Off-shell string amplitudes and singular states in bosonic string theory

The off-shell amplitudes with N external scalar particles are investigated. The dependence of the momenta is emphasized.     

Quantization of degenerate vacua and symmetry breaking in string theory

We consider the implications of the existence of continuous families of classically degenerate vacua in constructing quantum string theory in compact toroidal spacetimes. We show that in the presence of unbroken supersymmetry when quantum corrections do not lift the degeneracy, symmetries of particular compactifications can be broken by the presence of the neighbouring vacua. We explicitly demonstrate this in case of the heterotic string where the gauge group SO(32) or E₈×E₈ breaks down to U(1)¹⁶ due to neighbouring configurations of arbitrary Wilson lines.     

Hadronic density of states from string theory

We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nù?ez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of a Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM theory, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.     

High-energy zero-norm states and symmetries of string theory

High-energy limit of zero-norm states in the old covariant first quantized spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive infinitely many linear relations among the leading high-energy, fixed-angle behavior of four-point functions of different string states. As a result, ratios among all high-energy scattering amplitudes of four arbitrary string states can be calculated algebraically and the leading order amplitudes can be expressed in terms of that of four tachyons as conjectured by Gross in 1988. A dual calculation can also be performed and equivalent results are obtained by taking the high-energy limit of Virasoro constraints. Finally, we compute all high-energy scattering amplitudes of three tachyons and one massive state at the leading order by saddle-point approximation to verify our results.     

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.     

Cardy states as idempotents of fusion ring in string field theory

With some assumptions, the algebra between Ishibashi states in string field theory can be reduced to a commutative ring. From this viewpoint, Cardy states can be identified with its idempotents. The algebra is identified with the fusion ring for the rational conformal field theory and the group ring for the orbifold. This observation supports our previous observation that the boundary states satisfy a universal idempotency relation under the closed string star product.     

Matrix string theory

Via compactification on a circle, the matrix mode] of M-theory proposed by Banks et a]. suggests a concrete identification between the large N limit of two-dimensional N = 8 supersymmetric Yang-Mills theory and type IIA string theory. In this paper we collect evidence that supports this identification. We explicitly identify the perturbative string states and their interactions, and describe the appearance of D-particle and D-membrane states.     

Feigenbaum universality in string theory

Brane-like vertex operators, defining backgrounds with ghost-matter mixing in NSR superstring theory, play an important role in the world-sheet formulation of D-branes and M theory as creation operators for extended objects in the second quantized formalism. In this paper, we show that the dilaton beta function in ghost-matter mixing backgrounds becomes stochastic. The renormalization group (RG) equations in ghost-matter mixing backgrounds lead to non-Markovian Fokker-Planck equations whose solutions describe superstrings in curved space-times with brane-like metrics. We show that the Feigenbaum universality constant δ=4.669..., describing transitions from order to chaos in a huge variety of dynamical systems, appears analytically in these RG equations. We find that the appearance of this constant is related to the scaling of relative space-time curvatures at fixed points of the RG flow. In this picture, the fixed points correspond to the period doubling of Feigenbaum iteration schemes.     

Non-perturbative superpotentials in string theory

The non-perturbative superpotential can be effectively calculated in M-theory compactification to three dimensions on a Calabi-Yau four-fold X. For certain X, the superpotential is identically zero, while for other X, a non-perturbative superpotential is generated. Using F-theory, these results carry over to certain Type IIB and heterotic string compactifications to four dimensions with N = 1 supersymmetry. In the heterotic string case, the non-perturbative superpotential can be interpreted as coming from space-time and world-sheet instantons; in many simple cases contributions come only from finitely many values of the instanton numbers.     

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.     

Exotic branes in string theory

Besides the familiar D-branes, string theory contains a vast number of other non-perturbative objects. While a complete classification is lacking, many of these objects are related to each other through various dualities. Codimension two objects play a special role, because their charges are no longer additive but are instead expressed in terms of holonomies of scalar fields, which is given by an element of the relevant duality group. In this paper we present a detailed exposition of these “exotic” objects, the charges they carry, and their connection to non-geometric compactifications. Despite the name “exotic branes”, these objects are in fact ubiquitous in string theory, as they can automatically appear when describing bound states of conventional branes, and as such may be of particular importance in describing the microscopic degrees of freedom of black holes.     

Small instantons in string theory

A long-standing puzzle about the heterotic string has been what happens when an instanton shrinks to zero size. It is argued here that the answer at the quantum level is that an extra SU(2) gauge symmetry appears that is supported in the core of the instanton. Thus in particular the quantum heterotic string has vacua with higher rank than is possible in conformal field theory. When k instantons collapse at the same point, the enhanced gauge symmetry is Sp(k). These results, which can be tested by comparison to Dirichlet five-branes of Type I superstrings and to the ADHM construction of instantons, give the first example for the heterotic string of a non-perturbative phenomenon that cannot be turned off by making the coupling smaller. They have applications to several interesting puzzles about string duality.     

Tachyon dynamics in string theory

We summarize the recent developments in the study of time dependent solutions describing the rolling of a tachyon on a non-BPS D-brane system.