Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures

In this paper we examine the bi-Hamiltonian structure of the generalized KdV-hierarchies. We verify that both Hamiltonian structures take the form of Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated system. Classical extended conformal algebras are obtained from the second Poisson bracket. In particular, we construct the $W_n^l$ algebras, first discussed for the case $n=3$ and $l=2$ by A. Polyakov and M. Bershadsky.Comment: 41 page

QCD Strings as Constrained Grassmannian Sigma Model:

We present calculations for the effective action of string world sheet in R3 and R4 utilizing its correspondence with the constrained Grassmannian sigma model. Minimal surfaces describe the dynamics of open strings while harmonic surfaces describe that of closed strings. The one-loop effective action for these are calculated with instanton and anti-instanton background, reprsenting N-string interactions at the tree level. The effective action is found to be the partition function of a classical modified Coulomb gas in the confining phase, with a dynamically generated mass gap.Comment: 22 pages, Preprint: SFU HEP-116-9

Notes on D-branes in 2D Type 0 String Theory

In this paper we construct complete macroscopic operators in two dimensional type 0 string theory. They represent D-branes localized in the time direction. We give another equivalent description of them as deformed Fermi surfaces. We also discuss a continuous array of such D-branes and show that it can be described by a matrix model with a deformed potential. For appropriate values of parameters, we find that it has an additional new sector hidden inside its strongly coupled region.Comment: harvmac, 18 pages, 2 figures, references adde

A Matrix Model Dual of Type 0B String Theory in Two Dimensions

We propose that type 0B string theory in two dimensions admits a dual description in terms of a one dimensional bosonic matrix model of a hermitian matrix. The potential in the matrix model is symmetric with respect to the parity-like Z_2 transformation of the matrix. The two sectors in the theory, namely the NSNS and RR scalar sectors correspond to two classes of operators in the matrix model, even and odd under the Z_2 symmetry respectively. We provide evidence that the matrix model successfully reconstructs the perturbative S-matrix of the string theory, and reproduces the closed string emission amplitude from unstable D-branes. Following recent work in two dimensional bosonic string, we argue that the matrix model can be identified with the theory describing N unstable D0-branes in type 0B theory. We also argue that type 0A theory is described in terms of the quantum mechanics of brane-antibrane systems.Comment: Latex, 20 pages, typos corrected, explanations added, references adde

D-brane Decay in Two-Dimensional String Theory

We consider unstable D0-branes of two dimensional string theory, described by the boundary state of Zamolodchikov and Zamolodchikov [hep-th/0101152] multiplied by the Neumann boundary state for the time coordinate $t$. In the dual description in terms of the $c=1$ matrix model, this D0-brane is described by a matrix eigenvalue on top of the upside down harmonic oscillator potential. As suggested by McGreevy and Verlinde [hep-th/0304224], an eigenvalue rolling down the potential describes D-brane decay. As the eigenvalue moves down the potential to the asymptotic region it can be described as a free relativistic fermion. Bosonizing this fermion we get a description of the state in terms of a coherent state of the tachyon field in the asymptotic region, up to a non-local linear field redefinition by an energy-dependent phase. This coherent state agrees with the exponential of the closed string one-point function on a disk with Sen's marginal boundary interaction for $t$ which describes D0-brane decay.Comment: 19 pages, harvmac, minor change

Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas

We study a set of chiral symmetries contained in degenerate operators beyond the `minimal' sector of the c(p,q) models. For the operators h_{(2j+2)q-1,1}=h_{1,(2j+2)p-1} at conformal weight [ (j+1)p-1 ][ (j+1)q -1 ], for every 2j \in N, we find 2j+1 chiral operators which have quantum numbers of a spin j representation of SU(2). We give a free-field construction of these operators which makes this structure explicit and allows their OPEs to be calculated directly without any use of screening charges. The first non-trivial chiral field in this series, at j=1/2, is a fermionic or para-fermionic doublet. The three chiral bosonic fields, at j=1, generate a closed W-algebra and we calculate the vacuum character of these triplet models.Comment: 23 pages Late

Renormalization group flows and continual Lie algebras

We study the renormalization group flows of two-dimensional metrics in sigma models and demonstrate that they provide a continual analogue of the Toda field equations based on the infinite dimensional algebra G(d/dt;1). The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time. We provide the general solution of the renormalization group flows in terms of free fields, via Backlund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z_n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.Comment: latex, 73pp including 14 eps fig

Creation of the precision magnetic spectrometer SCAN-3

The new JINR project [1] is aimed at studies of highly excited nuclear matter created in nuclei by a high-energy deuteron beam. The matter is studied through observation of its particular decay products - pairs of energetic particles with a wide opening angle, close to 180°. The new precision hybrid magnetic spectrometer SCAN-3 is to be built for detecting charged (π±, K±, p) and neutral (n) particles produced at the JINR Nuclotron internal target in dA collisions. One of the main and complex tasks is a study of low-energy ηA interaction and a search for η-bound states (η-mesic nuclei). Basic elements of the spectrometer and its characteristics are discussed in the article