Classical and Quantum Composite p-branes

We discuss classical composite p-brane solutions and their quantization using the conjecture that their fluctuations may be described via degrees of freedom of Dirichlet strings ended on these p-branes. We work with Dirichlet (super)strings in framework of string field theory for open (super)strings. To elaborate in this scheme the eleventh dimension modes we take just a collection of Dirichlet strings which in their middle points have jumps in eleventh dimension. This theory can be seen as string field theory in infinite momentum frame of an eleven dimensional object.Comment: 7 pages, LaTex. Lecture at the XXXIII Karpacz Winter School "Duality -- String and Fields

Regge Regime in QCD and Asymmetric Lattice Gauge Theory

We study the Regge regime of QCD as a special regime of lattice gauge theory on an asymmetric lattice. This lattice has a spacing $a_0$ in the longitudinal direction and a spacing $a_t$ in the transversal direction. The limit $\frac{a_{0}}{a_{t}} \to 0$ corresponds to correlation functions with small longitudinal and large transversal coordinates, i.e. large $s$ and small $t$. On this lattice the longitudinal dynamics is described by the usual two-dimensional chiral field in finite volume and the transversal dynamics is emerged through an effective interaction of boundary terms of the longitudinal dynamics. The effective interaction depends crucially on the spectrum of the two-dimensional chiral field. Massless exitations produce an effective 2-dimensional action which is different from the action recently proposed by H.Verlinde and E.Verlinde. Massive exitations give raise to an effective action located on the contour in the longitudinal plane.Comment: LATEX, 13 pages, SMI-15-9

The Master Field for the Half-Planar Approximation for Large NN Matrix Models and Boltzmann Field Theory

In this talk results of study in various dimensions of the Boltzmann master field for a subclass of planar diagrams, so called half-planar diagrams, found in the recent work by Accardi, Volovich and one of us (I.A.) are presented.Comment: Contr. Proc. Buckow Symposium (1995); 6 pages, LATEX uses twoside.sty, fleqn.sty, espcrc2.sty, emlines.sty, bezier.st

UV/IR Mixing for Noncommutative Complex Scalar Field Theory, II (Interaction with Gauge Fields)

We consider noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY Yang-Mills theory. We show that one-loop renormalizability of noncommutative scalar electrodynamics requires the scalar potential to be an anticommutator squared. This form of the scalar potential differs from the one expected from the point of view of noncommutative gauge theories with extended SUSY containing a square of commutator. We show that fermion contributions restore the commutator in the scalar potential. This provides one-loop renormalizability of noncommutative N=2 SUSY gauge theory. We demonstrate a presence of non-integrable IR singularities in noncommutative scalar electrodynamics for general coupling constants. We find that for a special ratio of coupling constants these IR singularities vanish. Also we show that IR poles are absent in noncommutative N=2 SUSY gauge theory.Comment: 9 pages, 16 EPS figure

Non-Abelian Wilson Surfaces

A definition of non-abelian genus zero open Wilson surfaces is proposed. The ambiguity in surface-ordering is compensated by the gauge transformations.Comment: JHEP Latex, 10 pages, 6 figures; v2, refs and comments added in sec.

Tachyon condensation in cubic superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the non-BPS D-brane or brane-anti-D-brane pair, the negative energy density cancels the brane tension. We study this conjecture using a cubic superstring field theory with insertion of a double-step inverse picture changing operator. We compute the tachyon potential at levels (1/2,1) and (2,6). In the first case we obtain that the value of the potential at the minimum is 97.5% of the non BPS D-brane tension. Using a special gauge in the second case we get 105.8% of the tension.Comment: 19 pages, LaTeX, 3 figures. Eqs. (3.2), (3.3) and (4.6) are corrected, and new gauge fixing condition is use

Large N QCD at High Energies as Two-Dimensional Field Theory

Different aspects of the Verlinde and Verlinde relation between high-energy effective scattering in QCD and a two-dimensional sigma-model are discussed. Starting from a lattice version of the truncated 4-dimensional Yang-Mills action we derive an effective theory with non-trivial longitudinal dynamics which has a form of the lattice two-dimensional chiral field model with non-trivial boundary conditions. To get quantum corrections coming from non-trivial longitudinal dynamics to transversal high-energy effective action one has to solve the two-dimensional chiral field model with non-trivial boundary conditions. We do this within an approximation scheme which takes into account one-dimensional excitations. Contributions of the one-dimensional excitations to quantum corrections for the high-energy effective action are calculated in the large N limit using the character expansion method.Comment: Latex, 14pages, one reference added+ some minor correction

Large-N Quenching in the Kazakov-Migdal Model

To study the behavior of the Kazakov-Migdal at large N the quenched momentum prescription with constraints for treating the large N limit of gauge theories is used. It is noted that it leads to a quartic dependence of an action on unitary matrix instead of a quadratic dependence discussed in previous considerations. Therefore the model is not exactly solvable in the weak coupling limit. An approximation procedure for investigation of the model is outlined. In this approximation an indication to a phase transition for $d<4,8$ with $\beta_{cr}=\frac{1}{d-4,8}$ is obtained.Comment: LaTex, 9 page

Stringy Dark Energy Model with Cold Dark Matter

Cosmological consequences of adding the Cold Dark Matter (CDM) to the exactly solvable stringy Dark Energy (DE) model are investigated. The model is motivated by the consideration of our Universe as a slowly decaying D3-brane. The decay of this D-brane is described in the String Field Theory framework. Stability conditions of the exact solution with respect to small fluctuations of the initial value of the CDM energy density are found. Solutions with large initial value of the CDM energy density attracted by the exact solution without CDM are constructed numerically. In contrast to the LambdaCDM model the Hubble parameter in the model is not a monotonic function of time. For specific initial data the DE state parameter w_{DE} is also not monotonic function of time. For these cases there are two separate regions of time where w_{DE} being less than -1 is close to -1.Comment: 15 pages, 6 figures; references adde

A Simple Model Inducing QCD

A simple lattice model inducing a gauge theory is considered. The model describes an interaction of a gauge field to an $N\times N$ complex matrix scalar field transforming as a field in the fundamental representation. In contrast to the Kazakov-Migdal model the model contains only the linear interaction between scalar and gauge lattice fields. This model does not suffer from extra local U(1) symmetries. In an approximation of a translation invariant master field the large N limit of the model is investigated. At large N the gauge fields can be integrated out yielding an effective theory describing an interaction of eigenvalues of the master field. The reduced model exhibits phase transitions at the points $\beta_{\bar {cr}}$ and $\beta _{\underline{cr}}$ and the region $(\beta_{\bar{cr}}, \beta_{\underline{cr}})$ separates the strong and weak regions of the model. To study the behaviour of the model at large $N$ in more systematic way the quenched momentum prescription with constraints for treating the large N limit of gauge theories is used. With the help of the technique of orthogonal polynomials nonlinear equations describing the large N limit of the reduced model {\it with quenching} are presented.Comment: LaTex, 10 page