Tachyon condensation and open string field theory

We perform canonical quantization of open string on a unstable D-brane in the background of tachyon condensation. Evaluating the Polyakov path-integral on a strip, we obtain a field theoretical propagator in the open string theory. As condensation occurs the string field theory is continuously deformed. At the infrared fixed point of condensation, the open string field on the unstable D-brane transmutes to that on the lower-dimensional D-brane with the correct D-brane tension.     

Pre-geometrical field theory of the open string

We propose a gauge invariant, background independent string action, which contains open and closed string fields and no kinetic terms. The kinetic term is generated through the condensation of the string fields, which is the solution of the equations of motion. we solve the equations and show that the action is classically equivalent to the open string action proposed by Hata et al.     

Covariant open string field theory on multiple Dp-branes

We study covariant open bosonic string field theories on multiple Dp-branes by using the deformed cubic string field theory, which is equivalent to string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple Dp-branes, we obtain the field theoretical effective action in the zero-slope limit. On multiple D0-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind(BFSS) matrix model. We also discuss the relation between open string field theory on multiple D-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya(IKKT) matrix model.The covariant open string field theory on multiple Dp-branes could be useful to study the non-perturbative properties of quantum field theories in(p+1)-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using covariant string field theory.     

Four-photon scattering amplitude in bosonic open string field theory

The covariant string field theory, which is formulated as a natural generalization of the light-cone gauge approach, is used to calculate three- and four-photon scattering amplitudes explicitly at tree level. The results are found to be consistent with the first quantized covariant approach.     

On the associativity anomaly in open string field theory

The associativity anomaly in the star algebra of the open bosonic string is demonstrated by a simple oscillator calculation. In an associative algebra, formal arguments require that the “half string” BRST operator Q_L be nilpotent; however, we show that associativity is actually violated by computing Q_L² in an explicit operator representation of the star algebra.     

Schnabl's solution and boundary states in open string field theory

We discuss that Schnabl's solution is an off-shell extension of the boundary state describing a D-brane in the closed string sector. It gives the physical meaning of the gauge-invariant overlaps for the solution in our previous paper and supports Ellwood's recent proposal in the operator formalism.     

Quenched string field theory

We construct a toy model of Witten's open string field theory by truncating the Virasoro group to its SU(1,1) subgroup. The string field is given in terms of finite-dimensional matrices, which satisfy a non-trivial BRST cohomology. The string gauge group is found to be SO(3). Finally, we perform the gauge fixing of the action, finding an explicit formula for calculating the partition function.     

Perturbation theory for two-dimensional gauge models

Euclidean symmetric integration, previously proposed for the SU(N) Yang-Mills theory in the limit of large N, is used to study the propagators in the Schwinger model and the massive vector-meson model in two dimensions. The result of summing the perturbation series agrees with the exact solution in each case. Therefore, perturbation theory is here capable of dealing with non-analytic behaviour in the coupling constant.     

The spectrum of open string field theory at the stable tachyonic vacuum

We present a level (10,30)$(10,30)$ numerical computation of the spectrum of quadratic fluctuations of open string field theory around the tachyonic vacuum, both in the scalar and in the vector sector. Our results are consistent with Sen's conjecture about gauge-triviality of the small excitations. The computation is sufficiently accurate to provide robust evidence for the absence of the photon from the open string spectrum. We also observe that ghost string field propagators develop double poles. We show that this requires non-empty BRST cohomologies at non-standard ghost numbers. We comment about the relations of our results with recent work on the same subject.     

BRST-symmetries in free string field theory

A unitary field transformation useful for examination of the BRST-symmetries in free bosonic open-string field theory is introduced. It is similar to Siegel and Zwiebach's transformation, but leads to a hermitian BRST-charge in contrast to theirs. The transformed BRST-transformation factorizes into two parts, making the gauge-unfixing procedure rather trivial. Both the minimal-type gauge-invariant action and Witten's action are dealt with.     

Reparametrisation -invariant string field theory

A differential-geometric approach to the closed Bose-string field theory is developed in a framework where the Lorentz and reparametrisation invariances are manifest. The Virasoro anomaly in the quantum theory is cancelled by the minimal introduction of the conformal mode, extending the usual string functionals defined on the space of embeddings. An action is written down, and this approach to strings is compared with the second-quantised formalism for the single particle.     

Gauge-fixing in covariant string field theory

We discuss the gauge-fixing procedure of the covariant formulation of the open bosonic string recently proposed by Neveu, Nicolai and West (the so-called finite set). We show that this theory has new symmetries. However, it does not seem possible to recover the correct number of physical degrees of freedom.     

Dispersionless Toda hierarchy and two-dimensional string theory

The dispersionless Toda hierarchy turns out to lie in the heart of a recently proposed Landau-Ginzburg formulation of two-dimensional string theory at self-dual compactification radius. The dynamics of massless tachyons with discrete momenta is shown to be encoded into the structure of a special solution of this integrable hierarchy. This solution is obtained by solving a Riemann-Hilbert problem. Equivalence to the tachyon dynamics is proven by deriving recursion relations of tachyon correlation functions in the machinery of the dispersionless Toda hierarchy. Fundamental ingredients of the Landau-Ginzburg formulation, such as Landau-Ginzburg potentials and tachyon Landau-Ginzburg fields, are translated into the language of the Lax formalism. Furthermore, a wedge algebra is pointed out to exist behind the Riemann-Hilbert problem, and speculations on its possible role as generators of extra states and fields are presented.     

A covariant open bosonic string field theory including the endpoint and middlepoint interaction

Extending the usual endpoint and midpoint interactions, we introduce numerous kinds of interactions, labelled by a parameter λ and obtain a non-commutative and associative string field algebra by adding up all interactions. With this algebra we develop a covariant open bosonic string field theory, which reduces to Witten's open bosonic string field theory under a special string length choice.