The baryon spectrum in the Sakai-Sugimoto model in the D4 background with smeared D0 charges is studied. We follow the instanton description of baryons by Hata et al.[Prog. Theor. Phys. 117, 1157]. The background corresponds to an excited state with nonzero glue condensate $\langle {\rm tr} (F_{\mu\nu}\tilde F^{\mu\nu})\rangle$ which is proportional to the D0 charge density. The baryon size shrinks when we turn on small D0 charge density. But for larger D0 charge density where massive modes in the gauge theory may also take effect, the size of baryons will grow. The difference between baryon masses will become smaller when D0 charge density increases. There may also be indications that the baryon will become unstable and cannot exist for sufficiently large D0 density.Comment: 15 pages, 3 figure

We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential µ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.

A precise formula for the elliptic genus of three E-strings is presented. The related refined free energy coincides with the result calculated from topological string on local half K3 Calabi-Yau threefold up to genus twelve. The elliptic genus of three heterotic strings computed from M9 domain walls matches with the result from orbifold formula to high orders. This confirms the n = 3 case of the recent conjecture that n pairs of E-strings can recombine into n heterotic strings.

As an extension to our previous work, we study the transport properties of the Witten-Sakai-Sugimoto model in the black D4-brane background with smeared D0-branes (D0-D4/D8 system). Because of the presence of the D0-branes, in the bubble configuration this model is holographically dual to 4d QCD or Yang-Mills theory with a Chern-Simons term. And the number density of the D0-branes corresponds to the coupling constant (θ angle) of the Chern-Simons term in the dual field theory. In this paper, we accordingly focus on small number density of the D0-branes to study the sound mode in the black D0-D4 brane system since the coupling of the Chern-Simons term should be quite weak in QCD. Then we derive its 5d effective theory and analytically compute the speed of sound and the sound wave attenuation in the approach of Gauge/Gravity duality. Our result shows the speed of sound and the sound wave attenuation is modified by the presence of the D0-branes. Thus they depend on the θ angle or chiral potential in this holographic description.

Using the Witten-Sakai-Sugimoto model in the D0-D4 background, we holographically compute the vacuum decay rate of the Schwinger effect in this model. Our calculation contains the influence of the D0-brane density which could be identified as the θ angle or chiral potential in QCD. Under the strong electromagnetic fields, the instability appears due to the creation of quark-antiquark pairs and the associated decay rate can be obtained by evaluating the imaginary part of the effective Euler-Heisenberg action which is identified as the action of the probe brane with a constant electromagnetic field. In the bubble D0-D4 configuration, we find the decay rate decreases when the θ angle increases since the vacuum becomes heavier in the present of the glue condensate in this system. And the decay rate matches to the result in the black D0-D4 configuration at zero temperature limit according to our calculations. In this sense, the Hawking-Page transition of this model could be consistently interpreted as the confined/deconfined phase transition. Additionally there is another instability from the D0brane itself in this system and we suggest that this instability reflects to the vacuum decay triggered by the θ angle as it is known in the θ-dependent QCD. * whcai@shu.edu.cn †