LIOUVILLE GRAVITY ON BORDERED SURFACES

1993 ◽  
Vol 08 (06) ◽  
pp. 1041-1057 ◽  
Author(s):  
ZBIGNIEW JASKÓLSKI
Keyword(s):  
Hausdorff Dimension ◽  
Boundary Conditions ◽  
Path Integral ◽  
Critical Exponents ◽  
Geometrical Interpretation ◽  
Liouville Gravity ◽  
Conformal Gauge ◽  
Functional Quantization

The functional quantization of the Liouville gravity on bordered surfaces in the conformal gauge is developed. It was shown that the geometrical interpretation of the Polyakov path integral as a sum over bordered surfaces uniquely determines the boundary conditions for the fields involved. The gravitational scaling dimensions of boundary and bulk operators and the critical exponents are derived. In particular the boundary Hausdorff dimension is calculated.

scholarly journals Boundary conditions: The path integral approach

2007 ◽  
Vol 87 ◽  
pp. 012004 ◽  
Author(s):  
M Asorey ◽  
J Clemente-Gallardo ◽  
J M Muñoz-Castañeda
Keyword(s):  
Boundary Conditions ◽  
Path Integral ◽  
Integral Approach ◽  
Path Integral Approach

scholarly journals EFFECTIVE BOUNDARY ACTION IN THE FERMIONIC STRING THEORY

1989 ◽  
Vol 04 (21) ◽  
pp. 2041-2047
Author(s):  
A.V. MARSHAKOV
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Configuration Space ◽  
Path Integral ◽  
Riemann Surfaces ◽  
Special Choice ◽  
Local Boundary ◽  
Effective Boundary ◽  
Fermionic Fields ◽  
Fermionic String

The Polyakov path integral on Riemann surfaces with boundaries for the Neveu-Schwarz-Ramond (NSR) fermionic string is computed in the case of a special choice of the local boundary conditions for the fermionic fields. Effective boundary action is written explicitly by means of the functions defined on the double of the surface. The obtained expressions are used to study the behavior of the string propagator in the configuration space. The generalization of the effective fermionic action to the case of nonarchimedean strings is discussed.

scholarly journals Making the gravitational path integral more Lorentzian or Life beyond Liouville gravity

2000 ◽  
Vol 88 (1-3) ◽  
pp. 241-244 ◽  
Author(s):  
R. Loll ◽  
J. Ambjørn ◽  
K.N. Anagnostopoulos
Keyword(s):  
Path Integral ◽  
Liouville Gravity

TWO-DIMENSIONAL GRAVITY WITH BOUNDARY

1992 ◽  
Vol 07 (07) ◽  
pp. 619-629
Author(s):  
PARTHASARATHI MAJUMDAR
Keyword(s):  
Boundary Conditions ◽  
Central Charge ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Conformal Gauge

An attempt is made to incorporate the effects of a boundary in the conformal gauge solution of two-dimensional gravity. We discuss some possible choices for boundary conditions on the Liouville field and their implications for the renormalization of the central charge.

scholarly journals QUANTIZATION WITHOUT THE WITTEN ANOMALIES

1996 ◽  
Vol 11 (32n33) ◽  
pp. 2601-2609 ◽  
Author(s):  
T.D. KIEU
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Boundary Conditions ◽  
Path Integral ◽  
Quantum Field ◽  
Quantum Fields ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Gauge Transformations ◽  
Gauge Anomalies

It is argued that gauge anomalies are only artefacts of the conventional quantization of quantum field theory. When the Berry’s phase is taken into consideration to satisfy certain boundary conditions of the generating path integral, the gauge anomalies associated with homotopically nontrivial gauge transformations are explicitly shown to be eliminated, without any extra quantum fields introduced.

scholarly journals New boundary conditions for AdS2

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Victor Godet ◽  
Charles Marteau
Keyword(s):  
Boundary Conditions ◽  
Path Integral ◽  
Flat Space ◽  
Low Energy ◽  
Asymptotic Symmetry ◽  
Coadjoint Action ◽  
Matrix Ensemble ◽  
Virasoro Group ◽  
Random Matrix Ensemble ◽  
Extremal Black Holes

Abstract We describe new boundary conditions for AdS2 in Jackiw-Teitelboim gravity. The asymptotic symmetry group is enhanced to Diff(S1) ⋉ C∞(S1) whose breaking to SL(2, ℝ) × U(1) controls the near-AdS2 dynamics. The action reduces to a boundary term which is a generalization of the Schwarzian theory and can be interpreted as the coadjoint action of the warped Virasoro group. This theory reproduces the low-energy effective action of the complex SYK model. We compute the Euclidean path integral and derive its relation to the random matrix ensemble of Saad, Shenker and Stanford. We study the flat space version of this action, and show that the corresponding path integral also gives an ensemble average, but of a much simpler nature. We explore some applications to near-extremal black holes.

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