Aspects of Large N Gauge Theory Dynamics as Seen by String Theory

In this paper we explore some of the features of large N supersymmetric and nonsupersymmetric gauge theories using Maldacena's duality conjectures. We shall show that the resulting strong coupling behavior of the gauge theories is consistent with our qualitative expectations of these theories. Some of these consistency checks are highly nontrivial and give additional evidence for the validity of the proposed dualities.Comment: 31 pages, LaTeX, 11 eps figures, typos correcte

On absolute moments of characteristic polynomials of a certain class of complex random matrices

Integer moments of the spectral determinant $|\det(zI-W)|^2$ of complex random matrices $W$ are obtained in terms of the characteristic polynomial of the Hermitian matrix $WW^*$ for the class of matrices $W=AU$ where $A$ is a given matrix and $U$ is random unitary. This work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results in this context are discussed.Comment: 41 page, typos correcte

Classification of All 1/2 BPS Solutions of the Tiny Graviton Matrix Theory

The tiny graviton matrix theory [hep-th/0406214] is proposed to describe DLCQ of type IIB string theory on the maximally supersymmetric plane-wave or AdS_5xS^5 background. In this paper we provide further evidence in support of the tiny graviton conjecture by focusing on the zero energy, half BPS configurations of this matrix theory and classify all of them. These vacua are generically of the form of various three sphere giant gravitons. We clarify the connection between our solutions and the half BPS configuration in N=4 SYM theory and their gravity duals. Moreover, using our half BPS solutions, we show how the tiny graviton Matrix theory and the mass deformed D=3, N=8 superconformal field theories are related to each other.Comment: 40 pages, 12 figures, v

On the self-consistent spin-wave theory of layered Heisenberg magnets

The versions of the self-consistent spin-wave theories (SSWT) of two-dimensional (2D) Heisenberg ferro- and antiferromagnets with a weak interlayer coupling and/or magnetic anisotropy, that are based on the non-linear Dyson-Maleev, Schwinger, and combined boson-pseudofermion representations, are analyzed. Analytical results for the temperature dependences of (sublattice) magnetization and short-range order parameter, and the critical points are obtained. The influence of external magnetic field is considered. Fluctuation corrections to SSWT are calculated within a random-phase approximation which takes into account correctly leading and next-leading logarithmic singularities. These corrections are demonstrated to improve radically the agreement with experimental data on layered perovskites and other systems. Thus an account of these fluctuations provides a quantitative theory of layered magnets.Comment: 46 pages, RevTeX, 7 figure

Gravitational Fermion Production in Inflationary Cosmology

We revisit the gravitational production of massive Dirac fermions in inflationary cosmology with a focus on clarifying the analytic computation of the particle number density in both the large and the small mass regimes. For the case in which the masses of the gravitationally produced fermions are small compared to the Hubble expansion rate at the end of inflation, we obtain a universal result for the number density that is nearly independent of the details of the inflationary model. The result is identical to the case of conformally coupled scalars up to an overall multiplicative factor of order unity for reasons other than just counting the fermionic degrees of freedom.Comment: 21 pages, 1 figur

Tests of Classical and Quantum Electrodynamics with Intense Laser Fields

n this chapter classical and quantum electrodynamics in intense laser fields are discussed. We focus on the interaction of relativistic electrons with strong laser pulses. In particular, by analyzing the dynamics of this interaction, we show how the peak intensity of a strong laser pulse can be related to the spectrum of the radiation emitted by the electron during the interaction itself. The discussed method could be used to accurately measure high peak laser intensities exceeding 1020 W/cm2 up to about 1023 W/cm2 with theoretical envisaged accuracies of the order of 10 %. Furthermore, we investigate non-linear quantum effects originating from the interaction of an electron with its own electromagnetic field in the presence of an intense plane wave. These “radiative corrections” modify the electron wave-function in the plane wave. The self-interaction changes, amongst others, the dynamics of the electron’s spin in comparison with the prediction of the Dirac equation. We show that this effect can be measured, in principle, already at intensities of the order of 1022 W/cm