PHD, Kent State University, 2024, College of Arts and Sciences / Department of Physics

The thermodynamics of N = 4 supersymmetric Yang-Mills theory in four dimensions (SYM4,4) is of great interest since, at finite-temperature, the weak-coupling limit of this theory has many similarities with quantum chromodynamics (QCD). Unlike QCD, however, in SYM4,4 it is possible to make use of the AdS/CFT correspondence between gravity in anti-de Sitter space (AdS) and the large-Nc limit of conformal field theories (CFT) on the boundary of AdS to obtain results for SYM4,4 thermodynamics in the strong coupling limit. The mathematical structure of SYM4,4 is similar to that of QCD, the difference is mostly in the number of degrees of freedom and the representations of fields. There are four Majorana fermions and six scalars and all the fields are in the adjoint representation. In the last decade or so the thermodynamics of SYM4,4 in a strong-coupling regime received a great deal of attention due to AdS/CFT where in SYM4,4 is mapped to its gravity dual. In this limit, the thermodynamics has been computed to the order λ−3/2, where λ = Nc g2 is the ‘t Hooft coupling. In the opposite sector of weak coupling, prior to our work, the free energy density of SYM4,4 was known to the order λ3/2. In this regime, calculations are performed using perturbative field theory methods. This weak-coupling expansion of SYM4,4 like QCD can pushed until λ5/2, after which non-perturbative effects come into play. In this SYM4,4 free energy density expansion interesting observations are made by constructing a generalized Pade which interpolates between strong and weak coupling expansion. The weak coupling expansion converges towards this Pade for λ ≲ 1 and the strong coupling for λ ≳ 10. The makes the weak and strong coupling expansion and their convergence in the intermediate region of 1 ≲ λ ≲ 10 of a great deal of interest. On the weak-coupling side the free energy density calculations in SYM4,4, like in QCD, are done and improved upon using various perturbative field t (open full item for complete abstract)

Committee: Michael Strickland Dr. (Advisor); Zhangbu Xu Dr. (Committee Member); Artem Zvavitch Dr. (Committee Member); Edgar Koojiman Dr. (Committee Member); Khandker Quader Dr. (Committee Member) Subjects: Nuclear Physics; Particle Physics; Physics

PhD, University of Cincinnati, 2009, Arts and Sciences : Physics

The purpose of this study is to examine the adiabatic dynamics of heavy mesons consisting of one light quark and one heavy quark at non-zero temperature by using a conjectured equivalence between a string theory in an anti-de Sitter gravitational background with a black hole and a Yang-Mills theory at non-zero temperature. We do this by analyzing the string configurations equivalent to the mesons. We show that for certain mesons, there is a critical velocity where an adiabatically forced meson will become “dressed,” i.e., it will cease to gain momentum by increasing its speed and will instead increase its mass and slow down. The string associated with such a dressed meson assumes “drooped” configuration in which the string hangs down towards the black hole. Then at a subsequent lower velocity, the frequency of the first excited mode of the drooping string vanishes and the string becomes unstable. We present evidence that, at this instability, the two quarks of the meson dissociate and start to feel a drag force from the color degrees of freedom in the Yang-Mills thermal bath. We also discover new heavy-light stationary string configurations as well as new “glueball” string solutions.

Committee: Philip Argyres PhD (Committee Chair); Kay Kinoshita PhD (Committee Member); Frank Pinski PhD (Committee Member); L.C.R. Wijewardhana PhD (Committee Member) Subjects: Particle Physics; Physics

Doctor of Philosophy, The Ohio State University, 2010, Physics

The bound state of D1-branes and D5-branes in IIB string theory is an exceptionally fertile system for the study of black holes. The D1D5 system has two, dual descriptions: a gravitational and a conformal field theory (CFT) description. Here, we focus on using the two-dimensional CFT to understand black hole physics. After reviewing the D1D5 system, we first show how to perturbatively relax the decoupling limit to calculate the emission out of the AdS/CFT into the asymptotic flat space. We take the effect of the neck into account and fix the coupling between the CFT and the asymptotic flat space. This calculation is distinguished from other AdS-CFT calculations which only work in the strict decoupling limit and use the gravitational description to learn about strongly coupled field theory. We apply the formalism to particular smooth, horizonless three-charge nonextremal geometries. In the fuzzball proposal, these geometries are interpreted as black hole microstates, but they suffer from a classical instability. At first, the instability seems problematic in the fuzzball proposal; however, it was argued that if one used the D1D5 CFT then the instability could be interpreted as precisely the Hawking radiation process for the particular microstates. That the instability is classical, and not quantum mechanical results from a large Bose enhancement. In this document, we perform calculations that confirm this interpretation and demonstrate the above emission formalism. All of the calculations discussed thus far, and most of the calculations in the literature on the D1D5 CFT, are at the "orbifold point" in moduli space. This point is far from the black hole physics of interest, but some calculations agree anyway. To understand black holes better it seems likely that moving off of the orbifold point will become necessary. We present several calculations demonstrating the effect of a single application of the marginal deformation operator that moves the D1D5 CFT off its orb (open full item for complete abstract)

Committee: Samir Mathur (Advisor); Richard Kass (Committee Member); Yuri Kovchegov (Committee Member); Stuart Raby (Committee Member) Subjects: Physics

Doctor of Philosophy, The Ohio State University, 2010, Physics

Currently there exists no known way to construct the Stress-Energy tensor (Tμν) of the medium produced in heavy ion collisions at strong coupling from purely theoretical grounds. In this work, some steps are taken in that direction. In particular, the evolution of Tμν at strong coupling and at high energies is being studied for early proper times (τ). This is achieved in the context of the AdS/CFT duality by constructing the evolution of the dual geometry in an AdS5 background. We consider high energy collisions of two shock waves in AdS5 as a model of ultra-relativistic nucleus-nucleus collisions in the boundary theory. We first calculate the graviton field produced in the collisions in the LO, NLO and NNLO approximations, corresponding to two, three and four-graviton exchanges with the shock waves. We use this model to study Tμν and in particular the energy density of the strongly-coupled matter created immediately after the collision because as we argue, the expansion of the energy density (ε) in the powers of proper time τ squared corresponds on the gravity side to a perturbative expansion of the metric in graviton exchanges. We point out that shock waves corresponding to physical energy-momentum tensors of the nuclei is likely to completely stop after the collision; on the field theory side, this corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. This motivates a more detailed investigation. For this reason we consider the asymmetric limit where the energy density in one shock wave is much higher than in the other one. In the boundary theory this setup corresponds to proton-nucleus collisions. Employing the eikonal approximation we find the exact high energy analytic solution for the metric in AdS5 for the asymmetric collision of two delta-function shock waves. The solution resums all-order graviton exchanges with the nucleus-shock wave and a single-graviton exchange with the proton-shock wave. (open full item for complete abstract)

Committee: Yuri Kovchegov (Advisor); Richard Furnstahl (Committee Member); Eric Braaten (Committee Member); Michael Lisa (Committee Member); Wang DeLiang (Other) Subjects: Physics