne(α, n y) reaction atE _α=8.0 and 8.8 MeV and fromp-γ angular correlations measured in the²⁴Mg(d, p γ) reaction atE _d=6 MeV. Unique spin assignments ofJ=7/2, 5/2, 5/2, and 9/2 could be made to the levels atE _x=5005, 5511, 5851, and 5967 keV, respectively. Ambigious assignments have been made to the levels atE _x=5245, 5524, 5785, 6032 keV (J=11/2, 7/2), 5455 keVJ=13/2, 9/2), and 5738 keV (J=3/2, 5/2). The present data confirm previous assignments ofJ=1/2 to the levels atE _x=5108 and 5466 keV, respectively. Lifetime estimates have been obtained, using the Doppler-shift attenuation method, for the levels atE _x=5245 keV (τ=30–60 fs), 5785 keV (τ=50–100 fs), 5967 keV (τ=50–100 fs), and 5455 keV (τ>1ps). All other levels in theE _x=5–6 MeV region haveτ<60 fs. A breakdown of theK-selection rule has been observed in theγ-decay of some high spin states, indicating a deviation from the strong coupling model.     

Prediction for α3(Mz) in a string-inspired model

We apply the Renormalisation Group Evolution (RGE) to analyse the phenomenological implications of an extended supersymmetric model, for the value of the unification scale and the strong coupling at the electroweak scale. The model we consider is predicted to exist in Calabi–Yau string compactifications with Wilson line mechanism for E₆ symmetry breaking, contains additional matter beyond the MSSM spectrum and avoids the “doublet-triplet” splitting problem in the Higgs sector. The calculation is analytical in two-loop order and includes the effects of the heavy thresholds due to the additional matter considered. The value of α₃(M_z) can be brought within the experimental limits without a significant change of the unification scale from the MSSM prediction.     

Superconformal deformation,zero-norm states and space-time symmetries of the superstring theories

We present a formalism to study type II and Heterotic superstrings with massless and massive background fields in the bosonic sector. This formalism is appropriate to study high energy symmetries of the superstring. As an example, we explicitly relate all massless symmetries to the massless zero-norm states in the spectrum. This includes theE ₈ ?E ₈ andSO (32) gauge symmetries in the ten-dimensional Heterotic string. The first (evenG-parity) massive level is briefly described. We then argue the existence of new symmetries for the massive Yang-Mills-like gauge bosons and tensor fields at each fixed mass level. These enlarged stringy symmetries correspond to the decoupling of massive zero-norm states in the spectrum.     

Supersymmetry breaking and soft terms in M-theory

We investigate gaugino condensation in the framework of the strongly coupled heterotic E₈×E₈ string (M-theory). Supersymmetry is broken in a hidden sector and gravitational interactions induce soft breaking parameters in the observable sector. The resulting soft masses are of order of the gravitino mass. The situation is similar to that in the weakly coupled E₈×E₈ theory with one important difference: we avoid the problem of small gaugino masses which are now comparable to the gravitino mass.     

High-spin states in27Al

The²⁴Mg(α, p γ) reaction has been studied atα-particle energies of 13, 15, and 15.2 MeV. Using method II of Litherland and Ferguson spin assignments or restrictions thereof could be made to the²⁷Al levels atE _x =5500 keV (I=11/2, 7/2), 6950 keV (I=11/2, 7/2), 7226 keV (I=9/2), 7286 keV (I=9/2–13/2), 7399 keV (I=11/2, 7/2) and 7443 keV (I=13/2, 9/2). Using the Doppler-shift attenuation method a lifetimeτ=20–50 fs was obtained for theE _x =7399 keV level and a limitτ<20 fs for the levels atE _x =7443, 7286, 7226, 6950, 6718, and 6287 keV, respectively. Further spin assignments in²⁷Al were obtained by a study of the²⁶Mg(p, γ) reaction at the E_p=2174 keV resonance. Fromγ-ray angular distributions the resonance spin was determined as I=9/2 (previous assignmentI=7/2) and the spin of theE _x =5959 keV level was determined asI=7/2. Tentative spin assignments were made to the levels atE _x =6537 keV (I=7/2) and 6718 keV (I=9/2). From the combined evidence of the²⁴Mg(α, p) and²⁶Mg(p, γ) reactions the spin of the 6287 keV level was found to beI=7/2. The results are compared with shell model calculations and the Nilsson model.     

The reaction 36S(p,γ)37Cl: (I). Excitation energies and γ-ray branchings of bound states deduced from resonances in the range Ep = 500–2000 keV

Yield curves of the reaction ³⁶S(p, γ)³⁷Cl have been measured over the range E_p = 500–2000 keV with a highly enriched (81%) ³⁶S target. Proton energies, with a precision of typically 0.3 keV, and strengths are presented for the nearly 200 observed resonances. Several previously reported resonances, among which the well-known $\text{J}{}^{\mathrm{\pi }}\text{=}\text{7}\text{2}{}^{\mathrm{?}}\text{, E}{}_{\mathrm{p}}\text{= 1887}\text{keV}$ analogue resonance, are proven to be multiplets.At 75 selected resonances in the ranges E_p = 500–1200 and 1800–2000 keV the decay schemes have been studied. These measurements also provide rather detailed information on the γ-ray branching ratios of more than 50 bound states of which the majority has not been observed previously. Precision excitation energies have been determined; for the levels with E_x < 5 MeV the median uncertainty amounts to 30 ppm. The reaction Q-value is Q = 8386.34 ± 0.23 keV.These precision data invalidate several previous spin and parity assignments to low-lying bound states of ³⁷Cl. They also provide a basis for the lifetime measurements and spin and parity assignments to be discussed in the following paper.     

Untersuchungen zur Struktur des Kerns23Ne

Low-lying states of²³Ne up to about 3 MeV excitation energy have been investigated by studying the reactions²²Ne(d, p)²³Ne (E _d =4–6 MeV) and²³Na(n, p γ)²³Ne(E _n=8–9 MeV). From the (d, p) data,l-values and spectroscopic factors for the transferred neutron have been extracted by DWBA analyses. From the (n, p γ) data,γ-ray branchings and possible spin assignments have been derived. The results are used to discuss the applicability of the Nilsson model and the excited core model to the nucleus²³Ne.     

Non critical super strings on world sheets of constant curvature

We consider correlation functions in Neveu-Schwarz string theory coupled to two dimensional gravity. The actionfor the 2D gravity consists of the string induced Liouville action and the Jackiw-Teitelboim action describing pure 2D gravity. Then gravitational dressed dimensions of vertex operators are equal to their bare conformal dimensions. There are two possible interpretations of the model. Considering the 2D dilaton and the Liouville field as additional target space coordinates one gets ad+2-dimensional critical string. In thed-dimensional non critical string picture gravitational fields retain their original meaning and ford=4 one can get a mass spectrum via consistency requirements. In both cases a GSO projection is possible.     

Compactifications of the heterotic string with unitary bundles

We describe a large new class of four‐dimensional supersymmetric string vacua defined as compactifications of the E₈ × E₈ and the SO(32) heterotic string on smooth Calabi‐Yau threefolds with unitary gauge bundles and heterotic five‐branes. The conventional gauge symmetry breaking via Wilson lines is replaced by the embedding of non‐flat line bundles into the ten‐dimensional gauge group, thus opening up the way for phenomenologically interesting string compactifications on simply connected manifolds. After a detailed analysis of the four‐dimensional effective theory we exemplify the general framework by means of a couple of explicit examples involving the spectral cover construction of stable holomorphic bundles. As for the SO(32) heterotic string, the resulting vacua can be viewed, in the S‐dual Type I picture, as a generalisation of magnetized D9/D5‐brane models. In the case of the E₈ × E₈ string, we find a natural way to construct realistic MSSM‐like models, either directly or via a flipped SU(5) GUT scenario.     

Fermion spectra from superstrings

Some compactifications of the ten-dimensional anomaly-free E₈ × E₈ and SO(32) theories that correspond to superstrings are studied. Compactification is achieved by setting the classical gauge field equal to the spin connection. The resulting chiral fermion spectra are obtained for any six-dimensional manifold, under the condition Tr F² = 30 Tr R², plus a quantization condition for U(1) charges. For E₈ × E₈ these conditions lead to potentially realistic models for any irreducible six-dimensional manifold and any embedding of the holonomy group. Apart from a few more exotic examples, the four-dimensional models we obtain are more or less standard SU(5), SO(10), SU(4) × SU(2) × SU(2) or E₆ models.     

On aC*-algebra approach to phase transition in the two-dimensional Ising model

We investigate the state on theC*-algebra of Pauli spins on a one-dimensional lattice (infinitely extended in both directions) which gives rise to the thermodynamic limit of the Gibbs ensemble in the two-dimensional Ising model (with nearest neighbour interaction). It is shown that the representation of the Pauli spin algebra associated with the state is factorial above and at the known critical temperature, while it has a two-dimensional center below the critical temperature. As a technical tool, we derive a general criterion for a state of the Pauli spin algebra corresponding to a Fock state of the Fermion algebra to be primary. We also show that restrictions of two quasifree states of the Fermion algebra to its even part are equivalent if and only if the projection operatorsE ₁ andE ₂ (on the direct sum of two copies of the basic Hilbert space) satisfy the following two conditions: (1)E ₁ ?E ₂ is in the Hilbert-Schmidt class, (2)E ₁ ∧ (1 ?E ₂) has an even dimension, where the even-oddness of dimE ₁ ∧ (1 ?E ₂) is called ?₂-index ofE ₁ andE ₂ and is continuous inE ₁ andE ₂ relative to the norm topology.     

Rashba splitting in MIS structures HgCdTe

The measured parameters of spin-orbit spectral splitting in HgCdTe-based MIS structures with positive and negative Kane gap E _g are compared with the parameters calculated using the three-and four-band Kane model. The disregard of the finite spin-orbit splitting Δ of the valence band in calculations leads to exaggerated values of Rashba splitting (especially for E _g < 0) even for small ratios |E _g|/Δ, although the subband parameters averaged over two spin branches of the spectrum in the two-, three-, and four-band Kane approximations for the same concentrations are practically identical. In the zero-gap HgCdTe, the measured as well as calculated values are noticeably higher, but the four-band approximation leads to values of splitting for both materials which are 20–40% lower than the experimental value. The inclusion of the interband interaction reduces these discrepancies, but does not eliminate them completely. It is shown that the approximations of the 2D spectrum with spin-orbit splitting linear in quasimomentum, which are conventionally used in the analysis, may lower the effective Rashba parameter by a factor of 2–4.     

High-spin states in112Cd from the110Pd(α, 2n γ)-reaction

The decay scheme of¹¹²Cd has been studied by γ-ray spectroscopy with the¹¹⁰Pd(α, 2nγ) reaction. Spin and parity assignments were made on the basis of coincidence measurements, angular distributions and excitation functions. Twelve new energy levels were established. A vibrational-like positive-parity band up to spin 8⁺ and a negativeparity side band 5^?, (7^?), (9^?) were found. For the negative-parity states a (v_j, vh_11/2) configuration is suggested. Nuclear Reactions:¹¹⁰Pd(α,2nγ),E _α =15–22.5 MeV; measuredE _γ ,E _γ , (E,E _γ ),E _γ (θ),γ-γ- coincidence;¹¹²Cd deduced levels,J; enriched target.     

Higher derivative modifications ofD=10 superspace Yang-Mills theories

We extend the superspace treatment of higher derivative supersymmetric Yang-Mills theories, emphasizing the role played by manifestD=10 Lorentz covariance and supersymmetry invariance. As an example, the superspace formulation of the effective action is considered for the massless fields in the open superstring, as well as in theSO(32) andE ₈×E₈ superstring theories. We show that there exists a unique modification of thef-tensor supercurrent which can provide the embedding of theO(α'³) string corrections in the slope parameter expansion for the Yang-Mills sector inD=10 superspace. The new correction term is relevant for the understanding of nonperturbative effects.     

Spectrum generating algebra and no-ghost theorem for fermionic massive string

The covariant operator quantization of the ordinary free spinning BDH string modified by adding the supersymmetric Liouville sector is analysed in the even target space dimensions d = 2, 4, 6, 8. The spectrum generating algebra for this model is constructed and a general version of the no-ghost theorem is proven. The counterpart of the GSO projection leads to a family of tachyon-free unitary free string theories. One of these models is equivalent to the non-critical Ramond-Neveu-Schwarz spinning string truncated in the Neveu-Schwarz sector to the tachyon-free eigenspace of the fermion parity operator.