In this paper, we study the properties of baryons by using a holographic dual of QCD on the basis of the D4/D8-brane configuration, where baryons are described by a soliton. We first determine the asymptotic behavior of the soliton solution, which allows us to evaluate well-defined currents associated with the U(N f ) L × U(N f ) R chiral symmetry. Using the currents, we compute the static quantities of baryons such as charge radii and magnetic moments, and perform a quantitative comparison with experiments. It is emphasized that not only the nucleon but also excited baryons, such as ∆, N(1440), N(1535), etc., can be analyzed systematically in this model. We also investigate the form factors and find that our form factors agree well with the results that have been well established empirically. Using the form factors, the effective baryon-baryon-meson cubic coupling constants among their infinite towers in the model can be determined. Some physical implications following from these results are discussed. * ) See Ref. 15) for an attempt to include the effect of the ρ meson in the Skyrmion based on the holographic QCD. * ) Our notation is mostly consistent with Ref. 16) except that we do not use the rescaled variables defined in (3.9) of Ref. 16). * ) Again, the same expressions (3 . 32) and (3 . 35) can be found in Ref. 19) but with a different current. Eq. (3 . 32) also agrees with ∆µ an in Ref. 17), if we use the classical value (2 . 15) for ρ 2 . * ) Since the leading contribution to the baryon mass m B is M 0 = 8π 2 κ, we consider m B to be of order λN c . However, we will not use the relation m B ≃ M 0 , since we know that the subleading contributions in m B are not small as discussed in Ref. 16).

The out-of-time-order correlator (OTOC) is considered as a measure of quantum chaos. We formulate how to calculate the OTOC for quantum mechanics with a general Hamiltonian. We demonstrate explicit calculations of OTOCs for a harmonic oscillator, a particle in a one-dimensional box, a circle billiard and stadium billiards. For the first two cases, OTOCs are periodic in time because of their commensurable energy spectra. For the circle and stadium billiards, they are not recursive but saturate to constant values which are linear in temperature. Although the stadium billiard is a typical example of the classical chaos, an expected exponential growth of the OTOC is not found. We also discuss the classical limit of the OTOC. Analysis of a time evolution of a wavepacket in a box shows that the OTOC can deviate from its classical value at a time much earlier than the Ehrenfest time, which could be the reason of the difficulty for the numerical analyses to exhibit the exponential growth.

We study the Page curve for asymptotically flat eternal Schwarzschild black holes in four and higher spacetime dimensions. Before the Page time, the entanglement entropy grows linearly in time. After the Page time, the entanglement entropy of a given region outside the black hole is largely modified by the emergence of an island, which extends to the outer vicinity of the event horizon. As a result, it remains a constant value which reproduces the Bekenstein-Hawking entropy, consistent with the finiteness of the von Neumann entropy for an eternal black hole.

We provide a simple low energy description of recombination of intersecting D-branes using super Yang-Mills theory. The recombination is realized by condensation of an off-diagonal tachyonic fluctuation localized at the intersecting point. The recombination process is equivalent to brane-antibrane annihilation, thus our result confirms Sen's conjecture on tachyon condensation, although we work in the super Yang-Mills theory whose energy scale is much lower than α ′ . We also discuss the decay width of non-parallelly separated D-branes.

We study the rolling tachyon condensate in the presence of a gauge field. The generic vacuum admits both a rolling tachyon,Ṫ , and a uniform electric field, E, which together affect the effective metric governing the fluctuations of open string modes. If one suppresses the gauge field altogether, the light-cone collapses completely. This is the Carrollian limit, with vanishing speed of light and no possible propagation of signals. In the presence of a gauge field, however, the lightcone is squeezed to the shape of a fan, allowing propagation of signals along the direction of ± E at speed | E| ≤ 1. This shows that there are perturbative degrees of freedom propagating along electric flux lines. Such causal behavior appears to be a very general feature of tachyon effective Lagrangian with runway potentials. We speculate on how this may be connected to appearance of fundamental strings. * G.W.Gibbons@damtp.cam.ac.uk † koji@hep1.c.u-tokyo.ac.jp ‡ piljin@kias.re.kr * Rolling tachyon coupled to gauge fields has been investigated also in Refs. [31,32]. † This metric g is what one usually calls "open string co-metric," for instance, in noncommutative setting. In the current context, withṪ nonzero, this metric is no longer "open string metric".