Off‐shell Amplitudes in Superstring Theory

Computing the renormalized masses and S‐matrix elements in string theory, involving states whose masses are not protected from quantum corrections, requires defining off‐shell amplitude with certain factorization properties. While in the bosonic string theory one can in principle construct such an amplitude from string field theory, there is no fully consistent field theory for type II and heterotic string theory. In this paper we give a practical construction of off‐shell amplitudes satisfying the desired factorization property using the formalism of picture changing operators. We describe a systematic procedure for dealing with the spurious singularities of the integration measure that we encounter in superstring perturbation theory. This procedure is also useful for computing on‐shell amplitudes, as we demonstrate by computing the effect of Fayet‐Iliopoulos D‐terms in four dimensional heterotic string theory compactifications using this formalism.     

Gaussian quantization of the Klein-Gordon equation in variational derivatives and secondary quantization of a Boson string

A Klein-Gordon equation in variational derivatives is proposed for the quantum theory of a Boson string in a fixed gauge. By using this equation a secondary quantization is constructed for a Boson string in the functional space of string functionals that are square summable in a countable additive Gaussian measure.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 32–36, January, 1990.The author is grateful to V. S. Vladimirov and I. V. Volovich for useful discussions of the quantum and field theories of a boson string.     

26-Dimensional string from 4-dimensional geometry

A study of 4-dimensional volume preserving covariant changes of the metric leads directly to string theory in 26 dimensions. In any conformally invariant theory of such metric distortions, a new principle of relativity is shown to imply that the maximum number of independent components of the distortion tensor is 26. Within the simplest such theory allowing metric compatible spaces as trivial solutions, we show that this maximum is realized by a solution equivalent to the 26-dimensional bosonic string.This research was supported in part by U. S. Department of Energy grant number DE-FG05-85ER-40219.     

M-theory conifolds

Seven manifolds of G2 holonomy provide a bridge between M-theory and string theory, via Kaluza-Klein reduction to Calabi-Yau six manifolds. We find first-order equations for a new family of G2 metrics D7, with S3 x S3 principal orbits. These are related at weak string coupling to the resolved conifold, paralleling earlier examples B7 that are related to the deformed conifold, allowing a deeper study of topology change and mirror symmetry in M-theory. The D7 metrics' nontrivial parameter characterizes the squashing of an S3 bolt, which limits to S2 at weak coupling. In general the D7 metrics are asymptotically locally conical, with a nowhere-singular circle action.     

Tensor constructions of open string theories (I) foundations

The possible tensor constructions of open string theories are analyzed from first principles. To this end the algebraic framework of open string field theory is clarified, including the role of the homotopy associative A_∞ algebra, the odd symplectic structure, cyclicity, star conjugation, and twist. It is also shown that two string theories are off-shell equivalent if the corresponding homotopy associative algebras are homotopy equivalent in a strict sense.It is demonstrated that a homotopy associative star algebra with a compatible even bilinear form can be attached to an open string theory. If this algebra does not have a space-time interpretation, positivity and the existence of a conserved ghost number require that its cohomology is at degree zero, and that it has the structure of a direct sum of full matrix algebras. The resulting string theory is shown to be physically equivalent to a string theory with a familiar open string gauge group.     

Cosmic Strings and Domain Walls in a Scale-Covariant Theory of Gravitation

Axially symmetric space-time is considered in the presence of cosmic string source and thick domain walls in the frame work of a scale-covariant theory of gravitation. A relation between metric potential is assumed to get a determinate solution of the field equations of this theory. In this particular case, it is observed that the geometric (Nambu) string p-string (Takabayasi string) and Reddy string do not survive. It is also seen that the stiff (self-gravitating) domain walls do not exist in this theory.     

Are crossings of energy levels and charge exchange really quantum phenomena?

In this Letter a recently proposed gravity dual of noncommutative Yang-Mills theory is derived from the relations between closed string moduli and open string moduli recently suggested by Seiberg and Witten. The only new input one needs is a simple form of the running string tension as a function of energy. This derivation provides convincing evidence that string theory integrates with the holographical principle and demonstrates a direct link between noncommutative Yang-Mills theory and holography.     

A matrix model for 2D quantum gravity defined by Causal dynamical triangulations

A novel continuum theory of two-dimensional quantum gravity, based on a version of Causal Dynamical Triangulations which incorporates topology change, has recently been formulated as a genuine string field theory in zero-dimensional target space [J. Ambjørn, R. Loll, Y. Watabiki, W. Westra, S. Zohren, arXiv: 0802.0719]. Here we show that the Dyson–Schwinger equations of this string field theory are reproduced by a cubic matrix model. This matrix model also appears in the so-called Dijkgraaf–Vafa correspondence if the superpotential there is required to be renormalizable. In the spirit of this model, as well as the original large-N expansion by 't Hooft, we need no special double-scaling limit involving a fine tuning of coupling constants to obtain the continuum quantum-gravitational theory. Our result also implies a matrix model representation of the original, strictly causal quantum gravity model.     

Airy Equation for the Topological String Partition Function in a Scaling Limit

We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi–Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.     

Grassmannian and String Theory

The infinite-dimensional Grassmannian manifold contains moduli spaces of Riemann surfaces of all genera. This well known fact leads to a conjecture that non-perturbative string theory can be formulated in terms of the Grassmannian. We present new facts supporting this hypothesis. In particular, it is shown that Grassmannians can be considered as generalized moduli spaces; this statement permits us to define corresponding “string amplitudes” (at least formally). One can conjecture that it is possible to explain the relation between non-perturbative and perturbative string theory by means of localization theorems for equivariant cohomology; this conjecture is based on the characterization of moduli spaces, relevant to string theory, as sets consisting of points with large stabilizers in certain groups acting on the Grassmannian. We describe an involution on the Grassmannian that could be related to S-duality in string theory. Received: 19 December 1996 / Accepted: 27 March 1998     

Slow evolution of nearly-degenerate extremal surfaces

It was conjectured recently that the string worldsheet theory for the fast moving string in AdS times a sphere becomes effectively first order in the time derivative and describes the continuous limit of an integrable spin chain. In this paper we will try to make this statement more precise. We interpret the first order theory as describing the long term evolution of the tensionless string perturbed by a small tension. The long term evolution is a Hamiltonian flow on the moduli space of periodic trajectories. It should correspond to the renormgroup flow on the field theory side.     

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.     

Understanding fields using strings: A review

In addition to being a prime candidate for a fundamental unified theory of all interactions in nature, string theory provides a natural setting to understand gauge field theories. This is linked to the concept of ‘D-branes’: extended, solitonic excitations of string theory which can be studied using techniques of string theory and which support gauge fields localized along their world-volumes. It follows that the techniques of string theory can be very useful even for those particle physicists who are not specifically interested in unification and/or quantum gravity. In this talk I attempt to review how strings help us to understand fields. The discussion is restricted to 3+1 spacetime dimensions.     

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.     

Summations over equilaterally triangulated surfaces and the critical string measure

We propose a new approach to the summation over dynamically triangulated Riemann surfaces which does not rely on properties of the potential in a matrix model. Instead, we formulate a purely algebraic discretization of critical string path integral. This is combined with a technique which assigns to each equilateral triangulation of a two-dimensional surface a Riemann surface defined over a certain finite extension of the field of rational numbers, i.e. an arthmetic surface. Thus we establish a new formulation in which the sum over randomly triangulated surfaces defines an invariant measure on the moduli space of arithmetic surfaces. It is shown that because of this it is far from obvious that this measure for large genera approximates the measure defined by the continuum theory, i.e. Liouville theory or critical string theory. In low genus this subtlety does not exist. In the case of critical string theory we explicity compute the volume of the moduli space of arithmetic surfaces in terms of the modular height function and show that for low genus it approximates correctly the continuum measure. We also discuss a continuum limit which bears some resemblance with a double scaling limit in matrix models.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098Supported in part by NSF grant PHY85-15857     

On the universality of string theory

String theory is accused by some of its critics to be a purely abstract mathematical discipline, having lost the contact to the simple yet deeply rooted questions which physics provided until the beginning of this century. We argue that, in contrary, there are indications that string theory might be linked to a fundamental principle of a quantum computational character. In addition, the nature of this principle can possibly provide some new insight into the question of universality of string theory (string theory as the “theory of everything”).     

Two-Dimensional Topological Strings Revisited

The topological string of the type A with a two-dimensional target space is studied, an explicit formula for the string partition function is found and the target space field theory reproducing this partition function is proposed. This field theory has an infinite set of additional deformations overlooked by the standard definition of the topological string. It can be in turn coupled to gravity, thereby realizing the “worldsheets for worldsheets” idea. We also exhibit the wave function nature of the string partition function and suggest a new relation to quantum integrable systems.     

Homotopy Classification of Bosonic String Field Theory

We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.     

Stochastic confinement and dimensional reduction (II). Three-dimensional SU(2) lattice gauge theory

We study 3-dimensional SU(2) lattice gauge theory with respect to dimensional reduction. By Monte Carlo calculations we find that this reduction is valid to a good approximation (within ≈10%). The adjoint string tension is found to scale approximately. We also compare the adjoint string tension with a string theory.