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.     

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.     

E10, BE10 and arithmetical chaos in superstring cosmology

It is shown that the neverending oscillatory behavior of the generic solution, near a cosmological singularity, of the massless bosonic sector of superstring theory can be described as a billiard motion within a simplex in nine-dimensional hyperbolic space. The Coxeter group of reflections of this billiard is discrete and is the Weyl group of the hyperbolic Kac-Moody algebra E10 (for type II) or BE10 (for type I or heterotic), which are both arithmetic. These results lead to a proof of the chaotic ("Anosov") nature of the classical cosmological oscillations, and suggest a "chaotic quantum billiard" scenario of vacuum selection in string theory.     

ON GEOMETRIC QUANTIZATION FOR BOSONIC STRING (Ⅱ)

The Hilbert space and the representation of the generators of Virasoro algebra for bosonic string under a holomorphic polarization are given in this paper,It is shown that the contre term of Virasoro algebra may be interpreted as curvature of a holomorphic vector bundle (holomorphic Fock bundle) on coset space G¹¹=G/H where G denotes the conformal transformation group and H the one-parameter subgroup generated by the generator L₀.The condition of the conformal anomaly cancellation may be expressed as the vanishing curvature of the bundle which is obtained by the product of the holomorphic Fock bundle and the holomorphic ghost vacuum bundle.The geometric interpretations of both classical and quantized BRST operators,ghost and antighost operators are also discussed.     

BRST quantization of superstring field theory

We write the gauge fixed action which arises in the quantization of Witten's string field theory in a linear gauge, in a form which applies to both the superstring and the bosonic string. The corresponding BRST transformation is nilpotent only on-shell. We construct also an off-shell nilpotent BRST transformation which formally leaves invariant the quantum effective action. This BRST transformation has a geometrical interpretation which could allow to describe the gauge anomalies of the superstring field theory as the nontrivial cohomology of the BRST charge via the Wess-Zumino consistency condition.     

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.     

Symmetries of the interacting gauge-covariant bosonic string

We derive in detail the local gauge transformations and interaction lagrangian of the second-quantized bosonic string. We verify at lowest non-trivial order in the coupling constant the gauge invariance of the interacting action, and the closure of the field transformations. This gives the structure constants of the corresponding local gauge group. This group has its generators labelled by all the string states of the theory. We show that the fermionic part of the interaction is just the overlap condition for the ghost coordinates of the three strings, multiplied by an appropriate extra ghost at the point common to the three strings. Our treatment is based on an extensive use of Goto-Naka-type overlap equations. It avoids the use of ill-defined infinite matrices or series, and can be straightforwardly extended to other string theories. We explicitly derive the conformal transformation relating the gauge-covariant three-point function to the old Caneschi-Schwimmer-Veneziano vertex. We also deal with the closed bosonic string.     

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.     

Pseudo-supergravity extension of the bosonic string

We construct a “pseudo-supersymmetric” fermionic extension of the effective action of the bosonic string in arbitrary spacetime dimension D. The theory is invariant under pseudo-supersymmetry transformations up to the quadratic fermion order, which is sufficient in order to be able to derive Killing spinor equations in bosonic backgrounds, and hence to define BPS type solutions determined by a system of first-order equations. The pseudo-supersymmetric theory can be extended by coupling it to a Yang-Mills pseudo-supermultiplet. This also allows us to construct “α^′ corrections” involving quadratic curvature terms. An exponential dilaton potential term, associated with the conformal anomaly for a bosonic string outside its critical dimension, can also be pseudo-supersymmetrised.     

The interacting gauge covariant bosonic string

The interaction of the gauge covariant open bosonic string is presented in oscillator form, and in functional form. In the latter form, the string is described by commuting and anticommuting coordinates. The interaction is essentially the condition that the strings should overlap.     

A relation between tree amplitudes of closed and open strings

We derive a formula which expresses any closed string tree amplitude in terms of a sum of the products of appropriate open string tree amplitudes. This formula is applicable to the heterotic string as well as to the closed bosonic string and type II superstrings. In particular, we demonstrate its use by showing how to write down, without any direct calculation, all four-point heterotic string tree amplitudes with massless external particles.     

Off-shell structure of the string sigma model

The off-shell structure of the string sigma model is investigated. In the open bosonic string, nonperturbative effects appear to depend crucially on the regularization scheme. A scheme retaining the notion of string width reproduces the structure of Witten's string field theory.     

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.     

Non-commutative geometry and the closed bosonic string

We propose an action for an interacting closed bosonic string. Our formalism relies heavily on ideas discussed by Witten for the open bosonic string. We also obtain the gauge fixed quantum action for the fully interacting open bosonic string.     

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.     

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.     

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.     

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.     

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.     

Conformal gravity and the bosonic string

We show that the Callan et al. effective equations of motion for the bosonic closed string in a non-trivial background may not be derived only from the bosonic part of theN=1 supergravity action of Manton and Chapline, but also from just a general conformally invariant theory of gravity. In our scheme the invariance under gauge transformations of the antisymmetric tensor field turns out to be a consequence of the metricity condition.