FROM LOOPS TO FIELDS IN 2D QUANTUM GRAVITY

1992 ◽  
Vol 07 (11) ◽  
pp. 2601-2634 ◽  
Author(s):  
GREGORY MOORE ◽  
NATHAN SEIBERG
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Zero Mode ◽  
Integral Transform ◽  
Target Space ◽  
Two Dimensional ◽  
And Topology ◽  
The Matrix ◽  
Dimensional Gravity ◽  
Infinite Set

We discuss a target space field theory of macroscopic loops W(ℓ,…) in two-dimensional gravity. The propagator <W(ℓ1)W(ℓ2)> and topology-changing amplitudes <W(ℓ1)W(ℓ2)W(ℓ3)> (string interactions) are considered as off-shell Euclidean Green's functions in this field theory. In the course of the analysis, we identify a new set of operators in the c = 1 system and interpret them in two-dimensional gravity. We also identify an infinite set of new conserved charges in the c = 1 system which are associated with the special states in the theory. The analysis also shows that the eigenvalue coordinate of the matrix model and a zero mode of the Liouville field are not functionally related but are conjugate variables in an integral transform.

A COMPACT BOSON COUPLED TO TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 2743-2754 ◽  
Author(s):  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Riemann Surfaces ◽  
Partition Functions ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
The Continuum ◽  
Continuum Field

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.

Gravité quantique et modèles de matrices

1991 ◽  
Vol 69 (7) ◽  
pp. 837-854 ◽  
Author(s):  
David Sénéchal
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Gravity ◽  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Continuum Limit ◽  
Two Dimensional ◽  
Planar Approximation ◽  
Conformal Field ◽  
The Matrix

A review of the main results recently obtained in the study of two-dimensional quantum gravity is offered. The analysis of two-dimensional quantum gravity by the methods of conformal field theory is briefly described. Then the treatment of quantum gravity in terms of matrix models is explained, including the notions of continuum limit, planar approximation, and orthogonal polynomials. Correlation fonctions are also treated, as well as phases of the matrix models.

scholarly journals Quantum gravity as a multitrace matrix model

2017 ◽  
Vol 32 (31) ◽  
pp. 1750180
Author(s):  
Badis Ydri ◽  
Cherine Soudani ◽  
Ahlam Rouag
Keyword(s):  
Quantum Gravity ◽  
Matrix Models ◽  
Large Class ◽  
Matrix Model ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Topology Change ◽  
New Model ◽  
And Topology ◽  
Emergent Geometry

We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of two-dimensional quantum gravity which works away from two dimensions and captures a large class of spaces admitting a finite spectral triple. These multitrace matrix models sustain emergent geometry as well as growing dimensions and topology change.

scholarly journals BRST-FIXED POINTS AND TOPOLOGICAL CONFORMAL SYMMETRY

1992 ◽  
Vol 07 (24) ◽  
pp. 2215-2222 ◽  
Author(s):  
TOSHIO NAKATSU ◽  
YUJI SUGAWARA
Keyword(s):  
Field Theory ◽  
Fixed Points ◽  
Conformal Symmetry ◽  
Topological Field Theory ◽  
Two Dimensional ◽  
Brst Transformation ◽  
Dimensional Gravity ◽  
Matter System ◽  
Topological Field ◽  
Topological Matter

We study the twisted version of the supersymmetric G/T = SU (n)/ U (1)⊗(n−1) gauged Wess-Zumino-Witten model. By studying its fixed points under BRST transformation this model is shown to be reduced to a simple topological Field theory, that is, the topological matter system in the K. Li's theory of two-dimensional gravity for the case of n = 2, and its generalization for n ≥ 3.

A Linearized Two-Dimensional Theory for High-Speed Hydrofoils Near the Free Surface

1966 ◽  
Vol 10 (01) ◽  
pp. 25-48
Author(s):  
Richard P. Bernicker
Keyword(s):  
Direct Problem ◽  
High Speed ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Pressure Loading ◽  
Dimensional Theory ◽  
Linear Algebraic Equations ◽  
The Matrix ◽  
Sectional Shape ◽  
Infinite Set

A linearized two-dimensional theory is presented for high-speed hydrofoils near the free surface. The "direct" problem (hydrofoil shape specified) is attacked by replacing the actual foil with vortex and source sheets. The resulting integral equation for the strength of the singularity distribution is recast into an infinite set of linear algebraic equations relating the unknown constants in a Glauert-type vorticity expansion to the boundary condition on the foil. The solution is achieved using a matrix inversion technique and it is found that the matrix relating the known and unknown constants is a function of depth of submergence alone. Inversion of this matrix at each depth allows the vorticity constants to be calculated for any arbitrary foil section by matrix multiplication. The inverted matrices have been calculated for several depth-to-chord ratios and are presented herein. Several examples for specific camber and thickness distributions are given, and results indicate significant effects in the force characteristics at depths less than one chord. In particular, thickness effects cause a loss of lift at shallow submergences which may be an appreciable percentage of the total design lift. The second part treats the "indirect" problem of designing a hydrofoil sectional shape at a given depth to achieve a specified pressure loading. Similar to the "direct" problem treated in the first part, integral equations are derived for the camber and thickness functions by replacing the actual foil by vortex and source sheets. The solution is obtained by recasting these equations into an infinite set of linear algebraic equations relating the constants in a series expansion of the foil geometry to the known pressure boundary conditions. The matrix relating the known and unknown constants is, again, a function of the depth of submergence alone, and inversion techniques allow the sectional shape to be determined for arbitrary design pressure distributions. Several examples indicate the procedure and results are presented for the change in sectional shape for a given pressure loading as the depth of submergence of the foil is decreased.

scholarly journals D-instantons, string field theory and two dimensional string theory

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Matrix Model ◽  
String Field Theory ◽  
Scattering Amplitude ◽  
Two Dimensional ◽  
World Sheet ◽  
Numerical Result ◽  
Instanton Contribution ◽  
The Matrix

Abstract In [4] Balthazar, Rodriguez and Yin (BRY) computed the one instanton contribution to the two point scattering amplitude in two dimensional string theory to first subleading order in the string coupling. Their analysis left undetermined two constants due to divergences in the integration over world-sheet variables, but they were fixed by numerically comparing the result with that of the dual matrix model. If we consider n-point scattering amplitudes to the same order, there are actually four undetermined constants in the world-sheet approach. We show that using string field theory we can get finite unambiguous values of all of these constants, and we explicitly compute three of these four constants. Two of the three constants determined this way agree with the numerical result of BRY within the accuracy of numerical analysis, but the third constant seems to differ by 1/2. We also discuss a shortcut to determining the fourth constant if we assume the equality of the quantum corrected D-instanton action and the action of the matrix model instanton. This also agrees with the numerical result of BRY.

Quantization and topology: SL(2,R)-de Sitter invariant fields in two dimensions

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040018
Author(s):  
Henri Epstein ◽  
Ugo Moschella
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Two Dimensions ◽  
Quantum Field ◽  
Two Dimensional ◽  
De Sitter ◽  
Cosmological Background ◽  
Local Commutativity ◽  
And Topology ◽  
The Many

We explore the interplay between quantization, local commutativity and the analyticity properties of the two-point functions of a quantum field in a non trivial topological cosmological background in the example of the two-dimensional de Sitter manifold and its double covering. The global topological differences make the many of the well-known features of de Sitter quantum field theory disappear. In particular there is nothing like a Bunch-Davies vacuum and there are no [Formula: see text]-invariant fields whose mass is less than 1/2.

scholarly journals SOME ALGEBRAIC SYMMETRIES OF (2, 2)-SUPERSYMMETRIC SYSTEMS

2001 ◽  
Vol 16 (10) ◽  
pp. 663-671
Author(s):  
TRISTAN HÜBSCH
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Hilbert Spaces ◽  
Dimensional Space ◽  
Space Time ◽  
Effective Field ◽  
Target Space ◽  
Two Dimensional ◽  
Target Field ◽  
Dimensional Space Time

The Hilbert spaces of supersymmetric systems admit symmetries which are often related to the topology and geometry of the (target) field-space. Here, we study certain (2, 2)-supersymmetric systems in two-dimensional space–time which are closely related to superstring models. They all turn out to possess some hitherto unexploited and geometrically and topologically unobstructed symmetries, providing new tools for studying the topology and geometry of superstring target space–times, and so the dynamics of the effective field theory in these.

scholarly journals GRAVITY ON A FUZZY SPHERE

2004 ◽  
Vol 19 (03) ◽  
pp. 361-370 ◽  
Author(s):  
P. VALTANCOLI
Keyword(s):  
Matrix Model ◽  
Solution Space ◽  
Two Dimensional ◽  
Fuzzy Sphere ◽  
Gauge Transformations ◽  
The Matrix ◽  
Analogous Model ◽  
Dimensional Gravity ◽  
Noncommutative Gravity ◽  
Noncommutative Plane

We propose an action for gravity on a fuzzy sphere, based on a matrix model. We find striking similarities with an analogous model of two-dimensional gravity on a noncommutative plane, i.e. the solution space of both models is spanned by pure U(2) gauge transformations acting on the background solution of the matrix model, and there exist deformations of the classical diffeomorphisms which preserve the two-dimensional noncommutative gravity actions.

UNIVERSALITY OF THE MATRIX MODEL APPROACH TO TWO-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 1387-1396
Author(s):  
FREDDY PERMANA ZEN
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Scaling Limit ◽  
Numerical Calculations ◽  
Two Dimensional ◽  
Coupled Equations ◽  
The Matrix ◽  
Pure Gravity ◽  
Double Scaling Limit ◽  
Model Approach

Universality with respect to triangulations is investigated in the Hermitian one-matrix model approach to 2-D quantum gravity for a potential containing both even and odd terms, [Formula: see text]. With the use of analytical and numerical calculations, I find that the universality holds and the model describes pure gravity, which leads in the double scaling limit to coupled equations of Painlevé type.

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