111 research outputs found
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
. 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 matrix model with branching interactions
Motivated by understanding the phase structure of strings we
investigate the 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- reduced model of odd-dimensional matrix
field theory. We find three distinct phases: (i) an ordinary 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.
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