One loop partition functions in a compactified open bosonic string theory

We calculate the one loop partition functions of a toroidally compactified open bosonic string (fromD=26 toD=10) in the path integral formalism. By a certain combination of the compactified sectors it is shown that the partition functions of a compactified open bosonic string vanish in both annulus and Möbius strip topologies as in the open superstring case. We also discuss the consistency requirement for the equivalence between the compactified open bosonic string and the open superstring with the gauge groups (SO(8192) andSO(32), respectively.     

Tadpole resummations in string theory

While R–R tadpoles should be canceled for consistency, string models with broken supersymmetry generally have uncanceled NS–NS tadpoles. Their presence signals that the background does not solve the field equations, so that these models are in “wrong” vacua. In this Letter we investigate, with reference to some prototype examples, whether the true values of physical quantities can be recovered resumming the NS–NS tadpoles, hence by an approach that is related to the analysis based on String Field Theory by open–closed duality. We show that, indeed, the positive classical vacuum energy of a Dp-brane of the bosonic string is exactly canceled by the negative contribution arising from tree-level tadpole resummation, in complete agreement with Sen's conjecture on open-string tachyon condensation and with the consequent analysis based on String Field Theory. We also show that the vanishing classical vacuum energy of the SO(8192) unoriented bosonic open-string theory does not receive any tree-level corrections from the tadpole resummation. This result is consistent with the fact that this (unstable) configuration is free from tadpoles of massless closed-string modes, although there is a tadpole of the closed string tachyon. The application of this method to superstring models with broken supersymmetry is also discussed.     

Bosonic string in the hot Schwarzschild geometry

We study the bosonic string in the Schwarzschild-de Sitter black hole, which has a black hole horizon as well as a cosmological horizon. This generalizes the bosonic string in the cold Schwarzschild black hole already studied.     

Modifying the bosonic string vacuum

A nontrivial string vacuum can induce effects in open bosonic string theories which can be interpreted in terms of nonlocality of the mapping of the string world sheet into spacetime. This is achieved by modifying the sum over Riemann surfaces to include boundaries on which the bosonic fields satisfy a Dirichlet condition, as well as holes with the usual Neumann condition and crosscaps. Such effects profoundly alter the large-angle behaviour of string amplitudes. With suitable normalization, they also lead to a cancellation of the one-loop divergence associated with the vacuum emission of a soft dilaton.     

Improved proof of the no-ghost theorem for fermion states of the superstring

The purpose of this note is to extend the improved proof of the no-ghost theorem for the bosonic and Neveu–Schwarz dual resonance models, presented in my article [C.B. Thorn, Nucl. Phys. B 286 (1987) 61], to cover the Ramond fermion string. As in that paper, the improvement involves the identification of an efficient basis for string state space and a self-contained proof, based on the super-Virasoro algebra, of the linear independence of the basis elements. We use our results to calculate the BRST cohomology for this system.     

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.     

Amplitudes for the Bosonic String with Boundaries

We deal with the problem of the computation of amplitudes for the bosonic Polyakov string with boundaries and show that both conformal invariance and reparametrisation invariance are maintained in critical dimensional d = 26 as the case without boundaries. The amplitudes of the bosonic, closed oriented Polyakov string with boundaries are formulated aa integral over moduli space with respect to the Weil-Petersson measure.     

D-branes as coherent states in the open string channel

We show that bosonic D-branestates may be represented as coherent states in an open string representation. By using the thermo field dynamics (TFD) formalism, we may construct a condensed state of open string modes that encodes the information on the D-braneconfiguration. We also introduce a construction alternative to TFD, which does not require one to assume thermal equilibrium. It is shown that the dynamics of the system combined with the geometric properties of the duplication rules of TFD is sufficient to obtain the thermal states and their analytic continuations in a geometric fashion. We use this approach to show that a bosonic D-branestate in the open string sector may also be built as boundary states in a special sense. Some implications of this study for the interpretation of the open/closed duality and on the kinematic/algebraic structure of an open string field theory are also commented on.     

String loop divergences and effective lagrangians

We isolate logarithmic divergences from bosonic string amplitudes on a disc. These divergences are compared with “tadpole” divergences in the effective field theory, with a covariant cosmological term implied by the counting of string coupling constants. We find an inconsistency between the two. This might be a problem in eliminating divergences from the bosonic string.     

A relation between gauge-invariant formulation of QCD and string theory in two dimensions

We have studied the explicit relation between the gauge-invariant path-ordered operator (POO) and a string field in two dimensions. For this purpose, we use the hamiltonian of two-dimensional quantum chromodynamics reformulated in terms of POO. POO is expanded in a power series of a non-local bosonic operator. We show that such a bosonic operator describes Bars and Hanson's free string field in the second quantization. Interactions among bosonic operators are treated in perturbation theory. The coupling constant is proportional to 1/√N_c.     

All NSR-models in terms of bosonic strings: An explicit derivation

We construct the open and closed string NSR-models in terms ofD15 bosonic string theories. All anticommuting NSR-operators are obtained after fermionizing 4 bosonic dimensions, and the NSR-Hilbert spaces are embedded as linear subspaces of the bosonic Hilbert spaces. We thus show the existence of various 10D supersymmetric sectors of the state spaces ofD=26 consistent bosonic strings.     

CONSTRUCTION OF INTERACTING ACTIONS OF BOSONIC OPEN STRINGS AND CLOSED STRINGS BY SYMMETRY PRINCIPLES

Following Kaku's way, various interacting actions of bosonic open strings as well as closed strings are constructed, which are invariant under. local reparametrization transformations, string group and global transformations of a Lie group. Similar to open string, a multiplication rule of closed string fields is given which also satisfies associative law as in open string case.     

A bosonic representation of the twisted string emission vertex

We present an explicit construction of the twist fields which create states in the twisted sectors of the Hilbert space in twisted bosonic string models. Such vertex operators have a complicated structure, which intertwines between the various sectors in the theory, and therefore represents a bosonic analogue of the fermion emission vertex which intertwines between the two sectors of the spinning string.     

Explicit parametrizations of degenerate surfaces from the KP equation and closed bosonic string amplitudes

The p-loop amplitude of closed bosonic string theory involves the integration over the moduli space. We seek an explicit parametrization of Riemann matrices in terms of 3p - 3 complex variables by solving the Kadomcev-Petviasvili (KP) equation. We find explicit solutions of this problem (Schottky problem) for certain types of degenerate surfaces. For these classes of surfaces, we obtain closed bosonic string amplitudes from the Belavin-Knizhnik theorem using our parametrizations. We show in what precise way they are related to the correlation functions on the Riemann surfaces.     

Fock space formulation of gauge invariant interacting field theories of open and closed strings

We derive the conditions that must be satisfied by three string vertex operators, in order to have a gauge invariant Chern-Simons type action as proposed by Witten for the open bosonic string, in a Fock space formulation. Given a vertex which satisfies these conditions for the open string, we show how to construct an invariant action for the closed string.     

Factorization of bosonic string amplitudes

We consider the bosonic string path integral over degenerating Riemann surfaces. We first review the factorization of conformal field theory on a degenerating surface. A careful treatment of the degeneration of the measure for moduli leads to a modification of the usual ghost insertions so as to assure covariance under a change of conformal frame. More generally, amplitudes with BRST invariant but conformally non-invariant operators are well defined with the covariant ghost insertions. As a detailed application we study the string modifications to the background field equations. We find to first order in the tadpole and all orders in string coupling that the ratio of the graviton source, dilaton source, and zero-point amplitude agrees with that found from general covariance and the soft-dilaton theorem in the low-energy field theory. We also discuss the unitarity of the bosonic string theory,     

Superconducting cosmic strings. II. Spacetime curvature

We solve the Einstein-Maxwell and scalar field equations for an infinitely long bosonic superconducting cosmic string and explore the associated geometry of space-time. The metric describing the space-time is valid for both fermionic and bosonic superconducting cosmic strings. Due to general relativistic corrections, the magnetic field energy per unit length associated with the string does not diverge. A non-uniform charged Higgs field contribution to the stress-energy tensor endows the string with an effective mass that enables to attract gravitationally and alters its lensing properties.     

The Pomeron in Closed Bosonic String Theory

We review the features of the pomeron in the S-matrix theory and in quantum field theory. We extend those general properties to the pomeron of closed bosonic string theory in a Minkowskian background. We compute the couplings of the pomeron to the first few mass levels of closed bosonic string states in flat space. We recognize the deviation from the linearity of the Regge trajectories in a five dimensional anti De Sitter background.