The polyakov path integral over bordered surfaces

The geometrical approach to the functional integral over Faddeev-Popov ghost fields is developed and applied to construct the BRST extension of the off-shell closed string amplitudes in the constant curvature gauge. In this gauge the overlap path integral for off-shell amplitudes is evaluated. It leads to the nonlocal sewing procedure generating all off-shell amplitudes from the cubic interaction vertex. The general scheme of the reconstruction of a covariant closed string field theory from the off-shell amplitudes is discussed within the path integral framework.     

Gauge invariance based on the extrinsic geometry in the rigid string

The string model with the extrinsic curvature is studied which is a gauge invariant field theory with higher order derivatives. We present an equivalent action without any higher order derivatives which keeps the gauge invariance. We point out the difficulty caused by the second class constraints in Dirac's canonical method. Following a new method for dynamical systems with second class constraints, we construct an equivalent model which has no second class constrants but as a new gauge invariance. This gauge invariance guarantees the equivalence between the original model and the new one. We show that the model can be quantized in this formalism. We find the unitarity violation of the model.     

Antisymmetric string actions

An action is presented for the free bosonic string on external flat space in terms of an antisymmetric second-rank string background tensor which is classically equivalent to the Nambu-Goto action. Both action and field equations are entirely described in terms of 2D world-sheet forms, without any reference to a 2D metric tensor background. The analysis of its canonical formulation shows how the quadratic Virasoro constraints are generated in this case and what their connection with the Bianchi identities are. Since in the orthonormal gauge the reduced action coincides with the standard one, it has the same critical dimension D = 26. The existence of an interaction term of a purely geometric structure stemming in the extrinsic curvature is pointed out. Its action and the new string field equations are then derived. This polynomial antisymmetric string action is uniformly generalized in order to describe d < D-dimensional extended objects in D-dimensional flat space.     

The Effect of Spatial Curvature in Scalar-Tensor Theory

We investigate the effect of the spatial curvature in extra six dimensions of ten dimensional scalar-tensor theory. As a scalar-tensor theory both string theory effective action and Brans-Dicke type action are considered. For Brans-Dicke type action with positive spatial curvature (k=1) we obtain accelerating expansion of the spacetime for specific value of the Brans-Dicke parameter ω. The value, however, is negative and far from the present universe which requires big number.     

Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics

In conventional gauge theory, a charged point particle is described by a representation of the gauge group. If we propagate the particle along some path, the parallel transport of the gauge connection acts on this representation. The Lagrangian density of the gauge field depends on the curvature of the connection which can be calculated from the holonomy around (infinitesimal) loops. For Abelian symmetry groups, say G=U(1), there exists a generalization, known as p-form electrodynamics, in which (p−1)-dimensional charged objects can be propagated along p-surfaces and in which the Lagrangian depends on a generalized curvature associated with (infinitesimal) closed p-surfaces. In this article, we use Lie 2-groups and ideas from higher category theory in order to formulate a discrete gauge theory which generalizes these models at the level p=2 to possibly non-Abelian symmetry groups. An important feature of our model is that it involves both parallel transports along paths and generalized transports along surfaces with a non-trivial interplay of these two types of variables. Our main result is the geometric picture, namely the assignment of non-Abelian quantities to geometrical objects in a coordinate free way. We construct the precise assignment of variables to the curves and surfaces, the generalized local symmetries and gauge invariant actions and we clarify which structures can be non-Abelian and which others are always Abelian. A discrete version of connections on non-Abelian gerbes is a special case of our construction. Even though the motivation sketched so far suggests applications mainly in string theory, the model presented here is also related to spin foam models of quantum gravity and may in addition provide some insight into the role of centre monopoles and vortices in lattice QCD.     

Gauge unification in type I/I′ models

We discuss whether the (MSSM) unification of gauge couplings can be accommodated in string theories with a low (TeV) string scale. This requires either power law running of the couplings or logarithmic running extremely far above the string scale. In both cases it is difficult to arrange for the multiplet structure to give the MSSM result. For the case of power law running there is also enhanced sensitivity to the spectrum at the unification scale. For the case of logarithmic running there is a fine tuning problem associated with the light closed string Kaluza Klein spectrum which requires gauge mediated supersymmetry breaking on the “visible” brane with a dangerously low scale of supersymmetry breaking. Evading these problems in low string scale models requires a departure from the MSSM structure, which would imply that the success of gauge unification in the MSSM is just an accident.     

On second-quantized open superstring theory

The SO(32) theory, in the limit where it is an open superstring theory, is completely specified in the light-cone gauge as a second-quantized string theory in terms of a “matrix string” model. The theory is defined by the neighborhood of a 1 + 1-dimensional fixed point theory, characterized by an Abelian gauge theory with type IB Green-Schwarz form. Non-orientability and SO(32) gauge symmetry arise naturally, and the theory effectively constructs an orientifold projection of the (weakly coupled) matrix type IIB theory (also discussed herein). The fixed point theory is a conformal field theory with boundary, defining the free string theory. Interactions involving the interior of open and closed strings are governed by a twist operator in the bulk, while string endpoints are created and destroyed by a boundary twist operator.     

Covariant field theory of the compactified closed bosonic string

We covariantly first-quantize, via the BRST approach, the closed bosonic string compactified on a torus — in particular the 18-dimensional theory with E₈ × E₈ gauge bosons. Further, we give the corresponding free field theory. Thus the model is ready for the introduction of string interactions, and may be very useful for the study of gauge interactions in string theories.     

The field configurations of a static adjoint source in SU(2) lattice gauge theory

We study the spatial distribution and orientation of the colour fields around a static adjoint source using lattice gauge theory simulations in the pure gauge approximation. This configuration is not of immediate application to experiment although from a theoretical viewpoint it is the “hydrogen atom” of pure gauge QCD. We concentrate on the low-lying states of angular momentum J = 1 which are in the T₁₊ and T₁₋ representations of the cubic symmetry group. Sum rules relating integrals over the fields to the mass of the state are evaluated. The conclusion is that the colour fields are like those from a rough string rotating around the source.     

Classical dynamics of the rigid string from the Willmore functional

A new approach for investigating the classical dynamics of the relativistic string model with rigidity is proposed. It is based on the embedding of the string world surface into a space of constant curvature. It is shown that the rigid string in flat space-time is described by the Euler-Lagrange equation for the Willmore functional in a space-time of constant curvature K = −γ/(2α), where γ and α are constants in front of the Nambu-Goto term and the curvature term in the rigid string action, respectively. For simplicity the Euclidean version of the rigid string in three-dimensional space-time is considered. The Willmore functional (the action for the “Willmore string”) is obtained by dropping the Nambu-Goto term in the Polyakov-Kleinert action for the rigid string. Such a “reduction” of the rigid string model would be useful, for example, by applying some results about the Nambu-Goto string dynamics in the de Sitter universe to the rigid string model in the Minkowski space-time. It also allows us to use numerous mathematical results about Willmore surfaces in the context of the physical problem.     

Quenched string field theory

We construct a toy model of Witten's open string field theory by truncating the Virasoro group to its SU(1,1) subgroup. The string field is given in terms of finite-dimensional matrices, which satisfy a non-trivial BRST cohomology. The string gauge group is found to be SO(3). Finally, we perform the gauge fixing of the action, finding an explicit formula for calculating the partition function.     

Repulsive Gravity in the Very Early Universe

I present two examples in which the curvature singularity of a radiation-dominated Universe is regularized by (a) the repulsive effects of spin interactions, and (b) the repulsive effects arising from a breaking of the local gravitational gauge symmetry. In both cases the collapse of an initial, asymptotically flat state is stopped, and the Universe bounces towards a state of decelerated expansion. The emerging picture is typical of the pre-big bang scenario, with the main difference that the string cosmology dilaton is replaced by a classical radiation fluid, and the solutions are not duality-invariant.     

Double field formulation of Yang-Mills theory

Based on our previous work on the differential geometry for the closed string double field theory, we construct a Yang-Mills action which is covariant under O(D,D) T-duality rotation and invariant under three-types of gauge transformations: non-Abelian Yang-Mills, diffeomorphism and one-form gauge symmetries. In double field formulation, in a manifestly covariant manner our action couples a single O(D,D) vector potential to the closed string double field theory. In terms of undoubled component fields, it couples a usual Yang-Mills gauge field to an additional one-form field and also to the closed string background fields which consist of a dilaton, graviton and a two-form gauge field. Our resulting action resembles a twisted Yang-Mills action.     

Higher impurity AdS/CFT correspondence in the near-BMN limit

The pp-wave/BMN limit of the AdS/CFT correspondence has exposed the Maldacena conjecture to a new regimen of direct tests. In one line of pursuit, finite-radius curvature corrections to the Penrose limit (which appear in inverse powers of the string angular momentum J) have been found to induce a complicated system of interaction perturbations to string theory on the pp-wave; these have been successfully matched to corresponding corrections to the BMN dimensions of N=4 super-Yang–Mills (SYM) operators to two loops in the 't Hooft coupling λ. This result is tempered by a well-established breakdown in the correspondence at three loops. Notwithstanding the third-order mismatch, we proceed with this line of investigation by subjecting the string and gauge theories to new and significantly more rigorous tests. Specifically, we extend our earlier results at O(1/J) in the curvature expansion to include string states and SYM operators with three worldsheet or R-charge impurities. In accordance with the two-impurity problem, we find a perfect and intricate agreement between both sides of the correspondence to two-loop order in λ and, once again, the string and gauge theory predictions fail to agree at third order.     

Gauge fields and interactions in matrix string theory

It is shown that all possible N sheeted coverings of the cylinder are contained in type IIA matrix string theory as non-trivial gauge field configurations. Using these gauge field configurations as backgrounds the large N limit is shown to lead to the type IIA conformal field theory defined on the corresponding Riemann surfaces. The sum over string diagrams is identified as the sum over non-trivial gauge backgrounds of the SYM theory.     

Spreading of gauge coupling constants in minimal LR models

Minimal left-right (LR) models are often inconsistent with gauge unification at the Planck scale, as they imply too large a Weinberg angle. In (E₆) superstring-inspired models true gauge unification is nit required, and the absence of unification of coupling constants might be an indication of non-zero (string) renormalization effects. Here we perform a quantitative analysis of the necessary spreading of the gauge coupling constants in order to accommodate a realistic value of the Weinberg angle in minimal LR models motivated by the string.     

Gauge fixing in fully gauge-invariant field theory of closed bosonic and Neveu-Schwarz strings

The gauge fixing procedure is reanalyzed in our fully gauge-invariant closed bosonic and Neveu-Schwarz string field theory which does not have any constraint on string functionals and gauge parameters. The relations to other formulations are clarified; in particular, it is shown that our theory recovers other formulation with constraints L₊ − L₋ = 0 after partial gauge fixing but without any truncation. Complete gauge fixing is also made and the expected propagator is obtained. The constraint L₊ − L₋ = 0 appears as a field equation in our formulation.     

Generalized roughening transition and its effect on the string tension

The well-understood roughening transition of an interface in the d = 3 Ising model implies an essential singularity in the string tension of the dual Z₂ gauge model. The roughening transition corresponds to the delocalization of the string due to strong long-wavelength fluctuations, and this reformulation can be generalized to other gauge groups and to d = 4 also. It is not a deconfining transition - it is expected to occur deep in the confining region - but its presence would raise serious questions about the continuation of strong coupling expansions of the tension beyond this point. In this paper predictions on the roughening transition are confronted with the available information on the string tension for different gauge groups in three dimensions.     

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.     

Gauge coupling unification in realistic free-fermionic string models

We discuss the unification of gauge couplings within the framework of a wide class of realistic free-fermionic string models which have appeared in the literature, including the flipped SU(5), SO(6) × SO(4), and various SU(3) × SU(2) × U(1) models. If the matter spectrum below the string scale is that of the Minimal Supersymmetric Standard Model (MSSM), then string unification is in disagreement with experiment. We therefore examine several effects that may modify the minimal string predictions. First, we develop a systematic procedure for evaluating the one-loop heavy string threshold corrections in free-fermionic string models, and we explicitly evaluate these corrections for each of the realistic models. We find that these string threshold corrections are small, and we provide general arguments explaining why such threshold corrections are suppressed in string theory. Thus heavy thresholds cannot resolve the disagreement with experiment. We also study the effect of non-standard hypercharge normalizations, light SUSY thresholds, and intermediate-scale gauge structure, and similarly conclude that these effects cannot resolve the disagreement with low-energy data. Finally, we examine the effects of additional color triplets and electroweak doublets beyond the MSSM. Although not required in ordinary grand unification scenarios, such states generically appear within the context of certain realistic free-fermionic string models. We show that if these states exist at the appropriate thresholds, then the gauge couplings will indeed unify at the string scale. Thus, within these string models, string unification can be in agreement with low-energy data.