scholarly journals Sum over topologies and double-scaling limit in 2D Lorentzian quantum gravity

2005 ◽  
Vol 23 (2) ◽  
pp. 465-471 ◽  
Author(s):  
R Loll ◽  
W Westra
Keyword(s):  
Quantum Gravity ◽  
Scaling Limit ◽  
Double Scaling Limit

scholarly journals REGGE GRAVITY FROM SPINFOAMS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350001 ◽  
Author(s):  
ELENA MAGLIARO ◽  
CLAUDIO PERINI
Keyword(s):  
Fine Structure ◽  
Quantum Gravity ◽  
Scaling Limit ◽  
Einstein Equations ◽  
Quantum Corrections ◽  
Semiclassical Regime ◽  
Double Scaling Limit

We consider spinfoam quantum gravity in the flipped limit, which is the double scaling limit γ → 0, j → ∞ with γj = const. , where γ is the Immirzi parameter, j is the spin and γj gives the physical area in Planck units. In this regime the amplitude for a 2-complex becomes effectively an integral over Regge-like metrics and seems to enforce Einstein equations in the semiclassical regime. The Immirzi parameter must be considered as dynamical in the sense that it runs to zero when the fine structure of the foam is averaged. In addition to quantum corrections which vanish for ℏ → 0, we find new corrections due to the discreteness of geometric spectra.

NONPERTURBATIVE 2D QUANTUM GRAVITY VIA SUPERSYMMETRIC STRING

1990 ◽  
Vol 05 (30) ◽  
pp. 2565-2572 ◽  
Author(s):  
MAREK KARLINER ◽  
SASHA MIGDAL
Keyword(s):  
Quantum Gravity ◽  
Ground State ◽  
Scaling Limit ◽  
Linear Ordinary Differential Equation ◽  
Third Order ◽  
Quantum Oscillations ◽  
The Third ◽  
Nonperturbative Solution ◽  
Distribution Of Eigenvalues ◽  
Double Scaling Limit

The Parisi-Marinari suggestion to treat 2d quantum gravity as ground state of the 1d supersymmetric string is elaborated in some detail. The third order linear ordinary differential equation describing in the double scaling limit the distribution of eigenvalues of the random matrix (i.e., the Liouville field) is derived and studied numerically. Unlike the Painlevé equation, our equation leads to continuous spectrum; however, the nonperturbative effects display themselves as quantum oscillations on top of smooth WKB distribution. Nonperturbative solution is free of any ambiguities.

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.

scholarly journals NONPERTURBATIVE 2D QUANTUM GRAVITY AND HAMILTONIANS UNBOUNDED FROM BELOW

1993 ◽  
Vol 08 (07) ◽  
pp. 1259-1281 ◽  
Author(s):  
J. AMBJØRN ◽  
C.F. KRISTJANSEN
Keyword(s):  
Quantum Gravity ◽  
Discrete Spectrum ◽  
Strong Coupling ◽  
Weak Coupling ◽  
Scaling Limit ◽  
Strong Coupling Expansion ◽  
Stochastic Stabilization ◽  
Genus Expansion ◽  
Double Scaling Limit

We show how the stochastic stabilization provides both the weak coupling genus expansion and a strong coupling expansion of 2D quantum gravity. The double scaling limit is described by a Hamiltonian which is unbounded from below, but which has a discrete spectrum.

scholarly journals Characters of irrelevant deformations

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Shouvik Datta ◽  
Yunfeng Jiang
Keyword(s):  
Deformation Parameter ◽  
Central Charge ◽  
Scaling Limit ◽  
Small Deformation ◽  
State Dependent ◽  
Dependent Change ◽  
Left And Right ◽  
Double Scaling Limit

Abstract We analyse the $$ T\overline{T} $$ T T ¯ deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve $$ T\overline{T} $$ T T ¯ , $$ J\overline{T} $$ J T ¯ and $$ T\overline{J} $$ T J ¯ simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

scholarly journals THE CRITICAL POINT OF UNORIENTED RANDOM SURFACES WITH A NONEVEN POTENTIAL

1993 ◽  
Vol 08 (06) ◽  
pp. 1139-1152
Author(s):  
M.A. MARTÍN-DELGADO
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Critical Point ◽  
Discrete Model ◽  
Recursion Relation ◽  
Scaling Limit ◽  
Random Surfaces ◽  
Matrix Ensemble ◽  
Quartic Interaction ◽  
Double Scaling Limit

The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double scaling-limit of the recursion relation leads to a Miura transformation relating the contributions to the free energy coming from oriented and unoriented random surfaces. This transformation is the same kind as found with a quartic interaction.

scholarly journals Hexagon bootstrap in the double scaling limit

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Vsevolod Chestnov ◽  
Georgios Papathanasiou
Keyword(s):  
Function Space ◽  
Operator Product Expansion ◽  
General Pattern ◽  
Scaling Limit ◽  
Kinematic Region ◽  
Operator Product ◽  
Yang Mills ◽  
Codimension One ◽  
Double Scaling Limit ◽  
Super Yang Mills Theory

Abstract We study the six-particle amplitude in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory in the double scaling (DS) limit, the only nontrivial codimension-one boundary of its positive kinematic region. We construct the relevant function space, which is significantly constrained due to the extended Steinmann relations, up to weight 13 in coproduct form, and up to weight 12 as an explicit polylogarithmic representation. Expanding the latter in the collinear boundary of the DS limit, and using the Pentagon Operator Product Expansion, we compute the non-divergent coefficient of a certain component of the Next-to-Maximally-Helicity-Violating amplitude through weight 12 and eight loops. We also specialize our results to the overlapping origin limit, observing a general pattern for its leading divergences.

scholarly journals NON-PERTURBATIVE SOLUTION OF THE SUPER-VIRASORO CONSTRAINTS

1993 ◽  
Vol 08 (13) ◽  
pp. 1205-1214 ◽  
Author(s):  
K. BECKER ◽  
M. BECKER
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Scaling Limit ◽  
Virasoro Constraints ◽  
Perturbative Solution ◽  
The One ◽  
Genus Expansion ◽  
Double Scaling Limit

We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the non-perturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreement between our flows and the known supersymmetric extensions of KdV.

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