Spin content of string models

A previous analysis of the spin content of the bosonic string is extended to other string models. For the case of the spinning string, the O(D − 1) representation counting functions are expanded in terms of GL (∞|∞) supergroup characters.     

Spin content of the bosonic string

A new form is derived for the generating function, χ^[λ](x) = Σ_n=0^∞xⁿχ_n^[λ], which counts the number of times, χ_n^[λ], that the irreducible O(D − 1) rotation group representation [λ] appears at the nth mass level for the bosonic string. The derivation goes through for arbitrary old spatial dimensions, D − 1 = 2v + 1. Simplifications of the results are noted for large v and the relation to a previously obtained formula for χ^[λ](x) is explained.     

Spin chains and channels with memory

In most studies of quantum channels, it is assumed that the errors in each use of the channel are independent. However, recent investigations of the effect of memory or correlations in error have led to speculation that nonanalytic behavior may occur in the capacity. Motivated by these observations, we connect the study of channels with correlated error to the study of many-body systems. This enables us to use many-body theory to solve some interesting models of correlated error. These models can display nonanalyticities analogous to quantum phase transitions.     

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.     

Closed string-open string transitions and Witten's string field theory

Using conformal mapping techniques, we obtain a new BRST invariant operator ϒ encoding in closed form transition amplitudes between open strings and closed strings. The residues of the closed string poles in the non-planar one-loop two-point diagram of Witten's string field theory are finite sums of products of these amplitudes.     

Beltrami parametrization and string theory

By introducing Beltrami differentials to describe the conformal structure of the worldsheet, we prove the factorization of two-dimensional diffeomorphisms and of the corresponding BRS symmetry which is relevant for the string theory. Weyl invariance appears as a fundamental symmetry of the problem. Factorization of the connected tree diagrams is proven.     

The NMSSM and string theory

We study the possibility of constructing the NMSSM from the heterotic string. String-derived NMSSMs are much more rare than MSSMs due to the extra requirement that there exist a light singlet which couples to the Higgs pairs. They share the common feature that the singlet self-interactions are typically suppressed, leading to either the “decoupling” or the Peccei–Quinn limit of the NMSSM. In the latter case, the spectrum contains a light pseudoscalar which may be relevant to the MSSM fine-tuning problem. We provide a Z₆${\mathbb{Z}}_6$ heterotic orbifold example of the NMSSM with approximate Peccei–Quinn symmetry, whose origin lies in the string selection rules combined with our choice of the vacuum configuration.     

Superconformal geometry and string theory

We give a formula for the determinant of the super Laplace operator in a holomorphic hermitian line bundle over a superconformal manifold. This is then used to obtain an expression for the fermion string measure.     

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.     

Spin waves in linear magnetic chains

We have calculated the time-dependent spin-spin correlation function for the classical Heisenberg chain by computer simulation at a series of temperatures. The results show clearly the existence in the non-ordered system of spin-wave excitations at sufficiently low temperatures.     

Introduction to string theory and conformal field theory

A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.     

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.     

Spin fluctuations in mixed magnetic chains

The dynamic response of ferro- and antiferromagnetically coupled Heisenberg chains containing impurities is calculated in the low temperature and small concentration limit. Particular attention is given to impurity induced effects in the inelastic neutron cross-section, and explicit expressions are given for spin-wave linewidths.     

Supersymmetrical dual string theory

It is proved that the physical states of the open-string sector of the ten-dimensional string theory form supersymmetry multiplets. The proof is achieved by first constructing a new formulation of the spectrum generating algebra, and then forming the supersymmetry operator (as well as associated operators) and demonstrating that it transforms as a spinor under Lorentz transformations and has the correct anticommutation relations. The results can be interpreted either in terms of a covariant formulation or in terms of a light-cone gauge formulation. In the former case certain formulas are not completely proved, although they are in the latter. When interpreted in four dimensions (by dimensional reduction) the string theory provides an interacting theory of an infinite number of massive representations of N = 4 supersymmetry involving particles of arbitrarily high spin.     

第六讲超弦理论与宇宙学的挑战

超弦理论从根本上改变了人们对时空的看法，时空在弦论中只是一种宏观体现．弦论中的非经典时空影响早期宇宙的发展，在一些观测宇宙学的实验中人们也许会发现弦论的效应，例如微波背景辐射的功率谱的反常．最近发现的暗能量也对弦论宇宙学提出了挑战．     

Conformal geometry and string field theory

The covariant perturbation theory rules that should arise from any gauge invariant string field theory, such as those proposed on the basis of BRST formalism, are set forth. The resulting path integral expressions naturally produce coordinate invariant densities on the moduli space of Riemann surfaces; these include the Koba-Nielsen amplitudes. The connection between string field theory and modular invariance is discussed, and it is proposed that future explorations in string field theory focus on coordinate invariant quantities on moduli space.