On the standard model group in F-theory

We analyze the standard model gauge group SU(3)×SU(2)×U(1) constructed in F-theory. The non-Abelian part SU(3)×SU(2) is described by a surface singularity of Kodaira type. Blow-up analysis shows that the non-Abelian part is distinguished from the naïve product of SU(3) and SU(2) , but that it should be a rank three group along the chain of En groups, because it has non-generic gauge symmetry enhancement structure responsible for desirable matter curves. The Abelian part U(1) is constructed from a globally valid two-form with the desired gauge quantum numbers, using a similar method to the decomposition (factorization) method of the spectral cover. This technique makes use of an extra section in the elliptic fiber of the Calabi–Yau manifold, on which F-theory is compactified. Conventional gauge coupling unification of SU(5) is achieved, without requiring a threshold correction from the flux along the hypercharge direction

Twelve-dimensional effective action and T -duality

We propose a 12-dimensional supergravity action which describes low-energy dynamics of F -theory. Dimensional reduction leads the theory to become 11-dimensional, IIA, and IIB supergravities. Self-duality of the four-form field in IIB supergravity is understood. It is necessary to abandon 12-dimensional Poincaré symmetry by making one dimension compact, which is to be decompactified in some region of parameter space, such that the physical degrees of freedom are the same as those of 11-dimensional supergravity. This makes T -duality explicit as a relation between different compactification schemes

Supergravity in twelve dimension

We consider supergravity in twelve dimension, whose dimensional reduction yields eleven-dimensional, IIA, and IIB supergravities. This also provides the effective field theory of F-theory. We must take one direction as a compact circle, so that the Poincaré symmetry and the zero-mode field contents are identical to those of eleven-dimensional supergravity. We also have a tower of massive Kaluza-Klein states to be viewed as the wrapping modes of M2-branes. The twelfth dimension decompactifies only if other two directions are compactified on a torus, restoring different ten dimensional Poincaré symmetry of IIB supergravity, whose missing graviton is provided by components of the rank three tensor field. This condition prevents us from violating the condition on the maximal number of real supercharges, which should be thirty-two. The self-duality condition of the IIB four-form fields is understood from twelve-dimensional Hodge duality. In this framework T -duality is re-interpreted as taking different compactification routes

On the renormalization group flow in two dimensional superconformal models

We extend the results on the RG flow in the next to leading order to the case of the supersymmetric minimal models <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi mathvariant="italic">SM</mi></mrow><mrow><mi>p</mi></mrow></msub></math> for <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>≫</mo><mn>1</mn></math> . We explain how to compute the NS and Ramond fields conformal blocks in the leading order in <math altimg="si3.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo stretchy="false">/</mo><mi>p</mi></math> and follow the renormalization scheme proposed in [1] . As a result we obtained the anomalous dimensions of certain NS and Ramond fields. It turns out that the linear combination expressing the infrared limit of these fields in term of the IR theory <math altimg="si4.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi mathvariant="italic">SM</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msub></math> is exactly the same as those of the nonsupersymmetric minimal theory

Finite-size giant magnons on η -deformed AdS5×S5

We consider strings moving in the Rt×Sη3 subspace of the η -deformed AdS5×S5 and obtain a class of solutions depending on several parameters. They are characterized by the string energy and two angular momenta. Finite-size dyonic giant magnon belongs to this class of solutions. Further on, we restrict ourselves to the case of giant magnon with one nonzero angular momentum, and obtain the leading finite-size correction to the dispersion relation

Holographic Renormalization in Dense Medium

The holographic renormalization of a charged black brane with or without a dilaton field, whose dual field theory describes a dense medium at finite temperature, is investigated in this paper. In a dense medium, two different thermodynamic descriptions are possible due to an additional conserved charge. These two different thermodynamic ensembles are classified by the asymptotic boundary condition of the bulk gauge field. It is also shown that in the holographic renormalization regularity of all bulk fields can reproduce consistent thermodynamic quantities and that the Bekenstein-Hawking entropy is nothing but the renormalized thermal entropy of the dual field theory. Furthermore, we find that the Reissner-Nordström AdS black brane is dual to a theory with conformal matter as expected, whereas a charged black brane with a nontrivial dilaton profile is mapped to a theory with nonconformal matter although its leading asymptotic geometry still remains as AdS space

Some exact solutions of the semilocal Popov equations

We study the semilocal version of Popov's vortex equations on <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math> . Though they are not integrable, we construct two families of exact solutions which are expressed in terms of rational functions on <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math> . One family is a trivial embedding of Liouville-type solutions of the Popov equations obtained by Manton, where the vortex number is an even integer. The other family of solutions is constructed through a field redefinition which relates the semilocal Popov equation to the original Popov equation but with the ratio of radii <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msqrt></math> , which is not integrable. These solutions have vortex number <math altimg="si3.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>3</mn><mi>n</mi><mo>−</mo><mn>2</mn></math> where n is a positive integer, and hence <math altimg="si4.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>1</mn></math> solutions belong to this family. In particular, we show that the <math altimg="si4.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>1</mn></math> solution with reflection symmetry is the well-known <math altimg="si5.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msup></math> lump configuration with unit size where the scalars lie on <math altimg="si6.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math> with radius <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msqrt></math> . It generates the uniform magnetic field of a Dirac monopole with unit magnetic charge on <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math>

Measurements of cosmic-ray secondary nuclei at high energies with the first flight of the CREAM balloon-borne experiment

We present new measurements of heavy cosmic-ray nuclei at high energies per- formed during the first flight of the balloon-borne cosmic-ray experiment CREAM (Cosmic-Ray Energetics And Mass). This instrument uses multiple charge detectors and a transition radiation detector to provide the first high accuracy measurements of the relative abundances of elements from boron to oxygen up to energies around 1 TeV/n. The data agree with previous measurements at lower energies and show a relatively steep decline (~E$^-0.6$ to E$^-0.5$) at high energies. They further show the source abundance of nitrogen relative to oxygen is ~10% in the TeV/n region

Bethe states for the two-site Bose–Hubbard model: A binomial approach

We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the gl(2) -invariant R -matrix for the two-site Bose–Hubbard model. Using a binomial expansion of the n -th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed

Pulse-shape discrimination between electron and nuclear recoils in a NaI(Tl) crystal

We report on the response of a high light-output NaI(Tl) crystal to nuclear recoils induced by neutrons from an Am-Be source and compare the results with the response to electron recoils produced by Compton-scattered 662 keV γ-rays from a 137 Cs source. The measured pulse-shape discrimination (PSD) power of the NaI(Tl) crystal is found to be significantly improved because of the high light output of the NaI(Tl) detector. We quantify the PSD power with a quality factor and estimate the sensitivity to the interaction rate for weakly interacting massive particles (WIMPs) with nucleons, and the result is compared with the annual modulation amplitude observed by the DAMA/LIBRA experiment. The sensitivity to spin-independent WIMP-nucleon interactions based on 100 kg·year of data from NaI detectors is estimated with simulated experiments, using the standard halo model