February 1992 arXiv papers — page 2

Christopher Ting, C. H. Lai

The path integral approach to representing braid group is generalized for particles with spin. Introducing the notion of {\em charged} winding number in the super-plane, we represent the braid group generators as homotopically constrained Feynman kernels. In this framework, super Knizhnik-Zamolodchikov operators appear naturally in the Hamiltonian, suggestin

Richard H. Price, Jorge Pullin

We consider a source of gravitational waves of frequency $ω$, located near the center of a massive galaxy of mass $M$ and radius $R$, with $ω\gg R^{-1}$. In the case of a perfect fluid galaxy, and of odd-parity waves, there is no direct matter-wave interaction and the propagation of the waves is affected by the galaxy only through the curvature of the spacet

Lee Smolin

New results from the new variables/loop representation program of nonperturbative quantum gravity are presented, with a focus on results of Ashtekar, Rovelli and the author which greatly clarify the physical interpretation of the quantum states in the loop representation. These include: 1) The construction of a class of states which approximate smooth metric

Yun-Gang Ye

A complex contact threefold is a threefold with a two-dimensional non-integrable holomorphic distribution. A contact curve on a contact threefold is an integrable curve of the distribution. This work was inspired by two papers of Bryant, in which he used complex contact geometry to study superminimal surfaces in four-sphere and to investigate exotic holonomi

Erik Verlinde

A general method is presented for deriving on-shell Ward-identities in (2D) string theory. It is shown that all tree-level Ward identities can be summarized in a quadratic differential equation for the generating function of tree-amplitudes. This result is extended to loop amplitudes and leads to a master equation {\it à la} Batalin-Vilkovisky for the comple

F. Ravanini

We propose a Thermodynamic Bethe Ansatz (TBA) for G_k x G_l / G_{k+l} conformal coset models (G any simply-laced Lie algebra) perturbed by their operator ϕ_{1,1,Adj}. An interesting adjacency structure appears and can be depicted in a sort of ``product'' of Dynkin diagrams of G and A_{k+l-1}. UV and IR limits are computed and reproduce the expected v

Shahar Ben-Menahem

The D=0 matrix model is reformulated as a 2d nonlocal quantum field theory. The interactions occur on the one-dimensional line of hermitian matrix eigenvalues. The field is conjugate to the density of matrix eigenvalues which appears in the Jevicki-Sakita collective field theory. The classical solution of the field equation is either unique or labeled by a d

Bernd Bruegmann, Rodolfo Gambini, Jorge Pullin

We find a consistent formulation of the constraints of Quantum Gravity with a cosmological constant in terms of the Ashtekar new variables in the connection representation, including the existence of a state that is a solution to all the constraints. This state is related to the Chern-Simons form constructed from the Ashtekar connection and has an associated

Sheldon Katz

By considering mirror symmetry applied to conformal field theories corresponding to strings propagating in quintic hypersurfaces in projective 4-space, Candelas, de la Ossa, Green and Parkes calculated the ``number of rational curves on the hypersurface'' by comparing three point functions. Actually, the number of curves may be infinite for special e

Noah Linden, Malcolm Perry

We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global structure of the system. This perturbation expansion is evaluated for a simple example and leads to a new exactly soluble model

Barton Zwiebach

A minimal area problem imposing different length conditions on open and closed curves is shown to define a one parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable open-closed theory up to an extended version of Witten's open string field theory capable of incorporating on shell

C. F. E. Holzhey, F. Wilczek

It is argued that the qualitative features of black holes, regarded as quantum mechanical objects, depend both on the parameters of the hole and on the microscopic theory in which it is embedded. A thermal description is inadequate for extremal holes. In particular, extreme holes of the charged dilaton family can have zero entropy but non-zero, and even (for

V. Spiridonov

Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another by the q^2-factor scaling. A special class of the se

Sheldon Katz, David R. Morrison

We classify simple flops on smooth threefolds, or equivalently, Gorenstein threefold singularities with irreducible small resolution. There are only six families of such singularities, distinguished by Koll{á}r's {\em length} invariant. The method is to apply invariant theory to Pinkham's construction of small resolutions. As a by-product, generators

Sheldon Katz

The point is to compare the mathematical meaning of the ``number of rational curves on a Calabi-Yau threefold'' to the meaning ascribed to the same notion by string theorists.

Y. Imamura, M. Sakamoto, T. Sasada, M. Tabuse

We give various examples of asymmetric orbifold models to possess intertwining currents which convert untwisted string states to twisted ones, and vice versa, and see that such asymmetric orbifold models are severely restricted. The existence of the intertwining currents leads to the enhancement of symmetries in asymmetric orbifold models.

Satoshi Iso, Dimitra Karabali, B. Sakita

Based on the observation that a particle motion in one dimension maps to a two-dimensional motion of a charged particle in a uniform magnetic field, constrained in the lowest Landau level, we formulate a system of one-dimen- sional nonrelativistic fermions by using a Chern-Simons field theory in 2+1 dimensions. Using a hydrodynamical formulation we obtain a

P. Fendley, K. Intriligator

We study $N$=2 supersymmetric integrable theories with spontaneously-broken \Zn\ symmetry. They have exact soliton masses given by the affine $SU(n)$ Toda masses and fractional fermion numbers given by multiples of $1/n$. The basic such $N$=2 integrable theory is the $A_n$-type $N$=2 minimal model perturbed by the most relevant operator. The soliton content

G. Nagao

An effective Hamiltonian for the study of the quantum Hall effect is proposed. This Hamiltonian, which includes a ``current-current" interaction has the form of a Hamiltonian for a conformal field theory in the large $N$ limit. An order parameter is constructed from which the Hamiltonian may be derived. This order parameter may be viewed as either a coll

Jacek Graczyk, Grzegorz Swiatek, Folkert Tangerman, J. J. P. Veerman

Circle maps with a flat spot are studied which are differentiable, even on the boundary of the flat spot. Estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set are obtained. Also, a sharp transition is found from degenerate geometry similar to what was found earlier for non-differentiable maps with a flat spot to bounded geom

Petr Horava

We analyze topological string theory on a two dimensional torus, focusing on symmetries in the matter sector. Even before coupling to gravity, the topological torus has an infinite number of point-like physical observables, which give rise via the BRST descent equations to an infinite symmetry algebra of the model. The point-like observables of ghost number

Philip C. Argyres, James M. Grochocinski, S. -H. Henry Tye

We construct the K=8 fractional superconformal algebras. There are two such extended Virasoro algebras, one of which was constructed earlier, involving a fractional spin (equivalently, conformal dimension) 6/5 current. The new algebra involves two additional fractional spin currents with spin 13/5. Both algebras are non-local and satisfy non-abelian braiding

L. Chekhov, Yu. Makeenko

We reexamine the external field problem for $N\times N$ hermitian one-matrix models. We prove an equivalence of the models with the potentials $\tr{({1/over2N}X^2 + \log X - ΛX)}$ and $\sum_{k=1}^\infty t_k\tr{X^k}$ providing the matrix $Λ$ is related to $\{t_k\}$ by $t_k=\fr 1k \tr{Λ^{-k}}-\frac N2 δ_{k2}$. Based on this equivalence we formulate a method fo

David Gershon

We construct an exact CFT as an SL(2,R)xSU(2)/U(1)^2 gauged WZW model, which describes a black hole in 4 dimensions. Another exact solution, describing a black membrane in 4D (in the sense that the event horizon is an infinite plane) is found as an SL(2,R)xU(1)^2/U(1) gauged WZW model. Finally, we construct an exact solution of a 4D black hole with electroma

S. B. Giddings, A. Strominger

Particle scattering and radiation by a magnetically charged, dilatonic black hole is investigated near the extremal limit at which the mass is a constant times the charge. Near this limit a neighborhood of the horizon of the black hole is closely approximated by a trivial product of a two-dimensional black hole with a sphere. This is shown to imply that the

Marc Kamionkowski, John March-Russell

Global-symmetry violating higher-dimension operators, expected to be induced by Planck-scale physics, in general drastically alter the properties of the axion field associated with the Peccei-Quinn solution to the strong-CP problem, and render this solution unnatural. The particle physics and cosmology associated with other global symmetries can also be sign

N. Read, G. Moore

It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Fractional statistics can be extended to nonabelian statistics and examples can be constructed from conformal field theory. The Pfaffian state is related to the 2D Ising model and possesses fractionally charged exci

Stephen-wei Chung, S. -H. Henry Tye

The Wess-Zumino-Witten (WZW) theory has a global symmetry denoted by $G_L\otimes G_R$. In the standard gauged WZW theory, vector gauge fields (\ie\ with vector gauge couplings) are in the adjoint representation of the subgroup $H \subset G$. In this paper, we show that, in the conformal limit in two dimensions, there is a gauged WZW theory where the gauge fi

Vincente Cervera, Francisca Mascaró, Peter W. Michor

We study the action of the diffeomorphism group $\Diff(M)$ on the space of proper immersions $\Imm_{\text{prop}}(M,N)$ by composition from the right. We show that smooth transversal slices exist through each orbit, that the quotient space is Hausdorff and is stratified into smooth manifolds, one for each conjugacy class of isotropy groups.

Peter W. Michor

In the main part of this paper a connection is just a fiber projection onto a (not necessarily integrable) distribution or sub vector bundle of the tangent bundle. Here curvature is computed via the Froelicher-Nijenhuis bracket, and it is complemented by cocurvature and the Bianchi identity still holds. In this situation we determine the graded Lie algebra o

Andreas Kriegl, Peter W. Michor

The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent vectors as derivations. Manifolds of mappings and diffeomorphisms are treated. Finally the differential structure on the in