We present for the first time a Friedmann-like construction in the framework of an osculating Finsler–Randers–Sasaki (F–R–S) geometry. In particular, we consider a vector field in the metric on a Lorentz tangent bundle, and thus the curvatures of horizontal and vertical spaces, as well as the extra contributions of torsion and non-linear connection, provide an intrinsic richer geometrical structure, with additional degrees of freedom, that lead to extra terms in the field equations. Applying these modified field equations at a cosmological setup we extract the generalized Friedmann equations for the horizontal and vertical space, showing that we obtain an effective dark energy sector arising from the richer underlying structure of the tangent bundle. Additionally, as it is common in Finsler-like constructions, we obtain an effective interaction between matter and geometry. Finally, we consider a specific model and we show that it can describe the sequence of matter and dark-energy epochs, and that the dark-energy equation of state can lie in the quintessence or phantom regimes, or cross the phantom divide.

Greece

E. Kapsabelis

Chile

China

Emmanuel Saridakis

P. Stavrinos

Finsler–Randers–Sasaki gravity and cosmology

We study <math><mi>S</mi></math>-wave interactions in the <math><mrow><mi>I</mi><mrow><mo>(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>)</mo></mrow><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn><mrow><mo>(</mo><mn>1</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></mrow><mtext> </mtext><mtext> </mtext><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>−</mo><mi>p</mi><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> system on the basis of the coupled-channel Hadrons to Atomic nuclei from Lattice Quantum ChromoDynamics method. The potentials which are faithful to QCD S-matrix below the <math><mi>p</mi><msup><mi>D</mi><mo>*</mo></msup></math> threshold are extracted from Nambu-Bethe-Salpeter wave functions on the lattice in flavor SU(3) limit. For the simulation, we employ 3-flavor full QCD gauge configurations on a <math><mrow><msup><mrow><mo>(</mo><mn>1.93</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow></math> volume at <math><msub><mi>m</mi><mi>π</mi></msub><mo>≃</mo><mn>872</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. We present our results of the S-wave coupled-channel potentials for the <math><msub><mi>Λ</mi><mi>c</mi></msub><msup><mi>K</mi><mo>+</mo></msup><mo>−</mo><mi>p</mi><msub><mi>D</mi><mi>s</mi></msub></math> system in the <math><mn>1</mn><mo>/</mo><mn>2</mn><mrow><mo>(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></mrow></math> state as well as scattering observables obtained from the extracted potential matrix. We observe that the coupling between <math><msub><mi>Λ</mi><mi>c</mi></msub><msup><mi>K</mi><mo>+</mo></msup></math> and <math><mi>p</mi><msub><mi>D</mi><mi>s</mi></msub></math> channels is weak. The phase shifts and scattering length obtained from the extracted potential matrix show that the <math><msub><mi>Λ</mi><mi>c</mi></msub><msup><mi>K</mi><mo>+</mo></msup></math> interaction is attractive at low energy and stronger than the <math><mi>p</mi><msub><mi>D</mi><mi>s</mi></msub></math> interaction though no bound state at <math><msub><mi>m</mi><mi>π</mi></msub><mo>≥</mo><mn>872</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>.

Iran

Faisal Etminan

Japan

Kenji Sasaki

Takashi Inoue

Coupled-channel <math><mrow><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>−</mo><mi>p</mi><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> interaction in the flavor SU(3) limit of lattice QCD

We show that there are certain perturbatively stable non-supersymmetric AdS vacua which are also brane-jet stable. Also we extend the analysis of brane-jets to the AdS vacua from curved domain walls like Janus solutions. First, we apply the brane-jet analysis to the non-supersymmetric Janus solutions of type IIB supergravity found by Bak, Gutperle and Hirano. Second, we study the brane-jet of AdS 4 vacua from eleven-dimensional supergravity on Sasaki-Einstein manifolds: the supersymmetric and the skew-whiffed Freund-Rubin, the Pope-Warner, and the Englert solutions. Third, we examine the non-supersymmetric AdS 4 vacua from Q 1,1,1 and M 1,1,1 manifolds discovered by Cassani, Koerber and Varela. It turns out that all the AdS vacua we consider in this work are brane-jet stable. Especially, the Janus, the skew-whipped Freund-Rubin, and the AdS 4 vacua from Q 1,1,1 and M 1,1,1 are perturbatively stable within known subsectors of truncations and also brane-jet stable.

South Korea

Minwoo Suh

Brane-jet stabilities from Janus and Sasaki-Einstein

The 2d (0, 2) supersymmetric gauge theories corresponding to the classes of Y  p,k (ℂℙ1 × ℂℙ1) and Y  p,k (ℂℙ2) manifolds are identified. The complex cones over these Sasaki-Einstein 7-manifolds are non-compact toric Calabi-Yau 4-folds. These infinite families of geometries are the largest ones for Sasaki-Einstein 7-manifolds whose metrics, toric diagrams, and volume functions are known explicitly. This work therefore presents the largest list of 2d (0, 2) supersymmetric gauge theories corresponding to Calabi-Yau 4-folds with known metrics.

United States

Sebastián Franco

Dongwook Ghim

Rak-Kyeong Seong

Brane brick models for the Sasaki-Einstein 7-manifolds Y  p,k (ℂℙ1 × ℂℙ1) and Y  p,k (ℂℙ2)

First results on the interaction between the <math><mi>ϕ</mi></math>-meson and the nucleon (<math><mi>N</mi></math>) are presented based on the (<math><mn>2</mn><mo>+</mo><mn>1</mn></math>)-flavor lattice QCD simulations with nearly physical quark masses. Using the HAL QCD method, the spacetime correlation of the <math><mrow><mi>N</mi><mtext>−</mtext><mi>ϕ</mi></mrow></math> system in the spin <math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> channel is converted into the <math><mrow><mi>N</mi><mtext>−</mtext><mi>ϕ</mi></mrow></math> scattering phase shift through the interaction potential. The <math><mrow><mi>N</mi><mtext>−</mtext><mi>ϕ</mi></mrow></math> potential appears to be a combination of a short-range attractive core and a long-range attractive tail. The latter is found to be consistent with the two-pion exchange (TPE) obtained from the interaction between a color-dipole and the nucleon. The resultant scattering length and effective range for <math><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>146.4</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> are <math><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>(</mo><mn>3</mn><mo>/</mo><mn>2</mn><mo>)</mo></mrow></msubsup><mo>=</mo><mo>−</mo><mn>1.43</mn><mo>(</mo><mn>23</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><msub><mrow><msubsup><mrow><mtext> </mtext></mrow><mrow><mo>−</mo><mn>06</mn></mrow><mrow><mo>+</mo><mn>36</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mi>syst</mi></mrow></msub><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math> and <math><mrow><msubsup><mrow><mi>r</mi></mrow><mrow><mi>eff</mi></mrow><mrow><mo>(</mo><mn>3</mn><mo>/</mo><mn>2</mn><mo>)</mo></mrow></msubsup><mo>=</mo><mn>2.36</mn><mo>(</mo><mn>10</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><msub><mrow><mo>(</mo><msubsup><mrow><mtext> </mtext></mrow><mrow><mo>−</mo><mn>48</mn></mrow><mrow><mo>+</mo><mn>02</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mi>syst</mi></mrow></msub><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math>, respectively. The magnitude of the scattering length is shown to have nontrivial dependence of <math><msub><mi>m</mi><mi>π</mi></msub></math> and is sensitive to the existence of the long-range tail from TPE.

Yan Lyu

Takumi Doi

Tetsuo Hatsuda

Yoichi Ikeda

Jie Meng

Takuya Sugiura

Attractive <math><mrow><mi>N</mi><mtext>−</mtext><mi>ϕ</mi></mrow></math> interaction and two-pion tail from lattice QCD near physical point

We discuss in detail the different analogues of Dolbeault cohomology groups on Sasaki-Einstein manifolds and prove a new vanishing result for the transverse Dolbeault cohomology groups   <math> <msubsup> <mi>H</mi> <mover> <mi>∂</mi> <mo>¯</mo> </mover> <mfenced> <mi>p</mi> <mn>0</mn> </mfenced> </msubsup> <mfenced> <mi>k</mi> </mfenced> </math>  $$ {H}_{\overline{\partial}}^{\left(p,0\right)}(k) $$  graded by their charge under the Reeb vector. We then introduce a new cohomology, η-cohomology, which is defined by a CR structure and a holomorphic function f with non-vanishing η ≡ df. It is the natural cohomology associated to a class of supersymmetric type IIB flux backgrounds that generalise the notion of a Sasaki-Einstein manifold. These geometries are dual to finite deformations of the 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 SCFTs described by conventional Sasaki-Einstein manifolds. As such, they are associated to Calabi-Yau algebras with a deformed superpotential. We show how to compute the η-cohomology in terms of the transverse Dolbeault cohomology of the undeformed Sasaki-Einstein space. The gauge-gravity correspondence implies a direct relation between the cyclic homologies of the Calabi-Yau algebra, or equivalently the counting of short multiplets in the deformed SCFT, and the η-cohomology groups. We verify that this relation is satisfied in the case of S5, and use it to predict the reduced cyclic homology groups in the case of deformations of regular Sasaki-Einstein spaces. The corresponding Calabi-Yau algebras describe non-commutative deformations of ℙ2, ℙ1 × ℙ1 and the del Pezzo surfaces.

United Kingdom

Edward Tasker

From β to η: a new cohomology for deformed Sasaki-Einstein manifolds

We revisit non-rotating, dyonically charged, and supersymmetric AdS4 black holes, which are solutions of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 gauged supergravity with vector- and hyper-multiplets. Uplifting the near horizon solutions to D = 11 supergravity on seven-dimensional Sasaki-Einstein manifolds, we show that dyonic AdS4 black holes correspond to AdS2 solutions with electric and magnetic baryonic fluxes in D = 11 supergravity. We identify the off-shell AdS4 black hole solutions with parameters of D = 11 AdS2 solutions without imposing the equations of motion. We calculate the entropy of dyonic black holes, carefully analyzing the Page charge quantization conditions.

Hyojoong Kim

Nakwoo Kim

Uplifting dyonic AdS4 black holes on seven-dimensional Sasaki-Einstein manifolds

The ΔΔ dibaryon resonance <math><msup><mrow><mi>d</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mn>2380</mn><mo>)</mo></math> with <math><mo>(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>,</mo><mi>I</mi><mo>)</mo><mo>=</mo><mo>(</mo><msup><mrow><mn>3</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><mn>0</mn><mo>)</mo></math> is studied theoretically on the basis of the 3-flavor lattice QCD simulation with heavy pion masses (<math><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>=</mo><mn>679</mn><mo>,</mo><mn>841</mn></math> and 1018 MeV). By using the HAL QCD method, the central Δ-Δ potential in the <math><mmultiscripts><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>7</mn></mrow></mmultiscripts></math> channel is obtained from the lattice data with the lattice spacing <math><mi>a</mi><mo>≃</mo><mn>0.121</mn></math> fm and the lattice size <math><mi>L</mi><mo>≃</mo><mn>3.87</mn></math> fm. The resultant potential shows a strong short-range attraction, so that a quasi-bound state corresponding to <math><msup><mrow><mi>d</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mn>2380</mn><mo>)</mo></math> is formed with the binding energy 25-40 MeV below the ΔΔ threshold for the heavy pion masses. The tensor part of the transition potential from ΔΔ to NN is also extracted to investigate the coupling strength between the S-wave ΔΔ system with <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mn>3</mn></mrow><mrow><mo>+</mo></mrow></msup></math> and the D-wave NN system. Although the transition potential is strong at short distances, the decay width of <math><msup><mrow><mi>d</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mn>2380</mn><mo>)</mo></math> to NN in the D-wave is kinematically suppressed, which justifies our single-channel analysis at the range of the pion mass explored in this study.

Shinya Gongyo

Takaya Miyamoto

Sinya Aoki

Noriyoshi Ishii

(2380) dibaryon from lattice QCD

Abstract We investigate the HAL QCD potential in   scattering using the hybrid method for all-to-all propagators, in which a propagator is approximated by low eigenmodes, and the remaining high-eigenmode part is stochastically estimated. To verify the applicability of the hybrid method to systems containing quark creationannihilation contributions such as the  meson, we calculate the   potential with the -flavor gauge configurations on a  lattice with lattice spacing  fm and  MeV, in which the  meson appears as a deeply bound state. While we find that the naive stochastic evaluations for quark creationannihilation contributions lead to extremely large statistical fluctuations, additional noise reduction methods enable us to obtain a sufficiently precise potential, which shows a strong attractive force. We also confirm that the binding energy and  obtained from our potential are roughly consistent with an existing  meson bound state, within the large systematic error associated with our calculation, whose possible origin is also discussed.

Yutaro Akahoshi

Tatsumi Aoyama

The HAL QCD potential in the = 1 System With the Meson Bound State

The approximated partial-wave decomposition method for discrete data on a cubic lattice, developed by Misner, is applied to the calculation of <math><mi>S</mi></math>-wave hadron-hadron scatterings by the HAL QCD method in lattice QCD. We consider the Nambu-Bethe-Salpeter (NBS) wave function for the spin-singlet <math><msub><mi>Λ</mi><mi>c</mi></msub><mi>N</mi></math> system calculated in (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD on a <math><mrow><mo>(</mo><mn>32</mn><mi>a</mi><mtext> </mtext><mtext> </mtext><mi>fm</mi><msup><mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow></math> lattice with lattice spacing <math><mi>a</mi><mo>≃</mo><mn>0.0907</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and <math><msub><mi>m</mi><mi>π</mi></msub><mo>≃</mo><mn>700</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. We find that by Misner’s method the <math><mi>l</mi><mo>=</mo><mn>0</mn></math> component can be successfully extracted from the NBS wave function projected to the <math><msubsup><mi>A</mi><mn>1</mn><mo>+</mo></msubsup></math> representation of the cubic group, which contains small <math><mi>l</mi><mo>≥</mo><mn>4</mn></math> components. Furthermore, while the higher partial-wave components are enhanced so as to produce significant comb-like structures in the conventional HAL QCD potential if the Laplacian approximated by the usual second-order difference is applied to the NBS wave function, such structures are found to be absent in the potential extracted by Misner’s method, where the Laplacian can be evaluated analytically for each partial-wave component. Despite the difference in the potentials, the two methods give almost identical results on the central values and magnitude of statistical errors for the fits of the potentials, and consequently on the scattering phase shifts. This indicates not only that Misner’s method works well in lattice QCD with the HAL QCD method, but also that the contaminations from higher partial waves in the study of <math><mi>S</mi></math>-wave scatterings are well under control even in the conventional HAL QCD method. It will be of interest to study interactions in higher partial-wave channels in the HAL QCD method with Misner’s decomposition, where the utility of this new technique may become clearer.

Partial wave decomposition on the lattice and its applications to the HAL QCD method