Abstract In 1980, detecting the evidence of the so-called Grand Unified Theory (GUT) became a major challenge for experimentalists. The GUT predicted that protons would decay, and M. Koshiba proposed the Kamioka Nucleon Decay Experiment (Kamiokande), which was originally conceived and designed for the detection of proton decay signals. Kamiokande was a 3000-t water Cherenkov detector located 1000 m underground in the Kamioka mine. The unique feature of this experiment was the use of 1000 photomultiplier tubes with the world's largest diameter of 20 in (∼51 cm). This article describes the story of the Kamiokande experiment from the preparation stage to the observation of the first candidate events for proton decays.

Japan

Atsuto Suzuki

The start of things for Kamiokande: The Kamioka Nucleon Decay Experiment

Through data analysis, we present new sets of nonperturbative fragmentation functions (FFs) for <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> baryon both at leading and next-to-leading order and, for the first time, at next-to-next-to-leading order in the minimal subtraction factorization scheme with five massless quarks. The FFs are determined by fitting all available data of inclusive single <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> baryon production in <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation taken by the OPAL Collaboration at CERN LEP1 and Belle Collaboration at KEKB. We also estimate the uncertainties in the <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> FFs as well as in the corresponding observables. In a completely different approach based on the Suzuki model, we will theoretically calculate the <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> FF from charm quark and present our results at leading order perturbative QCD framework. A comparison confirms a good consistency between both approaches. We will also apply the <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> FFs to make theoretical predictions for the energy distribution of <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> produced through the top quark decay, to be measured at the CERN LHC.

Iran

Mahdi Delpasand

S. Mohammad Moosavi Nejad

Maryam Soleymaninia

<math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> fragmentation functions from pQCD approach and the Suzuki model

It is shown that Kazama-Suzuki conditions for the denominator subgroup of <math><mi>N</mi><mo>=</mo><mn>2</mn></math> superconformal <math><mi>G</mi><mo>/</mo><mi>H</mi></math> coset model determine Generalized Kähler geometry on the target space of the corresponding <math><mi>N</mi><mo>=</mo><mn>2</mn></math> supersymmetric σ-model.

Russia

S.E. Parkhomenko

Generalized Kähler geometry in Kazama-Suzuki coset models

Using equations proposed by J. Suzuki we compute numerically the first three integrals of motion for N=1 supersymmetric CFT. Our computation agrees with the results of ODE-CFT correspondence which was explained in a more general context by S. Lukyanov.

France

C. Babenko

F. Smirnov

Suzuki equations and integrals of motion for supersymmetric CFT

The N = 3 $$ \mathcal{N}=3 $$ Kazama-Suzuki model at the ‘critical’ level has been found by Creutzig, Hikida and Ronne. We construct the lowest higher spin currents of spins 3 2 2 2 2 5 2 5 2 5 2 3 $$ \left(\frac{3}{2},2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3\right) $$ in terms of various fermions. In order to obtain the operator product expansions (OPEs) between these higher spin currents, we describe three N = 2 $$ \mathcal{N}=2 $$ OPEs between the two N = 2 $$ \mathcal{N}=2 $$ higher spin currents denoted by 3 2 2 2 5 2 $$ \left(\frac{3}{2},2,2,\frac{5}{2}\right) $$ and 2 5 2 5 2 3 $$ \left(2,\frac{5}{2},\frac{5}{2},3\right) $$ (corresponding 36 OPEs in the component approach). Using the various Jacobi identities, the coefficient functions appearing on the right hand side of these N = 2 $$ \mathcal{N}=2 $$ OPEs are deter-mined in terms of central charge completely. Then we describe them as one single N = 3 $$ \mathcal{N}=3 $$ OPE in the N = 3 $$ \mathcal{N}=3 $$ superspace. The right hand side of this N = 3 $$ \mathcal{N}=3 $$ OPE contains the SO(3)-singlet N = 3 $$ \mathcal{N}=3 $$ higher spin multiplet of spins 2 5 2 5 2 5 2 3 3 3 7 2 $$ \left(2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3,3,3,\frac{7}{2}\right) $$ , the SO(3)-singlet N = 3 $$ \mathcal{N}=3 $$ higher spin multiplet of spins 5 2 3 3 3 7 2 7 2 7 2 4 $$ \left(\frac{5}{2},3,3,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},4\right) $$ , and the SO(3)-triplet N = 3 $$ \mathcal{N}=3 $$ higher spin multiplets where each multiplet has the spins 3 7 2 7 2 7 2 4 4 4 9 2 $$ \left(3,\frac{7}{2},\frac{7}{2},\frac{7}{2},4,4,4,\frac{9}{2}\right) $$ , in addition to N = 3 $$ \mathcal{N}=3 $$ superconformal family of the identity operator. Finally, by factoring out the spin − 1 2 $$ \mathrm{spin}-\frac{1}{2} $$ current of N = 3 $$ \mathcal{N}=3 $$ linear superconformal algebra generated by eight currents of spins 1 2 1 1 1 3 2 3 2 3 2 2 $$ \left(\frac{1}{2},1,1,1,\frac{3}{2},\frac{3}{2},\frac{3}{2},2\right) $$ , we obtain the extension of so-called SO (3) nonlinear Knizhnik Bershadsky algebra.

South Korea

Changhyun Ahn

Hyunsu Kim

Higher spin currents in the enhanced N = 3 $$ \mathcal{N}=3 $$ Kazama-Suzuki model

The large level limit of the N $$ \mathcal{N} $$ = 2 SO(2 N ) Kazama-Suzuki coset models is argued to be equivalent to the orbifold of 4 N free fermions and bosons by the Lie group SO(2 N ) × SO(2). In particular, it is shown that the untwisted sector of the continuous orbifold accounts for a certain closed subsector of the coset theory. Furthermore, the ground states of the twisted sectors are identified with specific coset representations, and this identification is checked by various independent arguments.

Switzerland

Kevin Ferreira

Matthias Gaberdiel

The so-Kazama-Suzuki models at large level

Limits of families of conformal field theories are of interest in the context of AdS/CFT dualities. We explore here the large level limit of the two-dimensional N = 2 , 2 $$ \mathcal{N}=\left(2,\ 2\right) $$ superconformal W n + 1 $$ {\mathcal{W}}_{n+1} $$ minimal models that appear in the context of the supersymmetric higher-spin AdS 3 /CFT 2 duality. These models are constructed as Kazama-Suzuki coset models of the form SU( n + 1) / U( n ). We determine a family of boundary conditions in the limit theories, and use the modular bootstrap to obtain the full bulk spectrum of N = 2 $$ \mathcal{N}=2 $$ super- W n + 1 $$ {\mathcal{W}}_{n+1} $$ primaries in the theory. We also confirm the identification of this limit theory as the continuous orbifold ℂ n / U n $$ {\mathbb{C}}^n/\mathrm{U}(n) $$ that was discussed recently.

Germany

Stefan Fredenhagen

Cosimo Restuccia

The large level limit of Kazama-Suzuki models

The primary goal of KamLAND is a search for the oscillation of Î½Â¯e âs emitted from distant power reactors. The long baseline, typically 180 km, enables KamLAND to address the oscillation solution of the âsolar neutrino problemâ with Î½Â¯e âs under laboratory conditions. KamLAND found fewer reactor Î½Â¯e events than expected from standard assumptions about Î½Â¯e propagation at more than 9 Ï confidence level (C.L.). The observed energy spectrum disagrees with the expected spectral shape at more than 5 Ï C.L., and prefers the distortion from neutrino oscillation effects. A three-flavor oscillation analysis of the data from KamLAND and KamLAND + solar neutrino experiments with CPT invariance, yields Îm212 = [ 7.54-0.18+0.19Ã 10 -5 eV 2 , 7.53-0.18+0.19Ã 10 -5 eV 2 ], tan 2Î¸12 = [ 0.481-0.080+0.092 , 0.437-0.026+0.029 ], and sin 2Î¸13 = [ 0.010-0.034+0.033 , 0.023-0.015+0.015 ]. All solutions to the solar neutrino problem except for the large mixing angle region are excluded. KamLAND also demonstrated almost two cycles of the periodic feature expected from neutrino oscillation effects. KamLAND performed the first experimental study of antineutrinos from the Earthâs interior so-called geoneutrinos (geo Î½Â¯e âs), and succeeded in detecting geo Î½Â¯e âs produced by the decays of 238 U and 232 Th within the Earth. Assuming a chondritic Th/U mass ratio, we obtain 116-27+28Î½Â¯e events from 238 U and 232 Th, corresponding a geo Î½Â¯e flux of 3.4-0.8+0.8Ã 10 6 cm -2 Â s -1 at the KamLAND location. We evaluate various bulk silicate Earth composition models using the observed geo Î½Â¯e rate.