Title Electromagnetic instability in AdS / CFT

Vacuum instability, leading to pair creation or annihilation of charged particles, is one of the most interesting physical quantities in particle physics. Among various kinds of particle creation process, quark antiquark pair creation is particularly interesting. Quarks and gluons are described by quantum chromodynamics(QCD), which has a strong gauge coupling constant at low energy, popularly known as the asymptotic freedom. In QCD, perturbation is not a good approximation at low energy, thus it is essential to evaluate non-perturbative e↵ects. To calculate QCD vacuum decay rates, we need to calculate non-perturbative e↵ects about the QCD vacuum. In 1951, Schwinger obtained a creation rate of an electron positron pair by evaluating an imaginary part of an e↵ective Lagrangian of electromagnetism, after integrating out the electron positron fields. We expect that, in a similar manner, a creation rate of a quark antiquark pair is obtained by computing an imaginary part of an e↵ective Lagrangian of QCD coupled to external electromagnetism. The Lagrangian includes quark fields, gluon fields and the electromagnetic fields as the external fields. The obstacle for the calculation for the quark case is that the gauge coupling of QCD is so strong that we have to evaluate quark antiquark 1-loop Feynman diagrams at all orders in gluon interaction, so any diagramatic calculations do not help at low energy. For this problem, recently developed notion known as a gauge/gravity duality, or equivalently AdS/CFT correspondence, can be applied, since the duality indeed enables us to calculate a strong coupling limit of quantum field theories. In 1997, Maldacena conjectured that N = 4 supersymmetric Yang-Mills theory is equivalent to type IIB superstring theory on AdS5⇥S. In particular, the large Nc limit and the strong coupling limit of the N = 4 supersymmetric Yang-Mills theory is conjectured to be equivalent to classical type IIB supergravity on AdS5⇥S. The limits are a large Nc limit and a large ’t Hooft coupling limit, ⌘ gNc 1. Nonperturbative quantum quantities of the large Nc strongly coupled gauge theory are derived from the classical gravity. However, how to calculate the creation rate of the quark antiquark have not been established yet in the AdS/CFT. In this doctor thesis, we study the vacuum instability in large Nc strongly coupled gauge theories. Recently, research on the vacuum instability in strongly coupled gauge theories by the AdS/CFT have started. Semeno↵ and Zarembo derived the creation rate of the quark antiquark pair from a classical minimal surface of an open string world2 sheet with the AdS/CFT. With a di↵erent method, Hashimoto and Oka derived the creation rate of the quark antiquark pair from the imaginary part of a probe D-brane action in electric fields. In our paper [arXiv:1403.6336 [hep-th]], by using the AdS/CFT, we obtained the creation rate of the quark antiquark pair in electromagnetic fields in the N = 4 SU(Nc) supersymmetric Yang-Mills theory with N = 2 hypermulitiplets in the fundamental representation. By using the Hashimoto-Oka conjecture, we evaluated the imaginary part of the D7-brane DBI action in not only constant electric fields but also constant magnetic fields. We found that the creation rate of the massless quark antiquark diverges at zero temperature, while it becomes finite if we introduce a nonzero temperature. In the case of massive quarks, the creation rate of the quark antiquark in the N = 2 SQCD was found to coincide with the creation rate of the hypermultiplets in the N = 2 supersymmetric QED, in the massless limit. In our paper [arXiv:1412.4254 [hep-th]], we worked on the decay rate in the Sakai-Sugimoto model. We evaluated the imaginary part of the D8-brane DBI action in the constant electromagnetic fields. We obtained the creation rate of the massless quark antiquark is non-zero at zero temperature, and also found a critical electric field in the confining phase of the strongly coupled large Nc gauge theory. The imaginary part of the D8-brane DBI action increases according to the increase of a magnetic field parallel to an electric field. On the other hand, the imaginary part decreases when we increase the magnetic field perpendicular to an electric field. We found that a critical electric field exists to have an imaginary part for the DBI action, and its value is identical to a QCD string tension between the quark and antiquark. In our paper [arXiv:1504.07836 [hep-th]], we found that the energy distribution of the meson at highly excited modes is subject to a power law under a constant electric field or in a nonzero temperature. In general, any energy distribution is expected to obey a Maxwell-Boltzmann distribution. However, in our analysis using the AdS/CFT correspondence, at a critical electric field, we found that the energy distribution of the mesons at high excited modes is proportional to a power of the meson mass. The power is found to be equal to 4 in the case of the gravity dual of the D3-D5 brane system. In this doctor thesis, we explain the contents explained above, with reviews on related subjects.