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1.
We point out that the coset space Diff S
1/ S
1 is a dense complex submanifold of the Universal Teichmüller Space S of compact Riemann spaces of genus g1. A holomorphic map of S into the inifinite dimensional Segal disk D
1 is constructed. This is the Universal analogue of the map of Teichmüller spaces into the Siegel disk provided by the period matrix. The Kähler potential for the general homogenous metric on Diff S
1/ S
1 is computed explicitly using the map into D
1. Some applications to string theory are discussed.This work was supported in part by the U.S. Department of Energy Contract No. DE-AC02-76ER13065 相似文献
2.
Given a gauge theory with gauge group G acting on a path space X, G and X being both infinite dimensional manifolds modelled on spaces of sections of vector bundles on a compact riemannian manifold without boundary, it is shown that when the action of G on X is smooth, free and proper, the same ellipticity condition on an operator naturally given by the geometry of the problem yields both the existence of a principal fibre bundle structure induced by the canonical projection : XX/G and the existence of the Faddeev-Popov determinant arising in the functional quantisation of the gauge theory. This holds for certain gauge theories with anomalies like bosonic closed string theory in non-critical dimension and also holds for a class of gauge theories which includes Yang-Mills theory. 相似文献
3.
Quark constants f
M and masses of B, D, and D
S mesons are calculated using the vacuum correlator method, suggested recently for long-distance nonperturbative QCD. The dynamical input is standard current quark masses, string tension and s(
QCD). The electronic width of , and calculated with the same parameters agrees with experiment. Hyperfine splitting of D, D
s mesons is also reproduced. The resulting values of f
B, f
D, f
Ds are 0.17, 0.21 and 0.25 GeV, respectively; f
D and f
Ds are within recent experimental bounds. It is shown that f
M does obey the asymptotic M
–1/2 law for M>5 GeV. 相似文献
4.
Precisely two of the homogeneous spaces that appear as coadjoint orbits of the group of string reparametrizations,
, carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex analytic Kähler manifolds. These are N=Diff( S
1)/Rot( S
1) and M=Diff( S
1)/Möb( S
1). Note that N is a holomorphic disc fiber space over M. Now, M can be naturally considered as embedded in the classical universal Teichmüller space T(1), simply by noting that a diffeomorphism of S
1 is a quasisymmetric homeomorphism. T(1) is itself a homomorphically homogeneous complex Banach manifold. We prove in the first part of the paper that the inclusion of M in T(1) is complex analytic.In the latter portion of this paper it is shown that the unique homogeneous Kähler metric carried by M = Diff ( S
1/ SL(2, ) induces precisely the Weil-Petersson metric on the Teichmüller space. This is via our identification of M as a holomorphic submanifold of universal Teichmüller space. Now recall that every Teichmüller space T(G) of finite or infinite dimension is contained canonically and holomorphically within T(1). Our computations allow us also to prove that every T(G), G any infinite Fuchsian group, projects out of M transversely. This last assertion is related to the fractal nature of G-invariant quasicircles, and to Mostow rigidity on the line.Our results thus connect the loop space approach to bosonic string theory with the sum-over-moduli (Polyakov path integral) approach. 相似文献
5.
The properties of analytic fields on a Riemann surface represented by a branch covering of 1 are investigated in detail. Branch points are shown to correspond to the vertex operators with simple conformal properties. As applications we compute determinants of
operators for Z
n
-symmetric surfaces and obtain various representations for the two-loop measure in the bosonic string theory together with various identities for theta-functions of hyperelliptic surfaces. We also present an integral representation for the quantum part of the twist field correlation functions, which describe propagation of the string on the orbifold background. We also calculate the quantum part of the structure constants of the twist-field operator algebra, generalizing the results of Dixon, Friedan, Martinec, and Shenker. 相似文献
6.
The geometry of N=2 supergravity is related to the variations of Hodge structure for formal Calabi-Yau spaces. All known results in this branch of algebraic geometry are easily recovered from supersymmetry arguments. This identification has a physical meaning for a type IIB superstring compactified on a Calabi-Yau 3-fold. We give exact (non-perturbative) results for the string effective lagrangian. Our geometrical framework suggests a re-formulation of the Gepner conjecture about (2,2) superconformal theories as the solution to the Schottky problem for algebraic complex manifolds having trivial canonical bundle. 相似文献
7.
Closed string models have recently been constructed in lower than their critical spacetime dimensions DD
cr. An ideal gas of closed strings with D4 undergoes a phase transition at a universal point (Hagedorn temperature). We argue that solitonic configurations on the string world-sheet (vortices) drive the system into a high-temperature phase where the vacuum is dominated by vortex condensates. Flat spacetime is identified with the dipole low-temperature phase of vortex antivortex pairs. This is a Kosterlitz-Thouless transition on the string world-sheet. It is suggestive of a stringy realization of the inflationary universe paradigm.This essay received the third award from the Gravity Research Foundation for the year 1988.—Ed. 相似文献
9.
The open p-adic string world sheet is a coset space F=T/, where T is the Bruhat-Tits tree for the p-adic linear group GL(2,
p
) and PGL(2,
p
) is some Schottky group. The string dynamics is governed by the local action on F, with the fields taking values in a compact group G. We find the correlation functions and partition functions for the p-adic string surfaces of arbitrary genus and G=U(1) xD
( D-dimensional torus). 相似文献
11.
We extend the recently constructed double field theory formulation of the low-energy theory of the closed bosonic string to the heterotic string. The action can be written in terms of a generalized metric that is a covariant tensor under O(D, D + n), where n denotes the number of gauge vectors, and n additional coordinates are introduced together with a covariant constraint that locally removes these new coordinates. For the abelian subsector, the action takes the same structural form as for the bosonic string, but based on the enlarged generalized metric, thereby featuring a global O(D, D + n) symmetry. After turning on non-abelian gauge couplings, this global symmetry is broken, but the action can still be written in a fully O(D, D + n) covariant fashion, in analogy to similar constructions in gauged supergravities. 相似文献
12.
Summary We show that a positive definite random Jacobi operator L over an abstract dynamical system T: XX can be factorized as L=D
2, where D is again a random Jacobi operator but defined over a new dynamical system S: YY which is an integral extension of T. An isospectral random Toda deformation of L corresponds to an isospectral random Volterra deformation of D. The factorization leads to commuting Bäcklund transformations which can be written explicitly in terms of Titchmarsh-Weyl functions. In the periodic case, the Bäcklund transformations are time 1 maps of a Toda flow with a time dependent Hamiltonian.This article was processed by the author using the Springer-Verlag TEX EconThe macro package 1991. 相似文献
13.
We discuss the action of diffeomorphisms on spinors on an oriented manifold M. To do this, we first describe the action of the diffeomorphism group D( M) on the set = H
1 ( M, Z
2) of inequivalent spin structures and show that it is affine. We argue that in the presence of spinors the gauge group of gravity is a certain double cover of D( M) which depends on the spin structure. We explicitly compute the action of D( M) on when M is a closed Riemann surface; is seen to consist of exactly two orbits, corresponding to even and odd spin structures.On leave of absence from I.F.T., University of Wrocaw, Poland 相似文献
14.
We discuss the algebras, representations, and thermodynamics of quantum group bosonic gas models with two different symmetries:
GL
p,q
(2) and
. We establish the nature of the basic numbers which follow from these GL
p,q
(2)- and
-invariant bosonic algebras. The Fock space representations of both of these quantum group invariant bosonic oscillator algebras
are analyzed. It is concisely shown that these two quantum group invariant bosonic particle gases have different algebraic
and high-temperature thermo-statistical properties. 相似文献
15.
We use the Feynman functional quantization scheme adapted to the gauge theories with reparametrization invariance to the functional covariant first quantization of the open bosonic BDHP string in a position representation. The consistent functional integral representation of the open string propagator is derived and evaluated. This result is used as a starting point for two kinds of constructions of the off-shell multiloop open string amplitudes. The general idea of the presented approach is to consider the off-shell amplitudes as functionals on the space of contours endowed with an intrinsic metric or on the space / +. 相似文献
16.
A mechanical system with perfect constraints can be described, under some mild assumptions, as a constrained Hamiltonian system (M, , H, D, W): (M, ) (the phase space) is a symplectic manifold, H (the Hamiltonian) a smooth function on M, D (the constraint submanifold) a submanifold of M, and W (the projection bundle) a vector sub-bundle of T
D
M, the reduced tangent bundle along D. We prove that when these data satisfy some suitable conditions, the time evolution of the system is governed by a well defined differential equation on D. We define constrained Hamiltonian systems with symmetry, and prove a reduction theorem. Application of that theorem is illustrated on the example of a convex heavy body rolling without slipping on a horizontal plane. Two other simple examples show that constrained mechanical systems with symmetry may have an attractive (or repulsive) set of relative equilibria. 相似文献
17.
Motivated by the problem of the moduli space of superconformal theories, we classify all the (normal) homogeneous Kähler spaces which are allowed in the coupling of vector multiplets to N=2 SUGRA. Such homogeneous spaces are in one-to-one correspondence with the homogeneous quaternionic spaces ( H
n
) found by Alekseevskii. There are two infinite families of homogeneous non-symmetric spaces, each labelled by two integers. We construct explicitly the corresponding supergravity models. They are described by a cubic function F, as in flat-potential models. They are Kähler-Einstein if and only if they are symmetric. We describe in detail the geometry of the relevant manifolds. They are Siegel (bounded) domains of the first type. We discuss the physical relevance of this class of bounded domains for string theory and the moduli geometry. Finally, we introduce the T-algebraic formalism of Vinberg to describe in an efficient way the geometry of these manifolds. The homogeneous spaces allowed in N=2 SUGRA are associated to rank 3 T-algebras in exactly the same way as the symmetric spaces are related to Jordan algebras. We characterize the T-algebras allowed in N=2 supergravity. They are those for which the ungraded determinant is a polynomial in the matrix entries. The Kähler potential is simply minus the logarithm of this naive determinant. 相似文献
18.
The possible presence of hairpin diagrams is analyzed in th model-independent quark-diagram scheme for two-body decays of charmed mesons. Current experimental data do not require the presence of hairpin diagrams in DVP ( V: vector meson, P: pseudoscalar meson), in accordance with the OZI rule. However, there is a possible indication that they are important in the decay of DPP. The measurement of D
s
+
+ is crucial to test the mechanism of hairpin diagrams. 相似文献
19.
We analyze in a simple calculation the way 2-dimensional moduli induce a noise-like mixing between the right and left sectors of the 1-loop partition function of bosonic closed strings. As it is a direct consequence of string interactions, we argue it must be taken as a renormalization to the tree-level dynamics as far as the Wilsonian view on renormalization group is kept. We also highlight the way this noise effect brings a thermodynamical meaning to space-filling D -branes. 相似文献
20.
The study of the properties of inclusive production of D
s
mesons and of events in which a and a muon are present in the same jet provides two independent measurements of the probability, f
s
w
, for a heavy quark to hadronize into a strange B or D meson. The data sample analysed corresponds to 243,000 hadronic Z
0 decays. The combined value of these measurements is f
s
w
=0.19±0.06±0.08. From the flight distance distributions of D
s and of (-lepton) secondary vertices, with the lepton emitted at high transverse momentum relative to the jet axis, two values are obtained for the B
s
0
meson lifetime. Combining these measurements with a previous result based on the study of D
s- events, the B
s
0
meson lifetime is measured to be: 0.96±0.37 ps. 相似文献
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