Comments on real tachyon vacuum solution without square roots

We analyze the consistency of a recently proposed real tachyon vacuum solution without square roots in open bosonic string field theory. We show that the equation of motion contracted with the solution itself is satisfied. Additionally, by expanding the solution in the basis of the curly $\mathcal{L}_0$ and the traditional $L_0$ eigenstates, we evaluate numerically the vacuum energy and obtain a result in agreement with Sen's conjecture.Comment: 20 pages; one subsection adde

Level truncation analysis of a simple tachyon vacuum solution in cubic superstring field theory

We evaluate the vacuum energy of a simple tachyon vacuum solution using the level truncation scheme in cubic superstring field theory. By truncating the standard Virasoro $L_0$ level expansion of the solution, we obtain a value of the vacuum energy in agreement with Sen's first conjecture.Comment: 20 pages, extra factor 2/\pi deleted from equation (3.2), some typos correcte

Pure Spinor Partition Function Using Pade Approximants

In a recent paper, the partition function (character) of ten-dimensional pure spinor worldsheet variables was calculated explicitly up to the fifth mass-level. In this letter, we propose a novel application of Pade approximants as a tool for computing the character of pure spinors. We get results up to the twelfth mass-level. This work is a first step towards an explicit construction of the complete pure spinor partition function.Comment: 16 page

Multibrane solutions in cubic superstring field theory

Using the elements of the so-called $KBc\gamma$ subalgebra, we study a class of analytic solutions depending on a single function $F(K)$ in the modified cubic superstring field theory. We compute the energy associated to these solutions and show that the result can be expressed in terms of a contour integral. For a particular choice of the function $F(K)$, we show that the energy is given by integer multiples of a single D-brane tension.Comment: 14 pages, some typos correcte

Hilbert space of curved \beta\gamma systems on quadric cones

We clarify the structure of the Hilbert space of curved \beta\gamma systems defined by a quadratic constraint. The constraint is studied using intrinsic and BRST methods, and their partition functions are shown to agree. The quantum BRST cohomology is non-empty only at ghost numbers 0 and 1, and there is a one-to-one mapping between these two sectors. In the intrinsic description, the ghost number 1 operators correspond to the ones that are not globally defined on the constrained surface. Extension of the results to the pure spinor superstring is discussed in a separate work.Comment: 45 page

N=1 Supersymmetric Yang-Mills on the lattice at strong coupling

We study N=1 supersymmetric SU(N) Yang-Mills theory on the lattice at strong coupling. Our method is based on the hopping parameter expansion in terms of random walks, resummed for any value of the Wilson parameter r in the small hopping parameter region. Results are given for the mesonic (2-gluino) and fermionic (3-gluino) propagators and spectrum.Comment: Latex file. 43 pages. Minor additional comments, references added, typos corrected. Accepted for publication in Int. J. Mod. Phys.

Combinatorics of lattice paths with and without spikes

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are useful when performing strong coupling (hopping parameter) expansions of lattice models. Some applications are described.Comment: Latex. 25 page