On Schwarzschild black hole in large N matrix theory

D0-brane gas picture of Schwarzschild black hole (SBH) is considered in the large N regime of Matrix theory. An entropy formula, which reproduces the thermodynamics of SBH in the large 0N limit for all dimensions (D≥6), is proposed. The equations of states for supersymmetric Yang-Mills theory at low temperature are obtained. We also give a proof of the Newton gravitation law between two SBHs, whose masses are not equal.     

N=1 formulation of general N=2 Yang-Mills supergravity couplings

We formulate general interactions of an N=2 Yang-Mills supermultiplet coupled to N=2 supergravity in terms of N=1 invariant functions. We show that the N=2 scalar potential of the complex scalar fields in the adjoint representation, superpartners of the Yang-Mills gauge fields, splits into a conventional gauge contribution as well as in a superpotential term contribution proportional to the SO(2) gauge coupling of N=2 de Sitter supergravity. The relation of these results to the σ model structure of N4 extended supergravities is also discussed, particularly in connection with the coset disintegration of scalar manifolds.     

Large N phase transition in the heat kernel on the U (N) group

The large N phase transition point is investigated in the heat kernel on the U(N) group with respect to arbitrary boundary conditions. A simple functional relation is found relating the density of eigenvalues of the boundary field to the saddle point shape of the typical Young tableaux in the large N limit of the character expansion of the heat kernel. Both strong coupling and weak coupling phases are investigated for some particular cases of the boundary holonomy.     

The large N limit of the O(N) Heisenberg spin system in two dimensions

The large N limit of the O(N) Heisenberg spin system in two dimensions (a lattice version of the non-linear σ-model) is analysed by the collective field technique. A compact expression for the mass gap and the β-function is obtained for arbitrary but fixed gN. The strong and weak coupling limits of this expression correctly reproduce the known results.     

Phase Dynamics in Nonlinear Coupled Oscillators

We discuss the phase dynamics in the system of a set of nonlinear coupled oscillators. We find a direct and simple geometric method to observe the geometric phase for this system, and it provides a possibility for the experimental measurements.     

Contrasting N→Δ and N→N parity-violating asymmetries in nuclei

Several perspectives that can be opened by studying the electroexcitation of the delta via parity-violating electron scattering from nuclei are examined, working within the context of the relativistic Fermi-gas model. A strong enhancement of the left–right asymmetry in the delta sector compared with that in the quasielastic regime is found and the potential to find clear signatures for the axial-vector contributions of the nucleon-to-delta transition to the asymmetry identified at specific low momentum transfer kinematics. Possibilities of probing the deformation of the delta are also explored, and using both the proton and nuclei as targets, the ability to study the asymmetry on neutrons is studied.     

On the effective lagrangian in the supersymmetric N = 1 Yang-Mills theory

It is shown that supersymmetry breaking does not occur in a supersymmetric Yang-Mills theory with an effective lagrangian (EL) constructed of the simplest composite colourless superfields. Our arguments appear also to be valid for the case of still more complicated models of EL.     

The self-dual Chern-Simons CP(N) models

We study the Chern-Simons CP(N) models with a global U(1) symmetry and found the self-dual models among them. The Bogomolnyi-type bound in these self-dual models is a nontrivial generalization of that in the pure CP(N) models. Our models have quite a rich vacuum and soliton structure and approach the many known gauged self-dual models in an appropriate limit.     

A construction of N = 2 and centerless N = 4 superconformal fields via affine superalgebras

In this paper we give a new construction of the N = 2 superconformal algebra using currents of the affine superalgebra and free bosonic fields, and also the N = 4 supercomformal algebra without central charge in terms of currents of and free bosonic fields.     

Hamiltonian superfield formalism with N supercharges

An action principle that applies uniformly to any number N of supercharges is proposed. We perform the reduction to the N=0 partition function by integrating out superpartner fields. As a new feature for theories of extended supersymmetry, the canonical Pfaffian measure factor is a result of a Gaussian integration over a superpartner. This is mediated through an explicit choice of direction n^a in the θ-space, which the physical sector does not depend on. Also, we re-interpret the metric g^ab in the Susy algebra [D^a,D^b]g^ab∂_t as a symplectic structure on the fermionic θ-space. This leads to a superfield formulation with a general covariant θ-space sector.     

Single-hole-core coupling in the N = 50 region

The level schemes and electromagnetic properties of ⁸⁵Kr, ⁸⁵Sr, ⁸⁷Sr and ⁸⁹Zr are calculated in a semi-microscopic model which couples the neutron hole motion in the N = 28–50 shell to the quadrupole and octupole vibrations of the core. The calculations are compared with recent experimental results.     

Self-dual supergravity from N = 2 strings

A new heterotic N = 2 string with manifest target space supersymmetry is constructed by combining a conventional N = 2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma mode] is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in t', all in superspace. The resulting field equations describe N = 1 self-dual supergravity.     

RNA folding and large N matrix theory

We formulate the RNA folding problem as an N×N matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is set up in such a way that the limit N→∞ yields the so-called secondary structure (Hartree theory). Tertiary structure and pseudo-knots are obtained by calculating the 1/N² corrections to the partition function. We propose a generalization of the Hartree recursion relation to generate the tertiary structure.     

C M ? C N D -computable state

The notions of D-computable state and D-concurrence are generalized to the C ^M ⊗ C ^N system. A class of D-computable state on C ^M ⊗ C ^N is given and the calculating method of the lower bound of D-concurrence is provided. The obvious expression of the lower bound of D-concurrence for the state mixed by two D-pure states is derived. Supported by the National Natural Science Foundation of China (Grant No. 60433050) and the Key Project of the Science Foundation of Xuzhou Normal University (Grant No. 06XLA05)     

Semiclassical expansions for confined N fermion systems

A new derivation of the Wigner-Kirkwood expansion for N-fermion systems is presented, showing explicitly the connection to the WKB approximation for a single level. This allows us to study separately the two ansatzes required to obtain the semiclassical expansions: the asymptotic expansions in powers of and the smoothing of quantal effects. We discuss the one dimensional and three dimensional, with spherical symmetry, cases. Applications for standard potentials used in nuclear physics are described in detail.     

Geometry of N = 1 dualities in four dimensions

We discuss how N = 1 dualities in four dimensions are geometrically realized by wrapping D-branes about 3-cycles of Calabi-Yau threefolds. In this setup the N = 1 dualities for SU, SO and USp gauge groups with fundamental fields get mapped to statements about the monodromy and relations among 3-cycles of Calabi-Yau threefolds. The connection between the theory and its dual requires passing through configurations which are T-dual to the well-known phenomenon of decay of BPS states in N = 2 field theories in four dimensions. We compare our approach to recent works based on configurations of D-branes in the presence of NS 5-branes and give simple classical geometric derivations of various exotic dynamics involving D-branes ending on NS branes.     

Anomalies in gravity-coupled SU(N) Yang-Mills theory

In a general even space-time dimension I consider spin-1/2 fermions coupled to SU(N) Yang-Mills fields and to gravity. It is shown (unexpectedly) that, once the chiral gauge anomaly is cancelled, gravitational anomalies do not further constrain the fermion representation.