Ward identities of W∞ symmetry and higher-genus amplitudes in 2D string theory

The Ward identities of the W_∞ symmetry in two-dimensional string theory in the tachyon background are studied in the continuum approach. We consider amplitudes different from 2D string ones by the external leg factor and derive the recursion relations among them. The recursion relations have non-linear terms which give relations among the amplitudes defined on different genus. The solutions agree with the matrix model results even in higher genus. We also discuss the differences of the roles of the external leg factor between the c_M = 1 model and the c_m < 1 model.     

Discrete-state moduli of string theory from the c = 1 matrix model

We propose a new formulation of the space-time interpretation of the c = 1 matrix model. Our formulation uses the well-known leg-pole factor that relates the matrix model amplitudes to that of the 2-dimensional string theory, but includes fluctuations around the Fermi vacuum on both sides of the inverted harmonic oscillator potential of the double-scaled model, even when the fluctuations are small and confined entirely within the asymptotes in the phase plane. We argue that including fluctuations on both sides of the potential is essential for a consistent interpretation of the leg-pole transformed theory as a theory of space-time gravity. We reproduce the known results for the string theory tree-level scattering amplitudes for flat space and linear dilaton background as a special case. We show that the generic case corresponds to more general space-time backgrounds. In particular, we identify the parameter corresponding to background metric perturbation in string theory (black-hole mass) in terms of the matrix model variables. Possible implications of our work for a consistent non-perturbative definition of string theory as well as for quantized gravity and black-hole physics are discussed.     

Cohomological Yang–Mills theories on Kähler 3-folds

We study topological gauge theories with N_c=(2,0) supersymmetry based on stable bundles on general Kähler 3-folds. In order to have a theory that is well defined and well behaved, we consider a model based on an extension of the usual holomorphic bundle by including a holomorphic 3-form. The correlation functions of the model describe complex 3-dimensional generalizations of Donaldson–Witten type invariants. We show that the path integral can be written as a sum of contributions from stable bundles and a complex 3-dimensional version of Seiberg–Witten monopoles. We study certain deformations of the theory, which allow us to consider the situation of reducible connections. We shortly discuss situations of reduced holonomy. After dimensional reduction to a Kähler 2-fold, the theory reduces to Vafa–Witten theory. On a Calabi–Yau 3-fold, the supersymmetry is enhanced to N_c=(2,2). This model may be used to describe classical limits of certain compactifications of (matrix) string theory.     

Heisenberg groups and noncommutative fluxes

We develop a group-theoretical approach to the formulation of generalized abelian gauge theories, such as those appearing in string theory and M-theory. We explore several applications of this approach. First, we show that there is an uncertainty relation which obstructs simultaneous measurement of electric and magnetic flux when torsion fluxes are included. Next, we show how to define the Hilbert space of a self-dual field. The Hilbert space is Z₂-graded and we show that, in general, self-dual theories (including the RR fields of string theory) have fermionic sectors. We indicate how rational conformal field theories associated to the two-dimensional Gaussian model generalize to (4k + 2)-dimensional conformal field theories. When our ideas are applied to the RR fields of string theory we learn that it is impossible to measure the K-theory class of a RR field. Only the reduction modulo torsion can be measured.     

On loop corrections to string theory effective actions

We make some comments concerning the structure of loop corrections to the effective action (EA) for massless fields of a string. The singular part of the α′→0 limit of the one-loop EA in the open (super)string theory is studied and is shown to be in correspondence with the ultraviolet divergent part of the one-loop effective action in the (super) Yang-Mills theory. In particular, we reproduce the known result about the absence of Λ^D−4 F_μν² one-loop infinities in D = 26 Yang-Mills theory starting from the open Bose string theory. We also discuss the path integral representation for EA (EA = generalized partition function for the σ-model) and use it to compute the open string theory EA on the disc and the annulus.     

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.     

Nontrivial critical behaviour in a lattice model of random surfaces

A model of “planar random surfaces without spikes” on hypercubical lattices was introduced some years ago as a discretization of quantum string theory. We review some general properties of this model and present results from a Monte Carlo study of its critical behaviour in d = 4, 8 and 10 dimensions. In d = 4 dimensions we find a Hausdorff dimension d_H ≈ 4 and an anomalous dimensions η ≈ 1. These critical exponents imply a deviation from mean field theory in contrast to other lattice random surface models. Furthermore, we find evidence for mean field behaviour in 8 and 10 dimensions, indicating an upper critical dimension d_c^u ⩽ 8.     

On Weyl invariance conditions in string theory coupled with two-dimensional gravity

The unified theory of string and two-dimensional quantum gravity is considered. We introduce nontrivial dynamics for the two-dimensional metric g_μν from the very beginning and calculate the path integral over the string coordinates and g_μν without taking into account the order of integrations. Throughout the paper we use two different kinds of gauges - the covariant one of the harmonic type and also the conformal gauge, where the original (D + 1)-dimensional sigma model with quantum gravity becomes the (D+2)-dimensional sigma model on the classical background of g_μν The general symmetries of the theory consist in the reparametrizations of the target space coordinates, in the conformal transformations of the metric and in the usual 2d diffeomorphisms. These symmetries do not disturb the structure of the background fields in the (D+2) -dimensional formulation. On the other hand the related arbitrariness of the renormalization does not affect the qualitative structure of the loop contributions to the Weyl anomaly. In the theory with quantum gravity the parameter a′ does not play as the parameter of the loop expansion. That is why the one-loop conditions of the Weyl invariance differs from the well known effective equations which arise in the standard approach when g_μν is not quantized simultaneously with the string coordinates. Therefore, despite the new conditions of the Weyl invariance for the background fields are different from the standard effective equations, our result does not contradict to the standard approach. The new one-loop conditions of the Weyl invariance are much more complicated and contain the higher derivatives in the dilaton sector.     

SU(2) Lattice gauge theory in (2+1)D

Cluster expansion methods are applied to theSU(2) lattice gauge model in (2+1) dimensions. Strong-coupling series are calculated for the vacuum energy per site, the axial string tension, and the scalar mass gap; while ELCE approximants are used to estimate the string tension beyond its roughening transition. The simple scaling behaviour expected of this super-renormalizable theory is clearly seen, and we estimate that in the continuum limit the string tension σ～(0.14±0.01)g ⁴, while the mass gapM _s ～(2.2±0.25)g ². More accurate Monte Carlo simulations are needed to check the universality between the Hamiltonian and Euclidean versions of this model.     

Non-linear sigma model in 1 + 1 dimensions,supergravity and the spinning string

The non-linear σ supersymmetric model in 1 + 1 dimensions is coupled to supergravity. When we quantize the theory, the matter fields acquire mass dynamically, which leads to the breaking of the Weyl invariance. This fact implies that the two-point functions of the gravitino and the graviton, obtained from the effective action, become non-trivial. Particularly, the two-point function of the gravitino presents a pole in the infrared region. We conjecture that this pole is related to the confinement of all supersymmetric degrees of freedom of the theory. If we restrain the integration domain of x₁ to a finite length L (breaking all invariances of the theory), there appears a mass term in the two-point function of the gravitino, which decreases exponentially with L. In this context we relate this model with that of the supersymmetric string and define a stability criterion for the latter.     

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.     

Model building on asymmetric Z3 orbifolds: Non-supersymmetric models

Four-dimensional string models arising in the asymmetric Z₃ orbifold compactifications of the heterotic string are studied. A mechanism for supersymmetry breaking that gives rise to chiral models in four dimensions is presented, and some typical models are discussed. A formalism for calculating one-loop partition functions in Z₃ models is developed. One partition function is constructed that may correspond to a non-supersymmetric, tachyon-free theory, with a vanishing cosmological constant as a consequence of Atkin-Lehner symmetry. The negative result of a search for the model corresponding to this partition function is reported.     

A string calculation of the Kähler potentials for moduli of ZN orbifolds

We present a method for calculating the Kähler potentials of the moduli of Z_N orbifolds directly from string theory. The explicit Kähler potentials associated with b_(1,1) and b_(1,2) moduli are given for any (2,0) symmetric Z_N orbifold. These results are exact at the string tree level.     

Thermodynamics of SU(3) lattice gauge theory

The pressure and the energy density of the SU(3) gauge theory are calculated on lattices with temporal extent N_τ = 4, 6 and 8 and spatial extent N_σ = 16 and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times T_c we observe a 15% deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent N_τ = 8 and 12. At the corresponding critical couplings the string tension is calculated on 32⁴ lattices to fix the temperature scale. An extrapolation to the continuum limit yields T_c/√σ = 0.629(3). We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension. These observables suggest that the temperature dependent running coupling remains large even at T ≅ 5T_c. For the spatial string tension we find √σ_s/T=0.566(13)g²2(T) with g² (5T_c) ≅ 1.5.     

Large N phases of chiral QCD2

A matrix model is constructed which describes a chiral version of the large NU (N) gauge theory on a two-dimensional sphere of area A. This theory has three separate phases. The large area phase describes the associated chiral string theory. An exact expression for the free energy in the large area phase is used to derive a remarkably simple formula for the number of topologically inequivalent covering maps of a sphere with fixed branch points and degree n.     

Supersymmetry breaking for the observable sector in superstring models

We discuss the supersymmetry breaking in four-dimensional supergravity models from superstrings including perturbative or non-perturbative string σ-model corrections. It is found that various soft supersymmetry breaking terms can appear with values of the order ofm _3/2 even at the tree level of effective field theory and of string theory.     

Field theory of interacting open superstrings in fermionic ghost representation

The field theory of interacting open superstring in the fermionic ghost representation based on anticommuting and commuting ghosts, corresponding respectively to world sheet bosonic x_μ and fermionic ψ_μ coordinates, is presented. We have to revise once more the field theory of the free Ramond (R) string and starting from a general algebraic point of view we obtain that the number of degrees of freedom in the R and NS (Neveu-Schwarz) sectors are equal, permitting us to construct a supersymmetric operator. We propose to solve a specific equation guaranteeing superinvariance in order to find the R-R-NS and NS-R-R vertices in the term of the NS-NS-NS vertex.     

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.