Research On The Elliptic Genus Of E- And Heterotic Strings,and Research On Gauge/Gravity Duality And Holographic Quantum Chromodynamics

In the first part of this thesis,we start with the research field of topological strings theory.In order to obtain the 4-dimensional particle physics from the 10-dimensional superstring theory,we compact on the 6-dimensional Calabi-Yau manifold with vari-ous topological structures.Since the mirror symmetry was discovered,there has been a great progress on the research of topological strings.E-string is identified with M2 brane stretched between the M5 brane and the M9 plane.Heterotic string can be identified with M2 brane stretched between the two M9 planes.So Vafa and his collaborators applied the domain wall approach on the elliptic genus of 1/2 E-and heterotic strings by com-parison with data given by the refined topological string.Based on their work,we further investigate the 3 pairs case in chapter 3.Via the transformation on the base expansion,we solve the specific problem in those cases of greater than or equal to three pairs and present an explicit expression for the elliptic genus of 3 E-strings.Then,we use the M9-domain walls to compute the elliptic genus of three heterotic strings and compare to results obtained by orbifold computations for the first time.The agreement confirms that pairs of E-strings recombine to heterotic strings.The result of the research is also an inspiration for the work about the reformulation of the topological string partition function.In chapter 4,we give a brief conclusion of this part.In the second part of this thesis,we study the research field of Gauge/gravity duali-ty or holographic QCD.First,we give a brief review on the topics:basic conceptions on string theory,relativistic heavy ion collisions,quantum chromodynamics and the holo-graphic principle.Gauge/gravity duality relates the(d+1)-dimensional strongly coupled gauge theory to the(d+2)-dimensional weakly coupled classical gravity theory.There are many mechanisms proposed to be the possible causes of the nonperturbative phe-nomenon of QCD,and Witten-Sakai-Sugimoto model is one of them.We extend this model from D4 to D0-D4.This generalized model corresponds to a field theory with non-trivial vacuum because of the appearance of DO-branes.This theta-depended term influences hadrodynamics near the vacuum.For application,we have worked on several relevant projects on this topic with our D0-D4/D8 model.In chapter 6,the properties of baryons are investigated based on the instanton description in the D0-D4 background.This constraint for the number density of DO-branes is consistent to subsequent result.The differences between the mass spectra are also given in the allowed region.In chap-ter 7,the speed of sound and the sound wave attenuation in an extension of the Witten-Sakai-Sugimoto model are investigated by including smeared DO branes and making several approximations technically.Our result is qualitatively similar to the result vi-a the boundary derivative expansion formalism.In chapter 8,the Schwinger effect in strongly coupled gauge theory is investigated holographically.We figure out the elec-tromagnetic instability is suppressed for all possible configurations of the embedded D8/D8-branes at zero or finite temperature.In the last chapter,we give a summary and related outlook of this part.