scholarly journals A Conformal Field Theory of Extrinsic Geometry of 2-d Surfaces

1997 ◽  
Vol 52 (1-2) ◽  
pp. 97-104
Author(s):  
K.S. Viswanathan ◽  
R. Parthasarathy
Keyword(s):  
Extrinsic Curvature ◽  
Universality Class ◽  
Gravity Theory ◽  
World Sheet ◽  
Light Cone Gauge ◽  
Conformal Field ◽  
Extrinsic Geometry ◽  
Wznw Model ◽  
The Mean ◽  
Conserved Currents

Abstract In the description of the extrinsic geometry of the string world sheet regarded as a conformal immersion of a 2-d surface in R3 it was previously shown that, restricting to surfaces with h √ g = 1, where h is the mean scalar curvature and g is the determinant of the induced metric on the surface, leads to Virasaro symmetry. An explicit form of the effective action on such surfaces is constructed in this article, which is the extrinsic curvature analog of the WZNW action. This action turns our to be the gauge invariant combination of the actions encountered in 2-d intrinsic gravity theory in light-cone gauge and the geometric action appearing in the quantization of the Virasaro group. This action, besides exhibiting Virasaro symmetry in z-sector, has SL (2, C) conserved currents in the z̅-sector. This allows us to quantize this theory in the z̅-sector along the lines of the WZNW model. The quantum theory on h √ g = 1 surfaces in R3 is shown to be in the same universality class as the intrinsic 2-d gravity theory.

scholarly journals ON SIX-DIMENSIONAL FUNDAMENTAL SUPERSTRINGS AS HOLOGRAMS

2009 ◽  
Vol 24 (01) ◽  
pp. 141-159 ◽  
Author(s):  
MOHSEN ALISHAHIHA ◽  
SUBIR MUKHOPADHYAY
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Sigma Model ◽  
Two Dimensional ◽  
World Sheet ◽  
Black String ◽  
Light Cone Gauge ◽  
Conformal Field ◽  
The World ◽  
Horizon Geometry

In this paper we discuss a possible holographic dual of the two-dimensional conformal field theory associated with the world-sheet of a macroscopic superstring in a compactification on a four-torus. We assume that the near-horizon geometry of the black string has symmetries of AdS 3×S3×T4 and construct a sigma model in the bulk. Analyzing the symmetries of the bulk theory and comparing them with those of the CFT in a special light-cone gauge, we find agreement between global symmetries. Due to nonstandard gauge realization it is not clear how affine symmetries can be realized.

A REALIZATION OF W GRAVITIES IN THE CONFORMAL GAUGE THROUGH GENERALIZED GAUSS MAPS

1992 ◽  
Vol 07 (02) ◽  
pp. 317-337 ◽  
Author(s):  
R. PARTHASARATHY ◽  
K. S. VISWANATHAN
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Extrinsic Curvature ◽  
Gauss Map ◽  
World Sheet ◽  
Hidden Symmetries ◽  
Extrinsic Geometry ◽  
Conformal Gauge ◽  
Conformal Immersion

String dynamics in ℝn with extrinsic geometry is studied in order to understand their hidden symmetries. String world sheet, realized as a conformal immersion in ℝn, is mapped into the Grassmannian G2, n through the Gauss map. This enables us to study the role of the extrinsic curvature in determining the WSO (n) gravities in the conformal gauge. It is shown that, classically, in ℝ3 and ℝ4 the geometry of surfaces of constant mean curvature densities is equivalent to WSO (n) (n = 3, 4) gravities, the corresponding W algebras being Virasoro (Vir) and Vir ⊕ Vir, respectively.

EXTRINSIC GEOMETRY OF WORLD-SHEET SUPERSYMMETRY THROUGH GENERALIZED SUPER-GAUSS MAPS

1992 ◽  
Vol 07 (24) ◽  
pp. 5995-6011 ◽  
Author(s):  
K.S. VISWANATHAN ◽  
R. PARTHASARATHY
Keyword(s):  
Riemann Surface ◽  
Extrinsic Curvature ◽  
Gauss Map ◽  
World Sheet ◽  
Invariant Action ◽  
Extrinsic Geometry ◽  
The World ◽  
Integrability Conditions ◽  
Gauss Maps

The extrinsic geometry of N=1 world-sheet supersymmetry is studied through generalized super-Gauss map. The world sheet, realized as a conformally immersed super-Riemann surface S in Rn (n=3 is studied for simplicity) is mapped into the supersymmetric Grassmannian G2,3. In order for the Grassmannian fields to form (super) tangent planes to S, certain integrability conditions are satisfied by G2,n fields. These conditions are explicitly derived. The supersymmetric invariant action for the Kähler σ-model G2,3 is reexpressed in terms of the world-sheet coordinates, thereby an off-shell supersymmetric generalization of the action proportional to the extrinsic curvature of the immersed surface is obtained.

scholarly journals GEOMETRICAL PROPERTIES OF CONFORMAL FIELD THEORIES COUPLED TO TWO-DIMENSIONAL QUANTUM GRAVITY

1996 ◽  
Vol 11 (11) ◽  
pp. 1913-1928 ◽  
Author(s):  
S. BRAUNE
Keyword(s):  
Functional Integral ◽  
Quasiclassical Approximation ◽  
Conformal Field Theories ◽  
Point Function ◽  
World Sheet ◽  
Geometrical Properties ◽  
Conformal Field ◽  
Noncritical Strings ◽  
Scaling Dimension ◽  
Distance Variable

In this work we discuss an approach due to F. David to the geometry of world sheets of noncritical strings in quasiclassical approximation. The gravitational dressed conformal dimension is related to the scaling behavior of the two-point function with respect to a distance variable. We show how this approach can reproduce the standard gravitational dressing in the next order of perturbation theory. Furthermore, we try to find this scaling dimension by studying the functional integral. With the same technique we calculate the intrinsic Hausdorff dimension of a world sheet.

scholarly journals CT-DUALITY AS A LOCAL PROPERTY OF THE WORLDSHEET

2005 ◽  
Vol 20 (12) ◽  
pp. 897-910 ◽  
Author(s):  
B. SAZDOVIĆ
Keyword(s):  
Field Equation ◽  
Present Article ◽  
Orthogonal Projection ◽  
Local Property ◽  
Extrinsic Curvature ◽  
Background Field ◽  
Local Features ◽  
Bosonic String ◽  
Minkowski Signature ◽  
The Mean

In this present article, we study the local features of the worldsheet in the case when probe bosonic string moves in antisymmetric background field. We generalize the geometry of surfaces embedded in spacetime to the case when the torsion is present. We define the mean extrinsic curvature for spaces with Minkowski signature and introduce the concept of mean torsion. Its orthogonal projection defines the dual mean extrinsic curvature. In this language, the field equation is just the equality of mean extrinsic curvature and extrinsic mean torsion, which we call CT-duality. To the worldsheet described by this relation we will refer as CT-dual surface.

scholarly journals HAMILTONIAN FORMULATION OF OPEN WZW STRINGS

2001 ◽  
Vol 16 (19) ◽  
pp. 3237-3271 ◽  
Author(s):  
S. GIUSTO ◽  
M. B. HALPERN
Keyword(s):  
Quantum Theory ◽  
Hamiltonian Formulation ◽  
Hamiltonian Approach ◽  
World Sheet ◽  
Classical Level ◽  
Time Coordinate ◽  
Equal Time ◽  
Conformal Field ◽  
The World ◽  
Generalized Dirichlet

Using a Hamiltonian approach, we construct the classical and quantum theory of open WZW strings on a strip. (These are the strings which end on WZW branes.) The development involves non-Abelian generalized Dirichlet images in an essential way. At the classical level, we find a new non-commutative geometry in which the equal-time coordinate brackets are non-zero at the world-sheet boundary, and the result is an intrinsically non-Abelian effect which vanishes in the Abelian limit. Using the classical theory as a guide to the quantum theory, we also find the operator algebra and the analogue of the Knizhnik–Zamolodchikov equations for the conformal field theory of open WZW strings.

PERCOLATION ON A FRACTAL WITH THE STATISTICS OF PLANAR FEYNMAN GRAPHS: EXACT SOLUTION

1989 ◽  
Vol 04 (17) ◽  
pp. 1691-1704 ◽  
Author(s):  
V.A. KAZAKOV
Keyword(s):  
Infinite Order ◽  
Log P ◽  
Theory Approach ◽  
Percolation Transition ◽  
Planar Lattice ◽  
Conformal Field ◽  
Feynman Graphs ◽  
Percolation Problem ◽  
The Mean ◽  
Volume Unit

A new bond-percolation problem on a graph (fractal) randomly chosen from all planar Feynman graphs of zero-dimensional φ3 (or φ4) theory in the thermodynamical limit (infinite order of graphs) is solved exactly. At the percolation transition point pc the mean number of clusters per volume unit has the singularity (pc−p)4 log (pc−p) which corresponds to the critical exponent α=−2. This model is a particular example of Potts models on dynamical planar lattice1 and the result agrees with the formulae obtained in Ref. 2 by conformal field theory approach for Potts spins interacting with 2D quantum gravity.

scholarly journals QUANTIZATION OF BOSONIC STRING MODEL IN (26+2)-DIMENSIONAL SPACE–TIME

2004 ◽  
Vol 19 (12) ◽  
pp. 1923-1959 ◽  
Author(s):  
TAKUYA TSUKIOKA ◽  
YOSHIYUKI WATABIKI
Keyword(s):  
Dimensional Space ◽  
String Model ◽  
Space Time ◽  
Bosonic String ◽  
World Sheet ◽  
Light Cone Gauge ◽  
Weyl Invariance ◽  
Background Space ◽  
Dimensional Space Time ◽  
Gauge Formulation

We investigate the quantization of the bosonic string model which has a local U (1) V × U (1) A gauge invariance as well as the general coordinate and Weyl invariance on the world-sheet. The model is quantized by Lagrangian and Hamiltonian BRST formulations á la Batalin, Fradkin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantization the model turns out to be formulated consistently in (26+2)-dimensional background space–time involving two time-like coordinates.

scholarly journals LINEARIZED FORM OF THE GENERIC AFFINE-VIRASORO ACTION

1994 ◽  
Vol 09 (14) ◽  
pp. 2451-2466 ◽  
Author(s):  
J. DE BOER ◽  
K. CLUBOK ◽  
M.B. HALPERN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Lie Algebra ◽  
World Sheet ◽  
Conformal Field ◽  
Highly Nonlinear

Halpern and Yamron have given a Lorentz, conformal, and Diff S2-invariant world-sheet action for the generic irrational conformal field theory, but the action is highly nonlinear. In this paper, we introduce auxiliary fields to find an equivalent linearized form of the action, which shows in a very clear way that the generic affine-Virasoro action is a Diff S2-gauged WZW model. In particular, the auxiliary fields transform under Diff S2 as local Lie g× Lie g connections, so that the linearized affine-Virasoro action bears an intriguing resemblance to the usual (Lie algebra) gauged WZW model.

scholarly journals ASYMPTOTIC BEHAVIOR OF THE PROPER LENGTH AND VOLUME OF THE SCHWARZSCHILD SINGULARITY

2009 ◽  
Vol 18 (03) ◽  
pp. 397-404 ◽  
Author(s):  
ASGHAR QADIR ◽  
AZAD A. SIDDIQUI
Keyword(s):  
Black Hole ◽  
Asymptotic Behavior ◽  
Extrinsic Curvature ◽  
York Time ◽  
Essential Singularity ◽  
Schwarzschild Black Hole ◽  
Proper Volume ◽  
The Mean ◽  
Proper Length

Though popular presentations give the Schwarzschild singularity as a point, it is known that it is spacelike and not timelike. Thus, it has a "length" and is not a "point." In fact, its length is necessarily infinite. It has been proven that the proper length of the Qadir–Wheeler suture model goes to infinity,1 while its proper volume shrinks to zero, and the asymptotic behavior of the length and volume has been calculated. That model consists of two Friedmann sections connected by a Schwarzschild "suture." The question arises whether a similar analysis could provide the asymptotic behavior of the Schwarzschild black hole near the singularity. It is proven here that, unlike the behavior for the suture model, for the Schwarzschild essential singularity Δs ~ K1/3 ln K and V ~ K-1 ln K, where K is the mean extrinsic curvature, or the York time.

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