The SU(N) Matrix Model at Two Loops

Multi-loop calculations of the effective action for the matrix model are important for carrying out tests of the conjectured relationship of the matrix model to the low energy description of M-theory. In particular, comparison with N-graviton scattering amplitudes in eleven-dimensional supergravity requires the calculation of the effective action for the matrix model with gauge group SU(N). A framework for carrying out such calculations at two loops is established in this paper. The two-loop effective action is explicitly computed for a background corresponding to the scattering of a single D0-brane from a stack of N-1 D0-branes, and the results are shown to agree with known results in the case N=2.Comment: 30 pages, 1 figure; v2 - typos corrected, references update

Phase transitions in a network with range dependent connection probability

We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit small world behaviour for $\delta < 2$ above which its behaviour is like a regular lattice. From the study of the clustering coefficients, we show that there is a transition to a random network at $\delta = 1$. The finite size scaling analysis of the clustering coefficients obtained from numerical simulations indicate that a continuous phase transition occurs at this point. Using these results, we find that the two transitions occurring in this network can be detected in any dimension by the behaviour of a single quantity, the average bond length. The phase transitions in all dimensions are non-trivial in nature.Comment: 4 pages, revtex4, submitted to Physical Review

Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page

Evaluation of Chemical Protective Clothing: A Comparative Study of Breakthrough Times with Sulphur Mustard and a Simulant, 1,3-Dichloropropane

Carbon-coated non-woven fabrics were evaluated against vesicant sulphur mustard and l,3-dichloropropane (DCP). Breakthrough times of these chemicals were compared andfitted in a linear equation. A correlation, better than 95 per cent was obtained. It is recommended that DCP be used in the valuation and quality control of fabric in the chemical protective clothing manufacturing industries to reduce the exposure and risks of handling lethal chemicals. However,-the clothing may be challenged with actual CW agents to determine their protective potentials, in the laboratory. Diffusion coefficients for DCP were also computed from the breakthrough data for carbon-coated fabric of different grades

Domain walls between gauge theories

Noncommutative U(N) gauge theories at different N may be often thought of as different sectors of a single theory: the U(1) theory possesses a sequence of vacua labeled by an integer parameter N, and the theory in the vicinity of the N-th vacuum coincides with the U(N) noncommutative gauge theory. We construct noncommutative domain walls on fuzzy cylinder, separating vacua with different gauge theories. These domain walls are solutions of BPS equations in gauge theory with an extra term stabilizing the radius of the cylinder. We study properties of the domain walls using adjoint scalar and fundamental fermion fields as probes. We show that the regions on different sides of the wall are not disjoint even in the low energy regime -- there are modes penetrating from one region to the other. We find that the wall supports a chiral fermion zero mode. Also, we study non-BPS solution representing a wall and an antiwall, and show that this solution is unstable. We suggest that the domain walls emerge as solutions of matrix model in large class of pp-wave backgrounds with inhomogeneous field strength. In the M-theory language, the domain walls have an interpretation of a stack of branes of fingerstall shape inserted into a stack of cylindrical branes.Comment: Final version; minor corrections; to appear in Nucl.Phys.

Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL models, and also non-supersymmetric extremal Kerr black hole and slowly rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black holes our results are in perfect agreement with the microscopic results derived from string theory. In particular we reproduce correctly the dependence of the logarithmic corrections on the number of U(1) gauge fields in the theory, and on the angular momentum carried by the black hole in different scaling limits. We also explain the shortcomings of the Cardy limit in explaining the logarithmic corrections in the limit in which the (super)gravity description of these black holes becomes a valid approximation. For non-supersymmetric extremal black holes, e.g. for the extremal Kerr black hole in four dimensions, our result provides a stringent testing ground for any microscopic explanation of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation between boundary condition and choice of ensemble, modified analysis for slowly rotating black holes, all results remain unchanged, typos corrected; v3: minor additions and correction

Sliding Singlet Mechanism Revisited

We show that the unification of the doublet Higgs in the standard model (SM) and the Higgs to break the grand unified theory (GUT) group stabilizes the sliding singlet mechanism which can solve the doublet-triplet (DT) splitting problem. And we generalize this attractive mechanism to apply it to many unified scenarios. In this paper, we try to build various concrete E_6 unified models by using the generalized sliding singlet mechanism.Comment: 13 page

Revisiting Cardassian Model and Cosmic Constraint

In this paper, we revisit the Cardassian model in which the radiation energy component is included. It is important for early epoch when the radiation cannot be neglected because the equation of state (EoS) of the effective dark energy becomes time variable. Therefore, it is not equivalent to the quintessence model with a constant EoS anymore. This situation was almost overlooked in the literature. By using the recent released Union2 557 of type Ia supernovae (SN Ia), the baryon acoustic oscillation (BAO) from Sloan Digital Sky Survey and the WiggleZ data points, the full information of cosmic microwave background (CMB) measurement given by the seven-year Wilkinson Microwave Anisotropy Probe observation, we constrain the Cardassian model via the Markov Chain Monte Carlo (MCMC) method. A tight constraint is obtained: $n= -0.0479_{- 0.0732- 0.148}^{+ 0.0730+ 0.142}$ in $1,2\sigma$ regions. The deviation of Cardassian model from quintessence model is shown in CMB anisotropic power spectra at high l's parts due to the evolution of EoS. But it is about the order of 0.1% which cannot be discriminated by current data sets. The Cardassian model is consistent with current cosmic observational data sets.Comment: 6 pages, 5 figures, match the published versio

Generalized Chaplygin Gas, Accelerated Expansion and Dark Energy-Matter Unification

We consider the scenario emerging from the dynamics of a generalized $d$-brane in a $(d+1, 1)$ spacetime. The equation of state describing this system is given in terms of the energy density, $\rho$, and pressure, $p$, by the relationship $p = - A/\rho^{\alpha}$, where $A$ is a positive constant and $0 < \alpha \le 1$. We discuss the conditions under which homogeneity arises and show that this equation of state describes the evolution of a universe evolving from a phase dominated by non-relativistic matter to a phase dominated by a cosmological constant via an intermediate period where the effective equation of state is given by $p = \alpha \rho$.Comment: 5 pages, 4 figures, revte

Boundary dynamics and multiple reflection expansion for Robin boundary conditions

In the presence of a boundary interaction, Neumann boundary conditions should be modified to contain a function S of the boundary fields: (\nabla_N +S)\phi =0. Information on quantum boundary dynamics is then encoded in the $S$-dependent part of the effective action. In the present paper we extend the multiple reflection expansion method to the Robin boundary conditions mentioned above, and calculate the heat kernel and the effective action (i) for constant S, (ii) to the order S^2 with an arbitrary number of tangential derivatives. Some applications to symmetry breaking effects, tachyon condensation and brane world are briefly discussed.Comment: latex, 22 pages, no figure