Non-polynomial Closed String Field Theory Research Articles

A universality in pp-waves

We discuss a universality property of any covariant field theory in space-time expanded around pp-wave backgrounds. According to this property the space-time lagrangian density evaluated on a restricted set of field configurations, called universal sector, turns out to be same around all the pp-waves, even off-shell, with same transverse space and same profiles for the background scalars. In this paper we restrict our discussion to tensorial fields only. In the context of bosonic string theory we consider on-shell pp-waves and argue that universality requires the existence of a universal sector of world-sheet operators whose correlation functions are insensitive to the pp-wave nature of the metric and the background gauge flux. Such results can also be reproduced using the world-sheet conformal field theory. We also study such pp-waves in non-polynomial closed string field theory (CSFT). In particular, we argue that for an off-shell pp-wave ansatz with flat transverse space and dilaton independent of transverse coordinates the field redefinition relating the low energy effective field theory and CSFT with all the massive modes integrated out is at most quadratic in fields. Because of this simplification it is expected that the off-shell pp-waves can be identified on the two sides. Furthermore, given the massless pp-wave field configurations, an iterative method for computing the higher massive modes using the CSFT equations of motion has been discussed. All our bosonic string theory analyses can be generalised to the common Neveu-Schwarz sector of superstrings.

Algebra of higher antibrackets

We present a simplified description of higher antibrackets, generalizations of the conventional antibracket of the Batalin-Vilkovisky formalism. We show that these higher antibrackets satisfy relations that are identical to those of higher string products in non-polynomial closed string field theory. Generalization to the case of Sp(2) symmetry is also formulated.

Subcritical closed string field theory in less than 26 dimensions.

We construct the second quantized action for sub-critical closed string field theory with zero cosmological constant in dimensions $ 2 \leq D < 26$, generalizing the non-polynomial closed string field theory action proposed by the author and the Kyoto and MIT groups for $D = 26$. The proof of gauge invariance is considerably complicated by the presence of the Liouville field $\phi$ and the non-polynomial nature of the action. However, we explicitly show that the polyhedral vertex functions obey BRST invariance to all orders. By point splitting methods, we calculate the anomaly contribution due to the Liouville field, and show in detail that it cancels only if $D - 26 + 1 + 3 Q ^ 2 = 0 $, in both the bosonized and unbosonized polyhedral vertex functions. We also show explicitly that the four point function generated by this action reproduces the shifted Shapiro-Virasoro amplitude found from $c=1$ matrix models and Liouville theory in two dimensions. LATEX file.

Non-polynomial string field theory and reparametrization of strings

Reparametrization invariance of string amplitudes is closely related to the non-polynomial closed string field theory. We show that it is possible to formulate the terms of the non-polynomial action just by using the SL(2, C ) properties of the so-called “restricted vertices”. In this context we work out in detail the four point amplitude in the different channels in terms of the reparametrization parameters.

The finite gauge transformations in closed string field theory

The finite gauge transformations for the classical nonpolynomial closed string field theory are constructed by iteration of infinitesimal transformations. A simple rule for the determination of the coefficients of the arising series is found.

Gauge and general coordinate invariance in non-polynomial closed string field theory

An appropriate field configuration in non-polynomial closed string field theory is shown to correspond to a general off-shell field configuration in low-energy effective field theory. A set of string field theoretic symmetries that act on the fields in low-energy effective field theory as general coordinate transformation and antisymmetric tensor gauge transformation is identified. The analysis is carried out to first order in the fields; thus the symmetry transformations in string field theory reproduce the linear and the first non-linear terms in the gauge transformations in the low-energy effective field theory.

Some all-order classical solutions in non-polynomial closed string field theory

If a conformal field theory is perturbed by a nearly marginal operator of dimension ( 1 h, 1 h ), then, under certain conditions and for a certain value of the perturbing parameter, we get a new conformal field theory. Starting from a string field theory based on the original conformal field theory, we show how to construct a classical solution in this string field theory to all orders in h , which represents string field theory formulated around the perturbed conformal field theory. We also show that the equation of motion of string field theory forces us to have a time-dependent dilaton background of the form ax 0 to order h 3 , which compensates for the change in the central charge of the conformal field theory under the perturbation.

LOOP COUNTERTERMS AND VERTICES IN CLOSED STRING FIELD THEORY

Starting with the classical nonpolynomial closed string field theory, the quantum action is constructed by subtracting counterterms which cancel the overcounting of moduli space, and by adding loop vertices in such a way that no possible surfaces are missed. A counterterm that gives the correct one-string one-loop amplitude is constructed. The lowest order loop vertices are analyzed in the cases of genus one and two.

Non-polynomial closed string field theory: loops and conformal maps

Recently, we proposed the complete classical action for the non-polynomial closed string field theory, which succesfully reproduced all closed string tree amplitudes. (The action was simultaneously proposed by the Kyoto group). In this paper, we analyze the structure of the theory. We (a) compute the explicit conformal map for all g-loop, p-puncture diagrams, (b) compute all one-loop, two-puncture maps in terms of hyper-elliptic functions, and (c) analyze their modular structure. We analyze, but do not resolve, the question of modular invariance.

Anomalies in non-polynomial closed string field theory

The complete classical action for the non-polynomial closed string field theory was written down last year by the author and the Kyoto group. It successfully reproduces all closed string tree diagrams, but fails to reproduce modular invariant loop amplitudes. In this paper we show that the classical action is also riddled with gauge anomalies. Thus, the classical action is not really gauge invariant and fails as a quantum theory. The presence of gauge anomalies and the violation of modular invariance appear to be a disaster for the theory. Actually, this is a blessing in disguise. We show that by adding new non-polynomial terms to the action, we can simultaneously eliminate both the gauge anomalies and the modular-violating loop diagrams. We show this explicitly at the one loop level and also for an infinite class of p-puncture, genus- g amplitudes, making use of a series of non-trivial identities. The theory is thus an acceptable quantum theory. We comment on the origin of this strange link between local gauge anomalies and global modular invariance.

Nonpolynomial closed-string field theory.

Recently, we announced the construction of a new nonpolynomial closed-string field theory which successfully reproduced all $N$-point tree amplitudes, thus solving a long-standing problem. This action generalized the four-string tetrahedron interaction that we introduced earlier, which was required to derive the Shapiro-Virasoro model. However, we gave no derivation of the nonpolynomial action. In this paper we present the detailed analysis of its derivation. We calculate all nonpolynomial graphs up to eighth order and their coefficients, and even the coefficients of several infinite series of polyhedra. We use gauge invariance to calculate all coefficients. Because of an enormous redundancy created by a web of overconstrained equations, we have multiple checks that our coefficients are correctly calculated.

Nonpolynomial closed string field theory: Action and its gauge invariance

The nonpolynomial closed string field theory, which was proposed by Saadi and Kugo, Kunitomo and Suehiro, is presented in detail. The string interaction vertices possessing the string overlapping patterns of polyhedra are constructed explicitly. The action based on those vertices is given and proved to be gauge invariant. The tree level N-point amplitudes are shown to reproduce the dual amplitudes correctly.

Equations of motion in non-polynomial closed string field theory and conformal invariance of two dimensional field theories

We show that given a solution Ψ cl of the classical equation of motionin the non-polynomial closed string field theory proposed recently, we can construct a BRST charge Q ̂ B such that ( Q ̂ B ) 2 = 0 . This shows the connection between solutions of the equations of motion in closed string field theory and conformal invariance of two dimensional field theories.

Non-polynomial closed string field theory

Abstract A non-polynomial closed string field theory is presented in a complete form, in the framework recently proposed by Saadi and Zwiebach. All the string interaction vertices possessing string overlapping patterns of polyhedra are specified by very simple conditions. It is shown that the Feynman diagrams with these vertices correctly cover the whole moduli space at the tree level. The connection of this fact to the gauge invariance of the tree level action is also discussed.