Witten's Open String Field Theory in Constant B-Field Background

In this paper we consider Witten's bosonic open string field theory in the presence of a constant background of the second-rank antisymmetric tensor field $B_{ij}$. We extend the operator formulation of Gross and Jevicki in this situation and construct the overlap vertices explicitly. As a result we find a noncommutative structure of the Moyal type only in the zero-mode sector, which is consistent with the result of the correlation functions among vertex operators in the world sheet formulation. Furthermore we find out a certain unitary transformation of the string field which absorbs the Moyal type noncommutative structure. It can be regarded as a microscopic origin of the transformation between the gauge fields in commutative and noncommutative gauge theories discussed by Seiberg and Witten.Comment: 35 pages, LaTeX, no figures, Arguments about string coupling constants are modified. final version to be published in JHE

Supersymmetric double-well matrix model as two-dimensional type IIA superstring on RR background

In the previous paper, the authors pointed out correspondence of a supersymmetric double-well matrix model with two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background from the viewpoint of symmetries and spectrum. In this paper we further investigate the correspondence from dynamical aspects by comparing scattering amplitudes in the matrix model and those in the type IIA theory. In the latter, cocycle factors are introduced to vertex operators in order to reproduce correct transformation laws and target-space statistics. By a perturbative treatment of the Ramond-Ramond background as insertions of the corresponding vertex operators, various IIA amplitudes are explicitly computed including quantitatively precise numerical factors. We show that several kinds of amplitudes in both sides indeed have exactly the same dependence on parameters of the theory. Moreover, we have a number of relations among coefficients which connect quantities in the type IIA theory and those in the matrix model. Consistency of the relations convinces us of the validity of the correspondence.Comment: 52 pages, version to appear in JHE

Area Law Violations and Quantum Phase Transitions in Modified Motzkin Walk Spin Chains

Area law violations for entanglement entropy in the form of a square root has recently been studied for one-dimensional frustration-free quantum systems based on the Motzkin walks and their variations. Here we consider a Motzkin walk with a different Hilbert space on each step of the walk spanned by elements of a {\it Symmetric Inverse Semigroup} with the direction of each step governed by its algebraic structure. This change alters the number of paths allowed in the Motzkin walk and introduces a ground state degeneracy sensitive to boundary perturbations. We study the frustration-free spin chains based on three symmetric inverse semigroups, \cS^3_1, \cS^3_2 and \cS^2_1. The system based on \cS^3_1 and \cS^3_2 provide examples of quantum phase transitions in one dimensions with the former exhibiting a transition between the area law and a logarithmic violation of the area law and the latter providing an example of transition from logarithmic scaling to a square root scaling in the system size, mimicking a colored \cS^3_1 system. The system with \cS^2_1 is much simpler and produces states that continue to obey the area law.Comment: 40 pages, 14 figures, A condensed version of this paper has been submitted to the Proceedings of the 2017 Granada Seminar on Computational Physics, Contains minor revisions and is closer to the Journal version. v3 includes an addendum that modifies the final Hamiltonian but does not change the main results of the pape

Lattice Formulation for 2d N=(2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions

We present a lattice formulation for two-dimensional N=(2,2) and (4,4) supersymmetric Yang-Mills theories that resolves vacuum degeneracy for gauge fields without imposing admissibility conditions. Cases of U(N) and SU(N) gauge groups are considered, gauge fields are expressed by unitary link variables, and one or two supercharges are preserved on the two-dimensional square lattice. There does not appear fermion doubler, and no fine-tuning is required to obtain the desired continuum theories in a perturbative argument. This formulation is expected to serve as a more convenient basis for numerical simulations. The same approach will also be useful to other two-dimensional supersymmetric lattice gauge theories with unitary link variables constructed so far -- for example, N=(8,8) supersymmetric Yang-Mills theory and N=(2,2) supersymmetric QCD.Comment: 19 pages, no figure, (v2) reference added, minor corrections, version to be published in JHE

Renyi entropy of highly entangled spin chains

Entanglement is one of the most intriguing features of quantum theory and a main resource in quantum information science. Ground states of quantum many-body systems with local interactions typically obey an "area law" meaning the entanglement entropy proportional to the boundary length. It is exceptional when the system is gapless, and the area law had been believed to be violated by at most a logarithm for over two decades. Recent discovery of Motzkin and Fredkin spin chain models is striking, since these models provide significant violation of the entanglement beyond the belief, growing as a square root of the volume in spite of local interactions. Although importance of intensive study of the models is undoubted to reveal novel features of quantum entanglement, it is still far from their complete understanding. In this article, we first analytically compute the Renyi entropy of the Motzkin and Fredkin models by careful treatment of asymptotic analysis. The Renyi entropy is an important quantity, since the whole spectrum of an entangled subsystem is reconstructed once the Renyi entropy is known as a function of its parameter. We find non-analytic behavior of the Renyi entropy with respect to the parameter, which is a novel phase transition never seen in any other spin chain studied so far. Interestingly, similar behavior is seen in the Renyi entropy of Rokhsar-Kivelson states in two-dimensions.Comment: 14+22 pages, 8 figures; (v2) references added, (v3) version to be published in International Journal of Modern Physics

Cohomological Field Theory Approach to Matrix Strings

In this paper we consider IIA and IIB matrix string theories which are defined by two-dimensional and three-dimensional super Yang-Mills theory with the maximal supersymmetry, respectively. We exactly compute the partition function of both of the theories by mapping to a cohomological field theory. Our result for the IIA matrix string theory coincides with the result obtained in the infra-red limit by Kostov and Vanhove, and thus gives a proof of the exact quasi classics conjectured by them. Further, our result for the IIB matrix string theory coincides with the exact result of IKKT model by Moore, Nekrasov and Shatashvili. It may be an evidence of the equivalence between the two distinct IIB matrix models arising from different roots.Comment: 26 pages, latex, no figures, minor corrections, the final version to be published in Int. J. Mod. Phys.

Critical behavior in c=1c=1 matrix model with branching interactions

Motivated by understanding the phase structure of $d >1$ strings we investigate the $c=1$ matrix model with g' (\tr M(t)^{2})^{2} interaction which is the simplest approximation of the model expected to describe the critical phenomena of the large-$N$ reduced model of odd-dimensional matrix field theory. We find three distinct phases: (i) an ordinary $c=1$ gravity phase, (ii) a branched polymer phase and (iii) an intermediate phase. Further we can also analyse the one with slightly generalized g^{(2)} (\frac{1}{N}\tr M(t)^{2})^{2} +g^{(3)} (\frac{1}{N}\tr M(t)^{2})^{3} + \cdots + g^{(n)} (\frac{1}{N}\tr M(t)^{2})^{n} interaction. As a result the multi-critical versions of the phase (ii) are found.Comment: 11pages. latex (The arguments in Discussions are corrected and more clarified! Several grammatical errors are corrected. And some preprints in references are replaced with the published versions.