From Gauge/Gravity Duality Towards Quantum Chromodynamics And Nuclear Physics

We apply the holographic method to study properties of nuclear matter and force. The main holographic tool we have used is the famous top-down model-the Witten-Sakai-Sugimoto model.In the introduction part, we start with basics of string theory, QCD, large N field theory, holography and relativistic heavy ion collisions, and nuclear physics. The conformal field the-ory (N=4super Yang-Mills theory) and Anti-de Sitter Spacetime are also introduced. Then we give a brief review on the main topics of the thesis:the holography, gauge/gravity duali-ty and AdS/CFT correspondence. Finally we review the Witten-Sakai-Sugimoto model, a the top-down holographic model.In the first part of the thesis work, we study the thermodynamics of the Witten-Sakai-Sugimoto model in the black brane background with various configurations of D8 and anti D8-branes(D8). By holography, different configurations of D8 and anti D8-branes can be in-terpreted as different phases of dense QCD at finite temperature. We consider the two possible configurations for D8/D8-branes, which are connected and parallel, corresponding to the chiral-ly broken and symmetric phase, respectively. Furthermore, in the configuration of the connected D8/D8-branes, we introduce the wrapped D4-branes, i.e. the baryon vertex, which corresponds to the dense QCD at finite temperature with broken chiral symmetry. Since the baryon vertex can be treated as instantons in the worldvolume theory of D8/D8-branes in the Witten-Sakai-Sugimoto model, we use two different instanton configurations to describe baryons, the Belavin-Polyakov-Schwarz-Tyupkin (BPST) instanton solution from SU(2) pure Yang-Mills theory and homogeneous instanton. Our numerical calculations of the BPST instanton gas show a quali-tatively same phase diagram as the NJL model for dense QCD at finite temperature. However the baryon onset is second order, which is still unrealistic since the baryon onset is first order in real-world nuclear matter. On the other hand, a realistic phase diagram can not be reproduced if we use the homogeneous instanton configuration, however the baryon onset is first order. If the coupling constant is allowed to run in our system with asymptotic freedom as QCD, it is possible that we can give a realistic phase structure.In the second part, we propose a mechanism for holographic baryon transition or decay by introducing a time-dependent gravitational perturbation to the bubble D4-brane background in the Witten-Sakai-Sugimoto model. We suggest this mechanism to describe the interaction between glueball and baryon. We employ the relation between D=11M-theory and D=10 type IIA string theory, since the calculation in D=11 supergravity is simpler than in Witten-Sakai-Sugimoto model. The bubble D4 solution in Witten-Sakai-Sugimoto model could be obtained by dimensional reduction from M5-brane solution by taking large N and near horizon limit, so we solve the gravitational perturbations in the M5-brane solution first and then reduce it to D=10 Witten-Sakai-Sugimoto model. Since baryons in this model are equivalent to instanton config-urations, we also use the BPST instanton solution for baryons. By using the soliton picture, we obtain the Hamiltonian for this baryonic quantum mechanical system in moduli space and the baryon mass spectra. It also gives a time-dependent perturbation part of the Hamiltonian since a time-dependent gravitational perturbation has already been introduced in the beginning. The transition probability and the selection rule are calculated by using the standard method to deal with time-dependent perturbation in quantum mechanics. In some previous works, the D=11 gravitational perturbation gives the mass spectra of glueballs, however in string theory, grav-itational perturbation comes from close string and baryons are D-branes, thus the interaction between glueballs and baryons can be interpreted as the interaction between close strings and D-branes. To our knowledge, this is the first time we combine these two different viewpoints by holography.In the third part, we study the Witten-Sakai-Sugimoto model in the D0-D4 background and the D0-D4 system corresponds to theta-depended QCD. We propose a matrix model to describe multi-baryon system by using the standard technique in string theory. The original matrix model is an effective theory of DO-brane obtained from super-Yang-Mills theory by T-duality. It may also be an effective theory of D=11 M-theory. We study the T-duality and its application in the Witten-Sakai-Sugimoto model. We obtain a matrix model which can be treated as a 0+1 quantum mechanical system. We use this matrix model to calculate the baryon spectrum in the two-flavor case and the result agrees with experimental data by adjusting parameters. We calculate the two-body force for baryons at short-distance, which exhibits a repulsive core and a tensor force. This system corresponds to a field theory with non-trivial vacuum because of the appearance of DO-branes. So our matrix model is also an effective theory for baryons with the effect from the non-trivial vacuum. In our calculation we find a constraint for the number density of DO-branes:the baryons in the system are unstable if the number density of the DO-branes breaks the constraint. This observation is consistent to previous results in the literature.As a summary, this thesis reviews the background knowledge of string theory, QCD and relativistic heavy ion collisions, gauge/gravity duality and the famous top-down holographic model-the Witten-Sakai-Sugimoto model. And it also includes three parts of our main works. They are the phase structure of QCD, a mechanism for holographic baryon transition and the matrix model for theta-depended QCD. We will have more various works in these topics.